From 50ac5d5768c62f98296f6531cc9ba42fab99db39 Mon Sep 17 00:00:00 2001
From: Florian Atteneder <florian.atteneder@uni-jena.de>
Date: Fri, 12 Jan 2024 16:05:40 +0000
Subject: [PATCH] Refactor GRHD project (dg/dg1d.jl!101)
* update examples once more
* remove comments
* cleanup: remove codegen for now
* IntegartionTests: add grhd_tov_spherical1d ref test
* IntegrationTests: remove reltol from grhd_bondi_accretion test
* spherical1d: fix missing shift from maxspeed computation
* cleanup
* make spherical1d formulation work when r=0 is included by removing potential nans in source terms by enforcing symmetry
* make impose_symmetry! dispatch on project
* add tov example that runs with spherical1d formulation
* wip: change maxspeed implementation for tov star initial data
* cons2prim: use non-zero values for rho, eps thresholds
* fix: set atm density in bondi_accretion initial data
* implement tov initial data for spherical1d formulation
* add formulation parameter
* implement rhs for FVElement and rescaled_spherical1d
* implement equations for FVElement and rescaled_spherical1d
* mesh: implement differentiate for FVElement
* add grhd example par files
* update notebooks
* fix missing lapse factor in source terms
* fix typos
* fixup initialdata setup
* derivative computation needs jacobi
* rename cons2prim routines
* add atmosphering to cons2prim
* implement rhs! for rescaled_spherical1d formulation
* specialize timespeed computation based on equations
* add specialized equations for the rescaled GRHD version
* implement initialdata setup for tov case
* spherical accretion:make sure K, Gamma agree with loaded data
* expose spectral differentiation
* wrap SphericalAccretion solver into module; recompute bondi_accretion.h5 with less radial points
* refactor TOV solver to use OrdinaryDiffEq
* initialdata: cleanup dir
* add bondi accretion as ref test
* fix up loading of id file
* fv_rhs: implement fv_update_step! with source term
* add ROOTDIR const global so that parfiles can specify paths relative to project root
* update SphericalAccretion.jl
* update sympy nb
* cleanup initialdata setup
* equations: fix up Tmunu computation
* Revert "fix source term in dg and fv rhs computation"
This reverts commit 161cc0346ff7cb854db0ea32b837ab7f0819bef2.
* Replace Interpolations.jl with BasicInterpolators.jl
* equation: add missing flux terms to sources; use outflow bdry condition on inner radius
* comments in cons2prim
* implement momentum constraint for debugging
* test SphericalAccretion
- copy Bugner's C version of the solver
- compare my results with Bugner's -- good agreement
- compare against literature results (Papadopoulos 1998,1999) --
discrepancy in sign of vr, ur, otherwise good agreement
* SphericalAccretion: fix wrong definition of uc^r and Vc
* tweak impl more
* fix source term in dg and fv rhs computation
* fix equations and implement fv method
* equations: combine flux and source computation
* math: update spherical_accretion notebook
* SRHD: export module
* re-implemented GRHD eqs with a non-zero shift
* initialdata: add grhd_source.codegen.jl that was generated with TensorComponents.jl
* deps: need Interpolations.jl for initial data setup
* update math/spherical_accretion.py
* update setup
* start initialdata setup for bondi problem
* rework rhs.jl
* update deps and parameters
* update type defs
* initialdata: add HDF5 dep; write h5 output for SphericalAccretion.jl
* rename cons2prim.jl
* remove unused files
---
Manifest.toml | 14 +-
Project.toml | 7 +-
examples/grhd_bondi/dg.toml | 28 +
examples/grhd_bondi/fv.toml | 25 +
examples/grhd_tov/dg.toml | 35 +
examples/grhd_tov/dg_spherical1d.toml | 36 +
initialdata/.gitignore | 2 +
initialdata/Makefile | 5 +
initialdata/Manifest.toml | 2181 +++++++++++++++++
initialdata/Project.toml | 8 +-
initialdata/SphericalAccretion.c | 95 +
initialdata/SphericalAccretion.jl | 314 ++-
initialdata/TOV.jl | 262 +-
initialdata/TOV_stable.h5 | Bin 0 -> 58040 bytes
initialdata/TOV_unstable.h5 | Bin 0 -> 36984 bytes
initialdata/bondi-acc_papadopoulos1998_p.png | Bin 0 -> 103125 bytes
.../bondi-acc_papadopoulos1998_rho.png | Bin 0 -> 117640 bytes
initialdata/bondi-acc_papadopoulos1998_v.png | Bin 0 -> 132232 bytes
.../bondi-acc_papadopoulos1999_eps.png | Bin 0 -> 47105 bytes
.../bondi-acc_papadopoulos1999_rho.png | Bin 0 -> 74969 bytes
initialdata/bondi-acc_papadopoulos1999_vr.png | Bin 0 -> 44201 bytes
initialdata/bondi_accretion.h5 | Bin 0 -> 52480 bytes
math/3plus1.py | 22 +-
math/gr_utils.py | 7 +-
math/grhd1d_characteristics.py | 4 +-
math/spherical_accretion.py | 151 +-
math/sympy_utils.py | 4 +-
math/tov.py | 4 +-
src/GRHD/GRHD.jl | 32 +-
src/GRHD/boundaryconditions.jl | 40 -
src/GRHD/callbacks.jl | 52 +-
src/GRHD/cons2prim.jl | 320 +++
src/GRHD/cons2prim_implementations.jl | 319 ---
src/GRHD/equation.jl | 600 +++--
src/GRHD/initialdata.jl | 612 +++--
src/GRHD/parameters.jl | 0
src/GRHD/rhs.jl | 209 +-
src/GRHD/setup.jl | 188 +-
src/GRHD/types.jl | 23 +-
src/SRHD/SRHD.jl | 1 +
src/dg1d.jl | 2 +-
src/fv_rhs.jl | 19 +-
src/mesh.jl | 37 +-
src/sandbox.jl | 2 +
src/spectralelement.jl | 9 +
.../grhd_bondi_accretion.toml | 25 +
.../refs/grhd_bondi_accretion/output.h5 | Bin 0 -> 149584 bytes
.../grhd_tov_spherical1d.toml | 27 +
.../refs/grhd_tov_spherical1d/output.h5 | Bin 0 -> 92488 bytes
test/IntegrationTests/refs/testconfig.toml | 8 +
50 files changed, 4489 insertions(+), 1240 deletions(-)
create mode 100644 examples/grhd_bondi/dg.toml
create mode 100644 examples/grhd_bondi/fv.toml
create mode 100644 examples/grhd_tov/dg.toml
create mode 100644 examples/grhd_tov/dg_spherical1d.toml
create mode 100644 initialdata/.gitignore
create mode 100644 initialdata/Makefile
create mode 100644 initialdata/Manifest.toml
create mode 100644 initialdata/SphericalAccretion.c
create mode 100644 initialdata/TOV_stable.h5
create mode 100644 initialdata/TOV_unstable.h5
create mode 100644 initialdata/bondi-acc_papadopoulos1998_p.png
create mode 100644 initialdata/bondi-acc_papadopoulos1998_rho.png
create mode 100644 initialdata/bondi-acc_papadopoulos1998_v.png
create mode 100644 initialdata/bondi-acc_papadopoulos1999_eps.png
create mode 100644 initialdata/bondi-acc_papadopoulos1999_rho.png
create mode 100644 initialdata/bondi-acc_papadopoulos1999_vr.png
create mode 100644 initialdata/bondi_accretion.h5
delete mode 100644 src/GRHD/boundaryconditions.jl
create mode 100644 src/GRHD/cons2prim.jl
delete mode 100644 src/GRHD/cons2prim_implementations.jl
delete mode 100644 src/GRHD/parameters.jl
create mode 100644 test/IntegrationTests/refs/grhd_bondi_accretion/grhd_bondi_accretion.toml
create mode 100644 test/IntegrationTests/refs/grhd_bondi_accretion/output.h5
create mode 100644 test/IntegrationTests/refs/grhd_tov_spherical1d/grhd_tov_spherical1d.toml
create mode 100644 test/IntegrationTests/refs/grhd_tov_spherical1d/output.h5
diff --git a/Manifest.toml b/Manifest.toml
index 29b2bbfd..576c4eb5 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -2,7 +2,7 @@
julia_version = "1.10.0-rc2"
manifest_format = "2.0"
-project_hash = "4772e5e6caf338d2c755b5d4461c2d0c5c7482c5"
+project_hash = "7e9cb4087253abe43f5a39d1ae318381c828bb4b"
[[deps.Adapt]]
deps = ["LinearAlgebra", "Requires"]
@@ -46,6 +46,12 @@ uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+[[deps.BasicInterpolators]]
+deps = ["LinearAlgebra", "Memoize", "Random"]
+git-tree-sha1 = "3f7be532673fc4a22825e7884e9e0e876236b12a"
+uuid = "26cce99e-4866-4b6d-ab74-862489e035e0"
+version = "0.7.1"
+
[[deps.BitTwiddlingConvenienceFunctions]]
deps = ["Static"]
git-tree-sha1 = "0c5f81f47bbbcf4aea7b2959135713459170798b"
@@ -409,6 +415,12 @@ deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.2+1"
+[[deps.Memoize]]
+deps = ["MacroTools"]
+git-tree-sha1 = "2b1dfcba103de714d31c033b5dacc2e4a12c7caa"
+uuid = "c03570c3-d221-55d1-a50c-7939bbd78826"
+version = "0.4.4"
+
[[deps.MicrosoftMPI_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b01beb91d20b0d1312a9471a36017b5b339d26de"
diff --git a/Project.toml b/Project.toml
index 2db747a5..587cbd46 100644
--- a/Project.toml
+++ b/Project.toml
@@ -5,6 +5,7 @@ version = "1.2.0"
[deps]
Base64 = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+BasicInterpolators = "26cce99e-4866-4b6d-ab74-862489e035e0"
FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
Jacobi = "83f21c0b-4282-5fbc-9e3f-f6da3d2e584c"
@@ -27,12 +28,12 @@ ToggleableAsserts = "07ecc579-1b30-493c-b961-3180daf6e3ae"
WriteVTK = "64499a7a-5c06-52f2-abe2-ccb03c286192"
[compat]
-julia = "1.9"
PrettyTables = "<2.3.0"
+julia = "1.9"
[extras]
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
[targets]
-test = ["Test","InteractiveUtils"]
+test = ["Test", "InteractiveUtils"]
diff --git a/examples/grhd_bondi/dg.toml b/examples/grhd_bondi/dg.toml
new file mode 100644
index 00000000..c0bc7dad
--- /dev/null
+++ b/examples/grhd_bondi/dg.toml
@@ -0,0 +1,28 @@
+[EquationOfState]
+eos = "polytrope"
+polytrope_k = 0.02143872868864732
+polytrope_gamma = "$(4/3)"
+
+[GRHD]
+bc = "from_id"
+id = "bondi_accretion"
+id_filename = "$(joinpath(ROOTDIR,\"initialdata\",\"bondi_accretion.h5\"))"
+# formulation = "spherical1d"
+
+[Mesh]
+range = [ 1.8, 10.0 ]
+n = 4
+k = 35
+basis = "lgl"
+periodic = false
+
+[Output]
+every_iteration = 1
+# every_dt = 0.1
+variables = [ "D", "Sr", "Ï„", "p", "Ï", "ϵ", "vr", "rhs_D", "rhs_Sr", "rhs_Ï„", "src_D", "src_Sr", "src_Ï„" ]
+# aligned_ts = "$(collect(range(0.01,0.6,step=0.01)))"
+enable1d = true
+
+[Evolution]
+cfl = 0.4
+tend = 20.0
diff --git a/examples/grhd_bondi/fv.toml b/examples/grhd_bondi/fv.toml
new file mode 100644
index 00000000..7577160c
--- /dev/null
+++ b/examples/grhd_bondi/fv.toml
@@ -0,0 +1,25 @@
+[EquationOfState]
+eos = "polytrope"
+polytrope_k = 0.02143872868864732
+polytrope_gamma = "$(4/3)"
+
+[GRHD]
+bc = "from_id"
+id = "bondi_accretion"
+id_filename = """$(joinpath(ROOTDIR,"initialdata","bondi_accretion.h5"))"""
+
+[Mesh]
+range = [ 1.8, 10.0 ]
+k = 1024
+scheme = "FV"
+periodic = false
+
+[Output]
+every_iteration = 1
+variables = [ "D", "Sr", "Ï„", "p", "Ï", "ϵ", "vr", "rhs_D", "rhs_Sr", "rhs_Ï„", "src_D", "src_Sr", "src_Ï„" ]
+# aligned_ts = "$(collect(range(0.01,0.6,step=0.01)))"
+enable1d = true
+
+[Evolution]
+cfl = 1.0
+tend = 20.0
diff --git a/examples/grhd_tov/dg.toml b/examples/grhd_tov/dg.toml
new file mode 100644
index 00000000..13c0f286
--- /dev/null
+++ b/examples/grhd_tov/dg.toml
@@ -0,0 +1,35 @@
+[EquationOfState]
+eos = "polytrope"
+polytrope_k = 100.0
+polytrope_gamma = 2.0
+
+[GRHD]
+bc = "from_id"
+id = "tov"
+id_filename = "$(joinpath(ROOTDIR,\"initialdata\",\"TOV_stable.h5\"))"
+atm_factor = 1e-8
+
+[Mesh]
+range = [ 0.5, 20.0 ]
+n = 1
+k = 2048
+basis = "lgl"
+periodic = false
+
+[Output]
+# every_iteration = 1
+every_dt = 0.2
+variables = [ "D", "Sr", "Ï„",
+ "p", "Ï", "ϵ", "vr",
+ # "rD", "rSr", "rτ",
+ # "rhs_rD", "rhs_rSr", "rhs_rτ",
+ # "src_rD", "src_rSr", "src_rτ",
+ # "flr_rD", "flr_rSr", "flr_rτ",
+ # "A", "∂Ar", "B", "∂Br"
+ ]
+# aligned_ts = "$(collect(range(0.01,0.6,step=0.01)))"
+enable1d = true
+
+[Evolution]
+cfl = 0.2
+tend = 40.0
diff --git a/examples/grhd_tov/dg_spherical1d.toml b/examples/grhd_tov/dg_spherical1d.toml
new file mode 100644
index 00000000..336c21a2
--- /dev/null
+++ b/examples/grhd_tov/dg_spherical1d.toml
@@ -0,0 +1,36 @@
+[EquationOfState]
+eos = "polytrope"
+polytrope_k = 100.0
+polytrope_gamma = 2.0
+
+[GRHD]
+bc = "from_id"
+id = "tov"
+id_filename = "$(joinpath(ROOTDIR,\"initialdata\",\"TOV_stable.h5\"))"
+atm_factor = 1e-8
+formulation = "spherical1d"
+
+[Mesh]
+range = [ 0.5, 20.0 ]
+# n = 1
+# k = 2048
+n = 4
+k = 124
+basis = "lgl"
+periodic = false
+
+[Output]
+# every_iteration = 1
+# every_dt = 0.2
+variables = [ "D", "Sr", "Ï„",
+ "p", "Ï", "ϵ", "vr",
+ "src_D", "src_Sr", "src_Ï„",
+ "flr_D", "flr_Sr", "flr_Ï„",
+ # "A", "∂Ar", "B", "∂Br"
+ ]
+aligned_ts = "$(collect(range(0.2,120.0,step=0.2)))"
+enable1d = true
+
+[Evolution]
+cfl = 0.2
+tend = 120.0
diff --git a/initialdata/.gitignore b/initialdata/.gitignore
new file mode 100644
index 00000000..29338d3b
--- /dev/null
+++ b/initialdata/.gitignore
@@ -0,0 +1,2 @@
+SphericalAccretion
+*.txt
diff --git a/initialdata/Makefile b/initialdata/Makefile
new file mode 100644
index 00000000..cda6cb9b
--- /dev/null
+++ b/initialdata/Makefile
@@ -0,0 +1,5 @@
+default:
+ gcc SphericalAccretion.c -o SphericalAccretion -lm
+
+clean:
+ rm SphericalAccretion bondi-acc-ref.txt
diff --git a/initialdata/Manifest.toml b/initialdata/Manifest.toml
new file mode 100644
index 00000000..80311f49
--- /dev/null
+++ b/initialdata/Manifest.toml
@@ -0,0 +1,2181 @@
+# This file is machine-generated - editing it directly is not advised
+
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+[[deps.x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2021.5.5+0"
+
+[[deps.x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.5.0+0"
diff --git a/initialdata/Project.toml b/initialdata/Project.toml
index 24389065..dd43dc08 100644
--- a/initialdata/Project.toml
+++ b/initialdata/Project.toml
@@ -1,6 +1,8 @@
[deps]
CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
-Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
+DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
+OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
-VimBindings = "51b3953f-5e5d-4a6b-bd62-c64b6fa1518a"
-dg1d = "dfc8a8d9-21b0-4914-8ba8-32d2ec29f3fd"
+UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
diff --git a/initialdata/SphericalAccretion.c b/initialdata/SphericalAccretion.c
new file mode 100644
index 00000000..e0c4fa66
--- /dev/null
+++ b/initialdata/SphericalAccretion.c
@@ -0,0 +1,95 @@
+// copied from bamps/src/projects/grhd/initialdata/michel.c
+
+#include <math.h>
+#include <stdlib.h>
+#include <stdio.h>
+
+void main(int argc, char *argv[]) {
+
+ double M = 1.0;
+ double rc = 200.0*M;
+ double rhoc = 7e-4;
+ double gamma = 4.0/3.0;
+
+ double urc = sqrt(.5 * M / rc);
+ double Vc2 = urc*urc / (1.-3.*urc*urc);
+
+ double K = Vc2*(gamma-1.)*pow(rhoc,1.-gamma) / (gamma*(-Vc2+gamma-1.));
+
+ double hc = 1. + gamma / (gamma-1.) * K * pow(rhoc,gamma-1.);
+ double c1 = rhoc * urc * rc * rc;
+ double c3 = hc * hc * (urc*urc + 1. - 2.*M / rc);
+
+ int nnn = 1000;
+ int i;
+ double r;
+ double rmin = 1.8*M, rmax = 200.0*M;
+ double dr = (rmax-rmin)/(nnn-1);
+
+ double *gr = malloc(nnn*sizeof(double));
+ double *grho = malloc(nnn*sizeof(double));
+ double *geps = malloc(nnn*sizeof(double));
+ double *gp = malloc(nnn*sizeof(double));
+ double *gvr = malloc(nnn*sizeof(double));
+ double *gur = malloc(nnn*sizeof(double));
+ double *gut2 = malloc(nnn*sizeof(double));
+
+ for(i=0; i<nnn; i++) {
+
+ r = rmax - dr*i;
+ gr[i] = r;
+
+ double ur = sqrt(fabs(-1. + 2.*M / r) + 0.01);
+ double ut2, h, f, df;
+
+ int it=0;
+ for(it=0;it<100;it++) {
+
+ ut2 = (ur*ur+1.-2.*M/r);
+ h = 1. + (gamma / (gamma-1.)) * K * pow(c1 / (ur*r*r), gamma-1.);
+ f = h*h*ut2 - c3;
+ df = 2. * h * (-(h-1.)*(gamma-1.)/ur) * ut2 + 2. * h * h * ur;
+
+ ur = ur - f/df;
+
+ if(fabs(f/df)<1.e-14) break;
+
+ }
+
+ grho[i] = c1 / (ur*r*r);
+ gp[i] = K * pow(grho[i],gamma);
+ geps[i] = gp[i] / (grho[i]*(gamma-1.));
+
+ ut2 = (ur*ur+1.-2.*M/r);
+ gur[i] = ur;
+ gut2[i] = ut2;
+
+ double alpha = sqrt(r / (r + 2.*M));
+ double betar = 2.*M / (r + 2.*M);
+ double ut = (-2.*M * ur / r + sqrt(ut2)) / (-1.+2.*M/r);
+ double vr = ur / (alpha*ut) + betar / alpha;
+
+ gvr[i] = vr;
+
+ }
+
+
+ FILE *io = fopen("bondi-acc-ref.txt", "w");
+ if (!io) {
+ printf("FAILED\n");
+ exit(-1);
+ }
+ for (i=nnn-1; i>=0; i--) {
+ fprintf(io, "% .6e % .6e % .6e % .6e % .6e % .6e % .6e\n", gr[i], grho[i], geps[i], gp[i], gvr[i], gur[i], gut2[i]);
+ }
+ fclose(io); io = NULL;
+
+ free(grho); grho = NULL;
+ free(geps); geps = NULL;
+ free(gp); gp = NULL;
+ free(gvr); gvr = NULL;
+ free(gr); gr = NULL;
+ free(gur); gur = NULL;
+ free(gut2); gut2 = NULL;
+
+}
diff --git a/initialdata/SphericalAccretion.jl b/initialdata/SphericalAccretion.jl
index 5b3cc8a0..15e4661f 100644
--- a/initialdata/SphericalAccretion.jl
+++ b/initialdata/SphericalAccretion.jl
@@ -1,5 +1,14 @@
+module SphericalAccretion
+
+
+
using CairoMakie
+using CairoMakie.FileIO
+using DelimitedFiles
using Printf
+using HDF5
+using Roots
+using UnPack
"""
@@ -7,53 +16,51 @@ Solution taken from Bugner [2017], section 4.2.
Kerr-Schild coordinates allow use to go beyond horizon towards the singularity.
However, it becomes more difficult for the Newton Rapshon solver to determine a solution
-once beyond the horizon. To this end, try increasing `N_rs` whenever you lower `rmin` and
+once beyond the horizon. To this end, try increasing `N_rs` whenever you lower `rmin` and
the solver aborts inside the horizon.
Alternatively, one could also add an adaptive stepper.
Note: We implicitly assume θ = π/2, because then sin(θ) = 1, although,
the sines should cancel out everywhere.
"""
-function solve()
-
- # parameters
- M = 1.0
- N_rs = 100000
- rmin, rmax = 0.1*M, 200*M
- rc, Ïc, Γ = 200*M, 7e-4, 4/3
+function solve(; rmin, rmax, rc, Ïc, Γ, M=1.0, N_rs=1000,
+ urc_sign=1)
- urc = sqrt(M / (2 * rc))
+ urc = urc_sign*sqrt(M /(2 * rc))
# cannot find solutions within these regions, cf. Michel 1972
@show urc
@assert rc >= 6*M
- @assert urc <= 1 / 3
+ @assert urc^2 <= 1 / 3
- Vc2 = urc^2 / (1 - 3 * urc^2)
- K = Vc2 * (Γ - 1) / ( (Γ - 1 - Vc2) * Γ * Ïc^(Γ - 1) )
+ Vc = urc^2 / (1 - 3 * urc^2)
+ K = Vc * (Γ - 1) / ( (Γ - 1 - Vc) * Γ * Ïc^(Γ - 1) )
+ @show K
# here we set θ = π/2 so that sin(θ) = 1
- C1 = rc^2 * Ïc * urc
hc = 1 + K * Γ * Ïc^(Γ - 1) / (Γ - 1)
u0c = sqrt(1 - 2 * M / rc + urc^2)
+ C1 = rc^2 * Ïc * urc
+ C2 = rc^2 * Ïc * hc * u0c * urc
C3 = hc^2 * u0c^2
function F(ur, r)
Ï = C1 / (r^2 * ur)
h = 1 + K * Γ * Ï^(Γ - 1) / (Γ - 1)
u0 = sqrt(1 - 2 * M / r + ur^2)
- u0 = sqrt(1 - 2 * M / r + ur^2)
return h^2 * u0^2 - C3
end
- function dF(ur, r)
- Ï = C1 / (r^2 * ur)
- h = 1 + K * Γ * Ï^(Γ - 1) / (Γ - 1)
- u0 = sqrt(1 - 2 * M / r + ur^2)
- dÏdur = - C1 / (r^2 * ur^2)
- dhdÏ = K * Γ * Ï^(Γ - 2)
- du0dur = ur / u0
- return 2 * (u0^2 * h * dhdÏ * dÏdur + h^2 * u0 * du0dur)
- end
+ # manually compute derviative and
+ # use Roots.find_zero((F_at_r,dF_at_r), ur_guess, Roots.Newton()) below
+ # function dF(ur, r)
+ # Ï = C1 / (r^2 * ur)
+ # h = 1 + K * Γ * Ï^(Γ - 1) / (Γ - 1)
+ # u0 = sqrt(1 - 2 * M / r + ur^2)
+ # dÏdur = - C1 / (r^2 * ur^2)
+ # dhdÏ = K * Γ * Ï^(Γ - 2)
+ # du0dur = ur / u0
+ # return 2 * (u0^2 * h * dhdÏ * dÏdur + h^2 * u0 * du0dur)
+ # end
# radial domain over which we solve
rs = collect(LinRange(rmin, rmax, N_rs))
@@ -65,52 +72,275 @@ function solve()
# - use the previous result for the remaining radi
# The following converges to the correct solution:
if r > 2*M
- ur_guess = sqrt(1 - 2 * M / r) # asymptotic value for ur
+ ur_guess = urc_sign*sqrt(1 - 2 * M / r) # = sqrt(1+gtt), =^= asymptotic value for ur when u0 -> 1
else
ur_guess = urs[idx+1] # use previous iterate where asymptotic value is not defined
end
F_at_r(ur) = F(ur, r)
- dF_at_r(ur) = dF(ur, r)
+ # dF_at_r(ur) = dF(ur, r)
ur = try
- Roots.find_zero((F_at_r,dF_at_r), ur_guess, Roots.Newton())
+ # Roots.find_zero((F_at_r,dF_at_r), ur_guess, Roots.Newton())
+ Roots.find_zero(F_at_r, ur_guess)
catch err
println()
- error("Could not determine solution for 'ur' at radius r = $r. " *
- "Remaining error: $err")
+ @info("Could not determine solution for 'ur' at radius r = $r. ")
+ rethrow(err)
end
# @show (ur, r)
- if ur < 0.0
- @warn "Aborting due to ur becoming negative at r = $r."
- @info "$(N_rs - idx) points skipped ..."
- break
- end
+ # if ur < 0.0
+ # @warn "Aborting due to ur becoming negative at r = $r."
+ # @info "$(N_rs - idx) points skipped ..."
+ # break
+ # end
urs[idx] = ur
end
Ïs = @. C1 / (rs^2 * urs)
ps = @. K * Ïs^Γ
ϵs = @. ps / ((Γ - 1) * Ïs)
- βr = @. 2 * M / (rs + 2 * M)
+ βr = @. 2 * M / (rs + 2 * M) # = β^r
α = @. sqrt( rs / (rs + 2 * M) )
-
- gtt_uu = @. - (2 * M + rs) / rs
- gtr_uu = @. 2 * M / rs
- grr_uu = @. (rs - 2 * M) / rs
+ γrr = @. 1 + 2*M/rs
+ γrr_uu = @. 1/γrr
+ gtt_uu = @. -1/α^2
+ gtr_uu = @. βr/α^2
+ grr_uu = @. γrr_uu - βr*βr/α^2
+ gtt = @. -α^2 + γrr*βr*βr
+ gtr = @. γrr * βr
+ grr = @. γrr
u0s_d = @. sqrt(1 - 2 * M / rs + urs^2)
u0s_u = @. gtt_uu * u0s_d + gtr_uu / grr_uu * (urs - gtr_uu * u0s_d)
+ # u0s_u_v2 = @. (gtt_uu * u0s_d + gtr_uu*grr*urs)/(1-gtr*gtr_uu)
+ # @show(maximum(abs, u0s_u .- u0s_u_v2))
vrs = @. urs / (α * u0s_u) + βr / α
+ vrs_d = @. γrr * vrs
+ hs = @. 1 + K * Γ * Ïs^(Γ - 1) / (Γ - 1)
+ res_C1 = @. rs^2 * Ïs * urs - C1
+ res_C2 = @. rs^2 * Ïs * hs * u0s_d * urs - C2
+ res_C3 = @. hs^2 * u0s_d^2 - C3
+ vs = @. sqrt(γrr * vrs^2)
+
+ return (; rs, urs, vrs, Ïs, ps, ϵs, res_C1, res_C2, res_C3, vs, vrs_d,
+ rmin, rmax, rc, Vc, Ïc, Γ, M, N_rs, K)
+
+end
+
+
+function solve_ref()
+ # reference data from bugner's solver SphericalAccretion.c (extracted from bamps)
+ M = 1.0
+ rmin, rmax = 1.8*M, 200*M
+ rc, Ïc, Γ = 200*M, 7e-4, 4/3
+ solve(; rmin, rmax, rc, Ïc, Γ, M)
+end
+
+function solve_papadopoulus_1998()
+ # arXiv:gr-qc/9803087v1
+ # works with Eddington-Finkelstein coords (same form as Bugner; but Bugner calls them Kerr-Schild?)
+ M = 1.0
+ rmin, rmax = 0.5*M, 50*M
+ rc, Ïc, Γ = 400*M, 1e-2, 4/3
+ solve(; rmin, rmax, rc, Ïc, Γ, M)
+end
+
+function solve_papadopoulus_1999()
+ # arXiv:gr-qc/9902018v1
+ # works with ingoing Eddington-Finkelstein coords, but the equations appear to be the same
+ # compare with the 1998 paper, in these coordinates G(r) = 0
+ M = 1.0
+ rmin, rmax = 1.5*M, 30*M
+ rc, Ïc, Γ = 200*M, 1e-2, 5/3
+ solve(; rmin, rmax, rc, Ïc, Γ, M)
+end
+
+
+function save(fname, data)
+ # save
+ filename = joinpath(@__DIR__, fname)
+ h5open(filename, "w") do file
+ @info "Saving results to '$filename' ..."
+ g = create_group(file, "bondi_accretion")
+ HDF5.attributes(g)["rc"] = data.rc
+ HDF5.attributes(g)["Ïc"] = data.Ïc
+ HDF5.attributes(g)["Vc"] = data.Vc
+ HDF5.attributes(g)["Γ"] = data.Γ
+ HDF5.attributes(g)["M"] = data.M
+ HDF5.attributes(g)["K"] = data.K
+ HDF5.attributes(g)["rmin"] = data.rmin
+ HDF5.attributes(g)["rmax"] = data.rmax
+ g["r"] = data.rs
+ g["ur"] = data.urs
+ g["vr"] = data.vrs
+ g["Ï"] = data.Ïs
+ g["p"] = data.ps
+ g["ϵ"] = data.ϵs
+ end
+ return
+end
+
+
+function plot(data)
+
+ @unpack M, Ïs, ps, ϵs, vrs, rs, res_C1, res_C2, res_C3, vrs_d = data
fig = Figure()
- ax_Ï = Axis(fig[1,1], xlabel="r", ylabel="Ï")
- ax_p = Axis(fig[1,2], xlabel="r", ylabel="p")
- ax_ϵ = Axis(fig[2,1], xlabel="r", ylabel="ϵ")
- ax_v_r = Axis(fig[2,2], xlabel="r", ylabel="v_r")
+ ax_Ï = Axis(fig[1,1], xlabel=L"r", ylabel=L"\rho")
+ ax_p = Axis(fig[1,2], xlabel=L"r", ylabel=L"p")
+ ax_ϵ = Axis(fig[2,1], xlabel=L"r", ylabel=L"\epsilon")
+ ax_v_r = Axis(fig[2,2], xlabel=L"r", ylabel=L"v^r")
+ # ax_res_C1 = Axis(fig[3,1], xlabel=L"r", ylabel=L"R_{C_1}")
+ # ax_res_C2 = Axis(fig[3,2], xlabel=L"r", ylabel=L"R_{C_2}")
+ # ax_res_C3 = Axis(fig[4,1], xlabel=L"r", ylabel=L"R_{C_3}")
+ # ax_v_r_d = Axis(fig[4,2], xlabel=L"r", ylabel=L"v_r")
+
+ rhor = 2*M # radius of horizon
lines!(ax_Ï, rs, Ïs)
lines!(ax_p, rs, ps)
lines!(ax_ϵ, rs, ϵs)
lines!(ax_v_r, rs, vrs)
+ # lines!(ax_res_C1, rs, res_C1)
+ # lines!(ax_res_C2, rs, res_C2)
+ # lines!(ax_res_C3, rs, res_C3)
+ # lines!(ax_v_r_d, rs, vrs_d)
+ vlines!(ax_Ï, rhor, linestyle=:dash)
+ vlines!(ax_p, rhor, linestyle=:dash)
+ vlines!(ax_ϵ, rhor, linestyle=:dash)
+ vlines!(ax_v_r, rhor, linestyle=:dash)
+ # vlines!(ax_v_r_d, rhor, linestyle=:dash)
+
+ # xlims!(ax_Ï, (1.8,10.0))
+ # xlims!(ax_p, (1.8,10.0))
+ # xlims!(ax_ϵ, (1.8,10.0))
+ # xlims!(ax_v_r, (1.8,10.0))
# use save("filename.pdf", fig) to save to pdf
return fig
end
+
+
+function plot_compare_ref()
+
+ mydata = solve_ref()
+ csv = readdlm(joinpath(@__DIR__, "bondi-acc-ref.txt"))
+ refdata = (; rs=csv[:,1],
+ Ïs=csv[:,2],
+ ϵs=csv[:,3],
+ ps=csv[:,4],
+ vrs=csv[:,5],
+ urs=csv[:,6],
+ ut2=csv[:,7])
+
+ fig = Figure()
+ ax_Ï = Axis(fig[1,1], xlabel=L"r", ylabel=L"\rho")
+ ax_p = Axis(fig[1,2], xlabel=L"r", ylabel=L"p")
+ ax_ϵ = Axis(fig[2,1], xlabel=L"r", ylabel=L"\epsilon")
+ ax_vr = Axis(fig[2,2], xlabel=L"r", ylabel=L"v^r")
+ ax_ur = Axis(fig[3,1], xlabel=L"r", ylabel=L"u^r")
+
+ lines!(ax_Ï, mydata.rs, mydata.Ïs)
+ lines!(ax_p, mydata.rs, mydata.ps)
+ lines!(ax_ϵ, mydata.rs, mydata.ϵs)
+ lines!(ax_vr, mydata.rs, mydata.vrs)
+ lines!(ax_ur, mydata.rs, mydata.urs)
+ lines!(ax_Ï, refdata.rs, refdata.Ïs, linestyle=:dash)
+ lines!(ax_p, refdata.rs, refdata.ps, linestyle=:dash)
+ lines!(ax_ϵ, refdata.rs, refdata.ϵs, linestyle=:dash)
+ lines!(ax_vr, refdata.rs, refdata.vrs, linestyle=:dash)
+ lines!(ax_ur, refdata.rs, refdata.urs, linestyle=:dash)
+
+ rhor = 2*mydata.M
+ vlines!(ax_Ï, rhor, linestyle=:dash, color=:grey)
+ vlines!(ax_p, rhor, linestyle=:dash, color=:grey)
+ vlines!(ax_ϵ, rhor, linestyle=:dash, color=:grey)
+ vlines!(ax_vr, rhor, linestyle=:dash, color=:grey)
+ vlines!(ax_ur, rhor, linestyle=:dash, color=:grey)
+
+ return fig
+
+end
+
+
+function plot_compare_papadopoulus_1998()
+
+ mydata = solve_papadopoulus_1998()
+ img_p = load("bondi-acc_papadopoulos1998_p.png")
+ img_Ï = load("bondi-acc_papadopoulos1998_rho.png")
+ # v = sqrt(γ_rr) v^r; is called total velocity in the paper (hidden in text)
+ # the label in the plot is just 'Velocity'
+ img_v = load("bondi-acc_papadopoulos1998_v.png")
+
+ xmin, xmax = 0.0, 15.0
+ ymin_Ï, ymax_Ï = 0, 120.0
+ ymin_p, ymax_p = 0, 2.5
+ ymin_vr, ymax_vr = -0.3, -0.2
+
+ fig = Figure()
+ ax_p = Axis(fig[1,1], xlabel=L"r", ylabel=L"p")
+ ax_Ï = Axis(fig[2,1], xlabel=L"r", ylabel=L"\rho")
+ ax_vr = Axis(fig[3,1], xlabel=L"r", ylabel=L"v^r")
+
+ image!(ax_Ï, xmin..xmax, ymin_Ï..ymax_Ï, rotr90(img_Ï))
+ image!(ax_p, xmin..xmax, ymin_p..ymax_p, rotr90(img_p))
+ image!(ax_vr, xmin..xmax, ymin_vr..ymax_vr, rotr90(img_v))
+
+ lines!(ax_Ï, mydata.rs, mydata.Ïs, linestyle=:dash, color=:orange)
+ lines!(ax_p, mydata.rs, mydata.ps, linestyle=:dash, color=:orange)
+ # don't understand why they plot with a minus here
+ # there seem to be ingoing and outgoing solutions (urc_sign parameter),
+ # but the value for v never fits
+ lines!(ax_vr, mydata.rs, -mydata.vs, linestyle=:dash, color=:orange)
+
+ xlims!(ax_Ï, (xmin,xmax))
+ xlims!(ax_p, (xmin,xmax))
+ xlims!(ax_vr, (xmin,xmax))
+ ylims!(ax_Ï, (ymin_Ï,ymax_Ï))
+ ylims!(ax_p, (ymin_p,ymax_p))
+ ylims!(ax_vr, (ymin_vr,ymax_vr))
+
+ return fig
+end
+
+
+function plot_compare_papadopoulus_1999()
+
+ mydata = solve_papadopoulus_1999()
+ img_ϵ = load("bondi-acc_papadopoulos1999_eps.png")
+ img_Ï = load("bondi-acc_papadopoulos1999_rho.png")
+ img_vr = load("bondi-acc_papadopoulos1999_vr.png")
+
+ xmin, xmax = 1.0, 10.0
+ ymin_Ï, ymax_Ï = 0, 10.0
+ ymin_ϵ, ymax_ϵ = 0, 0.25
+ ymin_vr, ymax_vr = -1.0, 0.0
+
+ fig = Figure()
+ ax_ϵ = Axis(fig[1,1], xlabel=L"r", ylabel=L"\epsilon")
+ ax_Ï = Axis(fig[2,1], xlabel=L"r", ylabel=L"\rho")
+ ax_vr = Axis(fig[3,1], xlabel=L"r", ylabel=L"u^r")
+
+ image!(ax_Ï, xmin..xmax, ymin_Ï..ymax_Ï, rotr90(img_Ï))
+ image!(ax_ϵ, xmin..xmax, ymin_ϵ..ymax_ϵ, rotr90(img_ϵ))
+ image!(ax_vr, xmin..xmax, ymin_vr..ymax_vr, rotr90(img_vr))
+
+ lines!(ax_Ï, mydata.rs, mydata.Ïs, linestyle=:dash, color=:orange)
+ lines!(ax_ϵ, mydata.rs, mydata.ϵs, linestyle=:dash, color=:orange)
+ # don't understand why they plot with a minus here
+ # there seem to be ingoing and outgoing solutions (urc_sign parameter),
+ # but the value for ur never fits
+ lines!(ax_vr, mydata.rs, -mydata.urs, linestyle=:dash, color=:orange)
+ display(extrema(mydata.urs))
+
+ xlims!(ax_Ï, (xmin,xmax))
+ xlims!(ax_ϵ, (xmin,xmax))
+ xlims!(ax_vr, (xmin,xmax))
+ ylims!(ax_Ï, (ymin_Ï,ymax_Ï))
+ ylims!(ax_ϵ, (ymin_ϵ,ymax_ϵ))
+ ylims!(ax_vr, (ymin_vr,ymax_vr))
+
+ return fig
+end
+
+
+
+end # module
diff --git a/initialdata/TOV.jl b/initialdata/TOV.jl
index 1ceca0fe..ddf49ec3 100644
--- a/initialdata/TOV.jl
+++ b/initialdata/TOV.jl
@@ -2,58 +2,65 @@ export TOV
module TOV
-using dg1d
-using LaTeXStrings
-using Plots
+import CairoMakie
+import CairoMakie: @L_str
+using HDF5
+using OrdinaryDiffEq
using Printf
# array indices of state vector
-const idx_p, idx_m, idx_Ï•, idx_R, idx_r = 1, 2, 3, 4, 5
+const idx_p, idx_m, idx_ϕ, idx_λ = 1, 2, 3, 4
-function TOV_rhs!(du, u, r, eos::Polytrope)
+function TOV_rhs!(du, u, p, r)
+
+ # parameters for polytropic equation of state
+ (; K, Γ) = p
if r == 0.0
du .= 0.0
else
p, m = u[idx_p], u[idx_m]
- ϵ = try
- rho = eos(Density, Pressure, p)
- eps = eos(InternalEnergy, Density, rho)
- eos(TotalEnergy, Density, rho, InternalEnergy, eps)
+ e = try
+ Ï = (p/K)^(1/Γ)
+ ϵ = K / (Γ-1) * Ï^(Γ-1)
+ Ï*(1+ϵ)
catch err
if err isa DomainError
0.0
else
- rethrow(e)
+ rethrow(err)
end
end
# dp/dr
- du[idx_p] = - (ϵ + p) * (m + 4.0 * π * r^3 * p) / (r * (r - 2.0 * m))
+ du[idx_p] = - (e + p) * (m + 4.0 * π * r^3 * p) / (r * (r - 2.0 * m))
# dm/dr
- du[idx_m] = 4.0 * π * r^2 * ϵ
+ du[idx_m] = 4.0 * π * r^2 * e
# dϕ/dr
- du[idx_ϕ] = - du[idx_p] / (ϵ + p)
- # dR/dr
- du[idx_R] = (1.0 - sqrt(1.0 - 2.0 * m / r)) / sqrt(r^2 - 2.0 * m * r)
+ du[idx_Ï•] = - du[idx_p] / (e + p)
+ # regular term of dR/dr ODE
+ du[idx_λ] = (1.0 - sqrt(1.0 - 2.0 * m / r)) / sqrt(r^2 - 2.0 * m * r)
end
return
end
-function solve()
+"""
+Compute TOV solution for a polytropic equation of state.
+ - Γ: polytropic exponent
+ - K: polytropic constant
+ - Ïc: central density
+ - rmax: [optional] maximum integration radius, increase when integration does not proceed till surface
+"""
+function solve(; Γ, K, Ïc, rmax=30.0)
- # equation of state
- Γ = 2
- K = 100
- # Ïc = 8.00 * 1e-3 # central rest mass density
- Ïc = 1.28 * 1e-3 # central rest mass density
- eos = Polytrope(K = K, Gamma = Γ)
- pc = eos(Pressure, Density, Ïc, InternalEnergy, nothing)
+ # equation of state parameters
+ prms = (; K, Γ)
+ pc = K*Ïc^Γ
# initial values
# Note: We put Ï•(0) = 0 as initial condition for the potential in the interior
@@ -70,155 +77,112 @@ function solve()
u0[idx_p] = pc
u0[idx_m] = 0.0
u0[idx_Ï•] = 0.0
- u0[idx_R] = 0.0
-
+ u0[idx_λ] = 0.0
dr = 1e-2 # inital step width for r
- r_range = [0.0, 30.0] # max integration range
- ODE!(du, u, r) = TOV_rhs!(du, u, r, eos)
-
-
- # post hook setup to
- # - store solution
- # - terminate ODE solver if pressure drops below p_threshold
- # solution = [u0..., r_range[1]]
- storage_increment = 1000
- n_variables = 5
- solution = zeros(Float64, storage_increment, n_variables)
- solution[1,:] .= [ u0..., r_range[1] ]
- counter = 1
- p_threshold = 1e-14
- function post_hook(u, r)
- counter += 1
- if counter >= size(solution)[1]
- zs = zeros(Float64, storage_increment, n_variables)
- solution = vcat(solution, zs)
- end
- solution[counter, :] .= [ u..., r ]
- p = u[idx_p]
- return (p > p_threshold) # continue as long as this is true
+ r_range = [0.0, rmax] # max integration range
+ prob = ODEProblem(TOV_rhs!,u0,r_range,prms)
+
+ sol = OrdinaryDiffEq.solve(prob, Tsit5(), dt=dr, adaptive=false)
+
+ nsteps = length(sol)
+ p, m, ϕ, λ, r = Float64[], Float64[], Float64[], Float64[], Float64[]
+ for (i,(ui,ri)) in enumerate(zip(sol.u,sol.t))
+ ui[idx_p] < 0 && break
+ push!(p, ui[idx_p])
+ push!(m, ui[idx_m])
+ push!(Ï•, ui[idx_Ï•])
+ push!(λ, ui[idx_λ])
+ push!(r, ri)
end
- # solve ODE
- pblm = dg1d.ODEProblem(:rk4)
- dg1d.evolve_adaptive_ERK(pblm, ODE!, u0, dr, r_range[2], post_hook=post_hook)
+ Ï = @. (p/K)^(1/Γ)
+ ϵ = @. K / (Γ-1) * Ï^(Γ-1)
- # chop off trailing zeros
- solution = solution[1:counter,:]
+ # attach Schwarzschild solution exterior to star's surface
+ M = m[end]
+ r_surf = r[end]
+ λ_surf = λ[end]
+ # potential difference (wrt Schwarzschild solution) at star's surface
+ Δϕ_surf = ϕ[end] - (0.5 * log(1.0 - 2.0 * M / r_surf))
+ # adjust interior potential to align with exterior at star's surface
+ ϕ .-= Δϕ_surf
- M = solution[end, idx_m]
- r_surf = solution[end, idx_r]
- R_surf = solution[end, idx_R]
- @info "M = $M"
- @info "r = $r_surf"
- @info "R = $R_surf"
+ R = @. 0.5*r/r_surf * (sqrt(r_surf^2 - 2*M*r_surf) + r_surf - M) * exp(λ - λ_surf)
+ R_surf = R[end]
+ @show M, r_surf, R_surf
+
+ return (; K, Γ, Ïc, M, dr, p, m, Ï•, R, Ï, ϵ, r)
+end
- # potential at star's surface
- Δϕ_surf = solution[end,idx_ϕ] - (0.5 * log(1.0 - 2.0 * M / r_surf))
- # adjust interior potential to align with exterior at star's surface
- solution[:,idx_ϕ] .-= Δϕ_surf
- # fix integration constant between isotropic and schwarzschild coordinate
- Rs = R_surf
- rs = r_surf
- r = solution[:,idx_r]
- R = solution[:,idx_R]
- @. solution[:,idx_R] = 0.5 * r / rs * (sqrt(rs^2 - 2 * M * rs) + rs - M) * exp(R - Rs)
+function solve_bugner_stable()
+ solve(Γ=2.0, K=100.0, Ïc=1.28e-3)
+end
+function solve_bugner_unstable()
+ solve(Γ=2.0, K=100.0, Ïc=8e-3)
+end
+
+function save(fname, data)
+ @assert endswith(fname, ".h5")
# save
- output_dir = dg1d.get_output_dir()
- filename = joinpath(output_dir, "TOV.h5")
+ filename = joinpath(@__DIR__, fname)
h5open(filename, "w") do file
@info "Saving results to '$filename' ..."
g = create_group(file, "TOV")
- attributes(g)["Γ"] = Γ
- attributes(g)["K"] = K
- attributes(g)["Ïc"] = Ïc
- attributes(g)["M"] = M
- g["Ï•"] = solution[:,idx_Ï•]
- g["p"] = solution[:,idx_p]
- g["m"] = solution[:,idx_m]
- g["R"] = solution[:,idx_R]
- g["r"] = solution[:,idx_r]
+ attributes(g)["Γ"] = data.Γ
+ attributes(g)["K"] = data.K
+ attributes(g)["Ïc"] = data.Ïc
+ attributes(g)["M"] = data.M
+ attributes(g)["dr"] = data.dr
+ g["Ï•"] = data.Ï•
+ g["p"] = data.p
+ g["m"] = data.m
+ g["R"] = data.R
+ g["r"] = data.r
+ g["Ï"] = data.Ï
+ g["ϵ"] = data.ϵ
end
-
return
end
+function plot(data)
-function read_data(filename)
- return h5open(filename, "r") do file
- g = file["TOV"]
- Γ = read_attribute(g, "Γ")
- K = read_attribute(g, "K")
- Ïc = read_attribute(g, "Ïc")
- M = read_attribute(g, "M")
- Ï• = read(g, "Ï•")
- p = read(g, "p")
- m = read(g, "m")
- R = read(g, "R")
- r = read(g, "r")
- (; Γ, K, Ïc, M, Ï•, p, m, R, r)
- end
-end
+ (; Ïc, dr, M, r, R, Ï, ϵ, m, p, Ï•) = data
+
+ r_surf = r[end]
+ R_surf = R[end]
+ rmax = r_surf*3
+
+ Ï•int = Ï•
+ Λint = @. -0.5 * log(1.0-2.0*m/r)
+
+ rext = collect(range(r[end], rmax, step=dr))
+ Ï•ext = @. 0.5 * log(1.0-2.0*M/rext)
+ Λext = -ϕext
+
+ fig = CairoMakie.Figure(title="TOV star, $(@sprintf "Ïc = %.5f, M = %.5f, R=%.5f" Ïc M R_surf)")
+ ax_metric = CairoMakie.Axis(fig[1,1], xlabel=L"r")
+ ax_eos = CairoMakie.Axis(fig[2,1], xlabel=L"r")
+ CairoMakie.linkxaxes!(ax_metric, ax_eos)
+ CairoMakie.lines!(ax_metric, r, @.(exp(2.0*Ï•int)), label=L"e^{2\phi_{int}}")
+ CairoMakie.lines!(ax_metric, r, @.(exp(-2.0*Λint)), label=L"e^{2\Lambda_{int}}")
+ CairoMakie.lines!(ax_metric, rext, @.(exp(2.0*Ï•ext)), label=L"e^{2\phi_{ext}}")
+ CairoMakie.lines!(ax_metric, rext, @.(exp(-2.0*Λext)), label=L"e^{2\Lambda_{ext}}")
+ CairoMakie.vlines!(ax_metric, r_surf, linestyle=:dash, color=:black, label=L"r_{surf}")
-function plot_potentials()
-
- output_dir = dg1d.get_output_dir()
- filename = joinpath(output_dir, "TOV.h5")
- Γ, K, Ïc, M, Ï•, p, m, R, r = read_data(filename)
-
- eos = Polytrope(K = K, Gamma = Γ)
- Ï = @. eos(Density, InternalEnergy, nothing, Pressure, p)
- ϵ = @. eos(InternalEnergy, Density, Ï, Pressure, p)
-
- r_ext = collect(range(r[end], 15.0, length=100))
- M = m[end]
- Ï•_ext = @. 0.5 * log(1.0 - 2.0 * M / r_ext)
-
- Ï•_int = Ï•
- Λ_int = @. - 0.5 * log(1.0 - 2.0 * m / r)
- Λ_ext = - ϕ_ext
-
- Plots.gr()
- plt_metric = Plots.plot()
- # Plots.plot(r, 100.0 * Ï, label="100 * Ï(r)")
- # Plots.plot!(plt, r, 100.0 * ϵ, label="100 * ϵ(r)")
- # Plots.plot!(plt, r, 100.0 * p, label="100 * p(r)")
- # Plots.plot!(plt, r, Ï•_int, label="Ï•_int(r)")
- # Plots.plot!(plt, r_ext, Ï•_ext, label="Ï•_ext(r)")
- # Plots.plot!(plt, r, Λ_int, label="Λ_int(r)")
- # Plots.plot!(plt, r_ext, Λ_ext, label="Λ_ext(r)")
- # Plots.plot!(plt, r, @.(r/R), label="R")
- # R_ext = @. 1/2 * (sqrt(r_ext^2 - 2 * M * r_ext) + r_ext - M)
- # Plots.plot!(plt, r_ext, R_ext, label="R")
- # Plots.plot!(plt, r, m, label="m")
-
- #### potentials are continuous and differential at surface
- Plots.plot!(plt_metric, r, @.( exp(2.0*Ï•_int) ), label=L"e^{2 \Phi_{int}}")
- Plots.plot!(plt_metric, r, @.( exp(-2.0*Λ_int) ), label=L"e^{2 \Lambda_{int}}")
- Plots.plot!(plt_metric, r_ext, @.( exp(2.0*Ï•_ext) ), label=L"e^{2 \Phi_{ext}}")
- Plots.plot!(plt_metric, r_ext, @.( exp(-2.0*Λ_ext) ), label=L"e^{2 \Lambda_{ext}}")
- rs = r[end]
- Rs = R[end]
- Plots.plot!(plt_metric, [rs, rs], [0,1], line=(:dash, :black), label=L"r=r_S")
-
- plt_eos = Plots.plot()
- Plots.plot!(plt_eos, r, p, label=L"p")
- Plots.plot!(plt_eos, r, Ï, label=L"\rho")
- # Plots.plot!(plt_eos, r, ϵ, label="ϵ")
-
- plt = Plots.plot(plt_metric, plt_eos, layout=(2,1),
- xlabel="r",
- plot_title="TOV star, $(@sprintf "Ïc = %.5f, M = %.5f, R = %.5f" Ïc M Rs)",
- legendfontsize = 20, guidefontsize = 20,
- tickfontsize = 20, titlefontsize = 20,
- size=(1200,1200), xlims=(0.0, 15.0))
- Plots.gui(plt)
+ CairoMakie.lines!(ax_eos, r, p.*100, label=L"100 p")
+ CairoMakie.lines!(ax_eos, r, Ï.*10, label=L"10 \rho")
+ CairoMakie.lines!(ax_eos, r, ϵ, label=L"\epsilon")
+ CairoMakie.vlines!(ax_eos, r_surf, linestyle=:dash, color=:black, label=L"r_{surf}")
+ CairoMakie.axislegend(ax_metric, orientation=:horizontal, position=:rb)
+ CairoMakie.axislegend(ax_eos, orientation=:horizontal, position=:rb)
+ return fig
end
diff --git a/initialdata/TOV_stable.h5 b/initialdata/TOV_stable.h5
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diff --git a/initialdata/TOV_unstable.h5 b/initialdata/TOV_unstable.h5
new file mode 100644
index 0000000000000000000000000000000000000000..b94e0e5a6251b83a0d403bba81f5ec5ea7385405
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diff --git a/initialdata/bondi_accretion.h5 b/initialdata/bondi_accretion.h5
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diff --git a/math/3plus1.py b/math/3plus1.py
index a0f1ec87..eb5534e6 100644
--- a/math/3plus1.py
+++ b/math/3plus1.py
@@ -7,7 +7,7 @@
# extension: .py
# format_name: light
# format_version: '1.5'
-# jupytext_version: 1.12.0
+# jupytext_version: 1.16.0
# kernelspec:
# display_name: Python 3 (ipykernel)
# language: python
@@ -95,6 +95,10 @@ display(γ4ud)
Γs = christoffels(γ_coords, γ, γinv)
display(Γs)
+# $$
+# \gamma_{ij} = \eta_{ij}
+# $$
+
η_coords = coords[1:]
display(η_coords)
η = sp.diag(1, r**2, r**2 * sp.sin(θ)**2)
@@ -147,6 +151,20 @@ display(γhat.det())
γhat_Γs = christoffels(γhat_coords, γhat, γhatinv)
display(γhat_Γs)
+# $$
+# \gamma_{ij} = r^{-8/3} \eta_{ij}
+# $$
+
+γhat_coords = coords[1:]
+display(γhat_coords)
+γhat = r**(sp.Rational(-8,3)) * η
+γhatinv = γhat.inv()
+display(γhat)
+display(γhatinv)
+display(γhat.det())
+γhat_Γs = christoffels(γhat_coords, γhat, γhatinv)
+display(γhat_Γs)
+
# ## Extrinsic curvature
#
@@ -195,7 +213,7 @@ for (c, Γ) in zip(sphere_coords, sphere_Γs):
if Γij:
ci = sphere_coords[i];
cj = sphere_coords[j];
- display(Math(f"\Gamma^{{ {c} }}_{{ {ci} {cj} }} = " + sp.latex(Γij)))
+ display(Math(fr"\Gamma^{{ {c} }}_{{ {ci} {cj} }} = " + sp.latex(Γij)))
# print(sp.latex(Γij))
diff --git a/math/gr_utils.py b/math/gr_utils.py
index 85a39d2c..5acf22af 100644
--- a/math/gr_utils.py
+++ b/math/gr_utils.py
@@ -3,9 +3,10 @@ import sympy_utils as spu
def christoffels(coords, g, invg):
- assert(len(coords) == 4)
- assert(g.shape == (4,4))
- assert(invg.shape == (4,4))
+ #assert(len(coords) == 4)
+ N = len(coords)
+ assert(g.shape == (N,N))
+ assert(invg.shape == (N,N))
N = len(coords)
gammas = [ sp.zeros(*g.shape) for i in range(N) ]
for (k,gamma_k) in enumerate(gammas):
diff --git a/math/grhd1d_characteristics.py b/math/grhd1d_characteristics.py
index 0dac1c9f..d88cffd1 100644
--- a/math/grhd1d_characteristics.py
+++ b/math/grhd1d_characteristics.py
@@ -7,9 +7,9 @@
# extension: .py
# format_name: light
# format_version: '1.5'
-# jupytext_version: 1.11.3
+# jupytext_version: 1.16.0
# kernelspec:
-# display_name: Python 3
+# display_name: Python 3 (ipykernel)
# language: python
# name: python3
# ---
diff --git a/math/spherical_accretion.py b/math/spherical_accretion.py
index 80b214bb..70b88cdb 100644
--- a/math/spherical_accretion.py
+++ b/math/spherical_accretion.py
@@ -6,7 +6,7 @@
# extension: .py
# format_name: light
# format_version: '1.5'
-# jupytext_version: 1.13.7
+# jupytext_version: 1.16.0
# kernelspec:
# display_name: Python 3 (ipykernel)
# language: python
@@ -17,12 +17,13 @@ import sympy as sp
import sympy_utils as spu
import gr_utils as gru
import rewrite_utils as rwu
+sp.init_printing()
# define parameters
-M = sp.symbols(r"M")
+M = sp.symbols(r"M", positive=True)
# define coordinates
-coords = t, r, θ, ϕ = sp.symbols(r"t, r, \theta, \phi")
+coords = t, r, θ, ϕ = sp.symbols(r"t, r, \theta, \phi", positive=True)
spu.display_math("(x^i) = ", coords)
# metric
@@ -38,12 +39,136 @@ g = sp.Matrix([[ gtt, gtr, 0, 0 ],
display(g)
spu.display_tensor2("g_{{ {}{} }} = ", g, coords, symmetric=True)
+g.det()
+
# inverse metric
invg = g.inv()
invg = sp.simplify(invg)
display(invg)
spu.display_tensor2("g^{{ {}{} }} = ", invg, coords, symmetric=True)
+
+# Christoffels
+def christoffels(coords, g, invg):
+ N = len(coords)
+ Γs = [ sp.zeros(*g.shape) for i in range(N) ]
+ for (k,Γk) in enumerate(Γs):
+ for i in range(N):
+ for j in range(N):
+ for l in range(N):
+ Γk[i,j] += sp.Rational(1,2) * invg[k,l] * (sp.diff(g[j,l],coords[i]) + sp.diff(g[i,l],coords[j]) - sp.diff(g[i,j],coords[l]))
+ Γk[i,j] = sp.simplify(Γk[i,j])
+ return Γs
+
+
+print("Computing Christoffel symbols of metric ...")
+Γs = gru.christoffels(coords, g, invg)
+for (k, Γ_k) in enumerate(Γs):
+ Γ_k = sp.expand(Γ_k)
+ str_Γ_k = rf"\Gamma^{{{{{coords[k]}}}}}"
+ spu.display_tensor2(str_Γ_k+"_{{ {} {} }} = ", Γ_k, coords, symmetric=True)
+
+# # 3+1
+
+# +
+# normal vector
+alpha = sp.sqrt(r/(r+2*M))
+betar = 2*M/r
+betar_u = 2*M/(r+2*M)
+n = sp.Matrix([-alpha, 0, 0, 0])
+n_u = sp.Matrix([1/alpha, -betar_u/alpha, 0, 0])
+beta = sp.Matrix([0, betar, 0, 0])
+beta_u = sp.Matrix([0, betar_u, 0, 0])
+beta = g * beta_u
+gamma = g[1:,1:]
+invgamma = gamma.inv()
+dgammas = [ sp.zeros(3,3) for _ in range(3) ]
+for i in range(1,3):
+ c = coords[i]
+ for j in range(3):
+ for k in range(3):
+ dgammas[i-1][j,k] = sp.simplify(sp.diff(gamma[j,k],c))
+
+
+dr_alpha = sp.simplify(sp.diff(alpha, r))
+dr_betar_u = sp.diff(betar_u, r)
+
+spu.display_math(r"\alpha = ", alpha)
+spu.display_math(r"\beta^r = ", betar_u)
+spu.display_tensor2(r"\gamma_{{ {}{} }} = ", gamma, coords[1:], symmetric=True)
+spu.display_math(r"\partial_r \alpha = ", dr_alpha)
+spu.display_math(r"\partial_r \beta^r = ", dr_betar_u)
+for (k, dgamma_k) in enumerate(dgammas):
+ dgamma_k = sp.expand(dgamma_k)
+ str_dgamma_k = rf"\partial_{{{{{coords[1+k]}}}}}\gamma"
+ spu.display_tensor2(str_dgamma_k+"_{{ {}{} }} = ", dgamma_k, coords[1:], symmetric=True)
+display(gamma.det())
+display(invgamma)
+# -
+
+display(invgamma[0,0])
+display(beta_u[1])
+display(alpha)
+
+sp.simplify(invgamma[0,0]-beta_u[1]*beta_u[1]/alpha**2)
+
+# sanity checks
+test_gtt = -alpha**2 + betar * betar_u
+sp.simplify(test_gtt - gtt)
+
+
+def delta(i,j):
+ return 1 if i == j else 0
+
+
+gamma_ud = sp.zeros(*g.shape)
+for i in range(len(coords)):
+ for j in range(len(coords)):
+ gamma_ud[i,j] = delta(i,j) + n_u[i] * n[j]
+ gamma_ud[i,j] = sp.simplify(gamma_ud[i,j])
+spu.display_tensor2(r"\gamma^{{ {} }}_{{ {} }} = ", gamma_ud, coords)
+
+gamma_ud
+
+# Extrinsic curvature
+# $$
+# K_{ij} = - \gamma_i^\mu \gamma_j^\nu \nabla_\mu n_\nu = - \gamma_i^\mu \gamma_j^\nu (\partial_\mu n_\nu - \Gamma^\lambda_{\mu\nu} n_\lambda)
+# $$
+
+# extrinsic curvature
+Dn = sp.zeros(*g.shape)
+for mu in range(len(coords)):
+ for nu in range(len(coords)):
+ tmp = sp.diff(n[nu], coords[mu])
+ #tmp = 0
+ for l in range(len(coords)):
+ tmp -= Γs[l][mu,nu] * n[l]
+ Dn[mu,nu] = sp.simplify(tmp)
+#spu.display_tensor2(r"(\nabla n)_{{ {}{} }} = ", Dn, coords)
+scoords = coords[1:]
+Kdd = sp.zeros(len(scoords),len(scoords))
+for i in range(len(scoords)):
+ for j in range(len(scoords)):
+ for mu in range(len(coords)):
+ for nu in range(len(coords)):
+ Kdd[i,j] += - gamma_ud[mu,1+i] * gamma_ud[nu,1+j] * Dn[mu,nu]
+ Kdd[i,j] = sp.simplify(Kdd[i,j])
+spu.display_tensor2("K_{{ {}{} }} = ", Kdd, scoords, symmetric=True)
+
+drKrrddd = sp.diff(Kdd[0,0],scoords[0])
+sp.simplify(drKrrddd)
+
+drKθddd = sp.diff(Kdd[1,1],scoords[0])
+sp.simplify(drKθddd)
+
+print("Computing Christoffel symbols of induced metric ...")
+scoords = coords[1:]
+hΓs = gru.christoffels(scoords, gamma, invgamma)
+for (k, hΓ_k) in enumerate(hΓs):
+ hΓ_k = sp.expand(hΓ_k)
+ str_hΓ_k_k = rf"\hat\Gamma^{{{{{scoords[k]}}}}}"
+ spu.display_tensor2(str_hΓ_k_k+"_{{ {} {} }} = ", hΓ_k, scoords, symmetric=True)
+
# ## Hydrodynamics
Ï, h, p, ϵ, Γ, K = sp.symbols(r"\rho h p \epsion \Gamma K")
@@ -77,4 +202,24 @@ u0
du0dur = u0.diff(ur).simplify()
du0dur
+# Stress-energy tensor for perfect fluid model
+# $$
+# T^{\mu\nu} = (\epsilon + p) u^\mu u^\nu + p g^{ij}
+# $$
+
+# perfect fluid model
+ϵ = sp.Function(r'\epsilon')(r)
+p = sp.Function('p')(r)
+ut_u = sp.Function('u^t')(r)
+ur_u = sp.Function('u^r')(r)
+u_u = sp.Matrix([ut_u, ur_u, 0, 0])
+T_uu = sp.zeros(*g.shape)
+N = len(coords)
+for i in range(N):
+ for j in range(N):
+ T_uu[i,j] = (ϵ + p) * u_u[i] * u_u[j] + p * invg[i,j]
+ T_uu[i,j] = sp.simplify(T_uu[i,j])
+T_uu = sp.simplify(T_uu)
+spu.display_tensor2("T^{{ {}{} }} = ", T_uu, coords, symmetric=True)
+
diff --git a/math/sympy_utils.py b/math/sympy_utils.py
index 580c81bd..2e4bb703 100644
--- a/math/sympy_utils.py
+++ b/math/sympy_utils.py
@@ -132,7 +132,7 @@ def display_nonzeros(T, coords, symmetric=False):
i = ij % N
j = int((ij - i) / N)
if symmetric and i > j: continue
- cij = (coords[i], coords[j])
+ cij = (coords[j], coords[i])
display(Math(my_doprint(cij) + ": " + my_doprint(Tij)))
@@ -146,7 +146,7 @@ def display_tensor2(fmt_tensor, T, coords, symmetric=False):
i = ij % N
j = int((ij - i) / N)
if symmetric and i > j: continue
- component = fmt_tensor.format(coords[i], coords[j])
+ component = fmt_tensor.format(coords[j], coords[i])
display(Math(component + my_doprint(Tij)))
return
diff --git a/math/tov.py b/math/tov.py
index 7ae7b445..6eecf1c3 100644
--- a/math/tov.py
+++ b/math/tov.py
@@ -7,9 +7,9 @@
# extension: .py
# format_name: light
# format_version: '1.5'
-# jupytext_version: 1.11.3
+# jupytext_version: 1.16.0
# kernelspec:
-# display_name: Python 3
+# display_name: Python 3 (ipykernel)
# language: python
# name: python3
# ---
diff --git a/src/GRHD/GRHD.jl b/src/GRHD/GRHD.jl
index f605c2a8..b8eef07b 100644
--- a/src/GRHD/GRHD.jl
+++ b/src/GRHD/GRHD.jl
@@ -3,10 +3,9 @@ module GRHD
using dg1d
-using dg1d.EquationOfState
-using dg1d.Roots
+using Roots
using LinearAlgebra
-using OrderedCollections
+using BasicInterpolators
include("types.jl")
@@ -14,8 +13,8 @@ include("equation.jl")
include("rhs.jl")
include("initialdata.jl")
include("callbacks.jl")
-include("boundaryconditions.jl")
include("setup.jl")
+include("cons2prim.jl")
#######################################################################
@@ -26,11 +25,9 @@ include("setup.jl")
dg1d.project_type(::Val{:GRHD}) = Project
# TODO Remove bdryconds
-dg1d.rhs!(env::Environment, P::Project, bdryconds) = rhs!(env, P, P.hrsc, bdryconds...)
+dg1d.rhs!(env::Environment, P::Project, bdryconds) = rhs!(env.mesh, P, P.hrsc)
-dg1d.plot(env::Environment, P::Project) = plot(env, P)
-
-dg1d.timestep!(env::Environment, P::Project) = timestep(env, P, P.hrsc)
+dg1d.timestep!(env::Environment, P::Project) = timestep(env.mesh, P, P.hrsc)
dg1d.@parameters GRHD begin
@@ -39,19 +36,22 @@ dg1d.@parameters GRHD begin
relative to the maximum of restmass density over the grid.
"""
atm_factor = 1e-10
+ @check atm_factor > 0.0
"""
Multiplicative factor to determine the cutoff restmass density below which
we impose artificial atmosphere.
"""
atm_threshold_factor = 100.0
+ @check atm_factor > 1.0
"""
Available options:
- `periodic`
- - `from_initia_data`
+ - `from_id`
"""
bc = "periodic"
+ @check bc in [ "periodic", "from_id" ]
"""
Available options:
@@ -60,11 +60,10 @@ dg1d.@parameters GRHD begin
- `atmosphere`
"""
id = "atmosphere"
+ @check id in [ "tov", "bondi_accretion", "atmosphere" ]
"""
- Path to an .h5 file containing initial data. Supported initial data types:
- - `tov`
- - `bondi_accretion`
+ Path to an .h5 file containing initial data.
"""
id_filename = ""
@@ -72,6 +71,15 @@ dg1d.@parameters GRHD begin
Restmass density for `atmosphere` initial data.
"""
id_atmosphere_density = 1e-11
+ @check id_atmosphere_density > 0.0
+
+ """
+ Choice of formulation of evolution equations. Available options:
+ - `spherical1d` ... singular at `r=0`
+ - `rescaled_spherical1d` ... regular at `r=0`
+ """
+ formulation = "spherical1d"
+ @check formulation in [ "spherical1d", "rescaled_spherical1d" ]
end
diff --git a/src/GRHD/boundaryconditions.jl b/src/GRHD/boundaryconditions.jl
deleted file mode 100644
index 1d387225..00000000
--- a/src/GRHD/boundaryconditions.jl
+++ /dev/null
@@ -1,40 +0,0 @@
-function make_BoundaryConditions(env, equation, rsolver, prms)
- @unpack bc = prms["GRHD"]
- @unpack cache = env
-
- broadcast_volume!(scaledcons2cons, equation, cache)
-
- lhs_bc, rhs_bc = if bc == "periodic"
- PeriodicBC(), PeriodicBC()
- elseif bc == "from_initial_data"
- @unpack sD, sSr, stau = get_dynamic_variables(cache)
- @unpack D, Sr, tau, A, B, r, rho, vr, eps, p = get_static_variables(cache)
- lhs_state = (sD[1], sSr[1], stau[1], p[1], rho[1], vr[1], eps[1],
- A[1], B[1], r[1])
- rhs_state = (sD[end], sSr[end], stau[end], p[end], rho[end], vr[end], eps[end],
- A[end], B[end], r[end])
- DirichletBC(lhs_state), DirichletBC(rhs_state)
- else
- error("GRHD: Boundary condition '$type' not implemented!")
- end
-
- return BoundaryConditions(lhs_bc, rhs_bc, rsolver)
-end
-
-
-function make_BoundaryConditions_LDG(env, equation, ldg_rsolver, prms)
-
- @unpack bc = prms["GRHD"]
-
- isnothing(ldg_rsolver) && return nothing
-
- lhs_bc, rhs_bc = if bc == "periodic"
- PeriodicBC(), PeriodicBC()
- elseif bc == "from_initial_data"
- OutflowBC(), OutflowBC()
- else
- error("GRHD: Boundary condition '$type' not implemented!")
- end
-
- return BoundaryConditions(lhs_bc, rhs_bc, ldg_rsolver)
-end
diff --git a/src/GRHD/callbacks.jl b/src/GRHD/callbacks.jl
index ba85cb32..6bec2fcc 100644
--- a/src/GRHD/callbacks.jl
+++ b/src/GRHD/callbacks.jl
@@ -1,11 +1,11 @@
-function make_callback(env, P::Project, bdryconds::BoundaryConditions)
- cbfn_equation(u, t) = callback_equation(u, t, env, P, isperiodic(bdryconds), P.equation)
+function make_callback(env, P::Project, isperiodic::Bool)
+ cbfn_equation(u, t) = callback_equation(u, t, env, P, isperiodic, P.equation)
cb_equation = FunctionCallback(cbfn_equation,
CallbackTiming(every_iteration=1,every_dt=0))
- cbfn_tci(u, t) = callback_tci(u, t, env, P, isperiodic(bdryconds), P.tci)
+ cbfn_tci(u, t) = callback_tci(u, t, env, P, isperiodic, P.tci)
cb_tci = FunctionCallback(cbfn_tci,
CallbackTiming(every_iteration=1, every_dt=0))
- cbfn_hrsc(u, t) = callback_hrsc(u, t, env, P, isperiodic(bdryconds), P.hrsc)
+ cbfn_hrsc(u, t) = callback_hrsc(u, t, env, P, isperiodic, P.hrsc)
cb_hrsc = FunctionCallback(cbfn_hrsc,
CallbackTiming(every_iteration=1,every_dt=0))
callbackset = CallbackSet(cb_equation, cb_tci, cb_hrsc)
@@ -43,20 +43,24 @@ end
function callback_hrsc(state_u, state_t, env, P, isperiodic, hrsc::HRSC.AbstractArtificialViscosity)
- @unpack cache, mesh = env
- @unpack equation = P
- @unpack max_v = get_static_variables(cache)
- @unpack mu, cellmax_v = get_cell_variables(cache)
- @unpack sD = get_dynamic_variables(cache)
- broadcast_volume!(speed, equation, cache)
- Npts, K = layout(mesh)
- mat_cellmax_v = reshape(view(max_v, :), (Npts, K))
- for k = 1:K
- cellmax_v[k] = maximum(view(mat_cellmax_v, :, k))
+ @unpack cache, mesh = env
+ @unpack equation = P
+ @unpack max_v = get_static_variables(cache)
+ @unpack mu, cellmax_v = get_cell_variables(cache)
+ @unpack D = get_dynamic_variables(cache)
+
+ # prevent AV recomputation when callbacks are forced on initial data
+ # need this for shock tube tests so that we have non-zero viscosity in troublesome places
+ # although we start with smoothed initial data
+ t[1] <= tm1[1] && return
+
+ for (k,vi) in enumerate(eachcell(mesh, max_v))
+ cellmax_v[k] = maximum(vi)
end
+
HRSC.compute_viscosity!(
mu,
- sD, cellmax_v,
+ D, cellmax_v,
hrsc)
end
@@ -71,21 +75,9 @@ end
function callback_hrsc(state_u, state_t, env, P, isperiodic, hrsc::HRSC.SmoothedArtificialViscosity)
callback_hrsc(state_u, state_t, env, P, isperiodic, hrsc.av)
@unpack cache, mesh = env
- @unpack mu = get_cell_variables(cache)
- indices = findall(muk -> muk > 0.0, mu)
- tmp = zeros(size(mu))
- _, K = layout(mesh)
- # artificially broaden viscosity
- for k in indices
- k_lhs, k_rhs = periodic_index(k-1, K), periodic_index(k+1, K)
- muk = mu[k]
- tmp[k_lhs] = max(muk, tmp[k_lhs])
- tmp[k] = max(muk, tmp[k])
- tmp[k_rhs] = max(muk, tmp[k_rhs])
- end
- @. mu = tmp
@unpack smoothed_mu = get_static_variables(cache)
- smoothed_mu .= vec(hrsc.smoother(mu, isperiodic))
+ @unpack mu = get_cell_variables(cache)
+ hsrc.smoother(smoothed_mu, mu, mesh, false)
end
@@ -135,6 +127,8 @@ function callback_tci(state_u, state_t, env, P, isperiodic,
tci::Union{TCI.Diffusion, TCI.Minmod, TCI.Threshold,
TCI.ModalDecayAverage, TCI.ModalDecayHighest})
+ TODO()
+
@unpack cache, mesh = env
@unpack sD, sSr, stau = get_dynamic_variables(cache)
@unpack flag, sD_flag, sSr_flag, stau_flag = get_cell_variables(cache)
diff --git a/src/GRHD/cons2prim.jl b/src/GRHD/cons2prim.jl
new file mode 100644
index 00000000..4d8e7d85
--- /dev/null
+++ b/src/GRHD/cons2prim.jl
@@ -0,0 +1,320 @@
+#######################################################################
+# Conservative fixing #
+#######################################################################
+
+
+@with_signature function conservative_fixing(equation::AbstractEquation)
+ @accepts D, S, Ï„, r
+
+ TODO()
+
+ @unpack atm_density, atm_threshold, eos = equation
+ # atm_density = equation.atmosphere.Ï
+ # atm_threshold = equation.atmosphere.threshold
+ Ïmin = atm_density * atm_threshold
+
+ # B = 1.0 # in special relativity
+
+ #####
+ # conservative variable fixing following Deppe et al. arXiv:2109.12033
+ ######
+
+ fixed = false
+
+ if D < Ïmin || Ï„ < 0.0
+ D = Ïmin
+ Ï„ = 1e-12
+ fixed = true
+ end
+
+ # if D < 0.001 * Ïmin
+ # # @warn "fixing D $D @ r = $r"
+ # D = Ïmin
+ # fixed = true
+ # end
+ #
+ # if Ï„ < 0.0
+ # # @warn "fixing Ï„ $Ï„ @ r = $r"
+ # Ï„ = 1e-12
+ # fixed = true
+ # end
+ # fix Ï„ such that v < 0.999
+ # if Ï„ < 0.0
+ # @warn "fixing Ï„ $Ï„ @ r = $r"
+ # # What = 1 + Ï„ / D = 1 / sqrt(1 - v^2)
+ # v2 = 0.999
+ # Ï„ = max(D * (1.0 / sqrt(1.0 - v2) - 1), 1e-12)
+ # display(Ï„)
+ # fixed = true
+ # end
+
+ # (48)-(50) in arXiv:2109.12033 we put B=0, ̂μ = 0
+ # solution to (52) is then
+ What = 1.0 + Ï„ / D
+
+ S2 = S^2
+ D2 = D^2
+ ϵs = 1e-12
+ factor = sqrt( (1.0-ϵs) * (What^2-1.0) * D2 / (S2 + D2 * 1e-16) )
+ # @show factor, What
+ if factor < 1.0 && What > 1.0
+ # @warn "fixing ..."
+ Sold = S
+ S = 0.99 * sign(S) * sqrt( (1.0-ϵs) * (What^2-1.0) * D2 - D2 * 1e-16 )
+ # @warn "S = $Sold => $S @ r = $r"
+ S2 = S^2
+ factor = max(1.0, sqrt( (1.0-ϵs) * (What^2-1.0) * D2 / (S2 + D2 * 1e-16) ))
+ # @show factor
+ @assert factor >= 1.0
+ fixed = true
+ end
+
+ # h0 = 1e-3
+ # S2 = S^2 / B^2
+ # r2 = S2 / D^2
+ # z02 = r2 / h0^2
+ # v02 = z02 / (1.0 + z02)
+ # max_v2 = 0.999
+ # if v02 > max_v2
+ # S = sign(S) * sqrt(max_v2/(1-max_v2) * h0^2 * D^2)
+ # end
+
+ flag_consfixed = Float64(fixed)
+
+ @returns D, S, Ï„, flag_consfixed
+end
+
+
+#######################################################################
+# cons2prim a la Kastaun et al 2021 #
+#######################################################################
+
+
+@with_signature [simd=false] function cons2prim(equation::AbstractEquation)
+ @accepts D, Sr, Ï„, r
+ @accepts γrr
+ D, Sr, Ï„, Ï, vr, ϵ, p = cons2prim_kastaun_impl(equation, D, Sr, Ï„, r, γrr)
+ @returns D, Sr, Ï„, Ï, vr, ϵ, p
+end
+@with_signature [simd=false] function cons2prim_rescaled_spherical1d(equation::AbstractEquation)
+ @accepts D, Sr, Ï„, r
+ @accepts B
+ γrr = 1/B^2
+ D, Sr, Ï„, Ï, vr, ϵ, p = cons2prim_kastaun_impl(equation, D, Sr, Ï„, r, γrr)
+ # in case something was adjusted by cons2prim
+ rD = r*B^3*D
+ rSr = r*B^3*Sr
+ rτ = r*B^3*τ
+ @returns D, Sr, Ï„, rD, rSr, rÏ„, Ï, vr, ϵ, p
+end
+
+
+@inline function cons2prim_kastaun_impl(equation, D, Sr, τ, r, γrr)
+
+ rcoord = r
+
+ @unpack atm_density, atm_threshold, eos = equation
+ Ïmin = atm_density * atm_threshold
+ @unpack K, Gamma = eos
+ pmin = K * Ïmin^Gamma
+ ϵmin = pmin / ((Gamma-1)*Ïmin)
+ Ïmax = Inf
+ Ïatm = atm_density
+ h0 = 1e-3
+
+ #### cons2prim from Kastaun et al. arXiv:2005.01821
+
+ γuurr = 1/γrr
+ q = Ï„ / D # (22)-(23)
+ rr = Sr / D # (22)-(23), Si := S_i is 3-vector
+ r2 = γuurr*rr*rr
+ r = sqrt(r2)
+ z0 = r/h0
+ v0 = z0 / sqrt(1.0 + z0^2)
+ h02 = h0^2
+
+ if v0 > 1
+ error((v0,z0,Sr,D))
+ end
+
+ # What is not a question but rather W^hat, cf. (40)
+ fn_What = let r = r, v0 = v0
+ mu -> begin
+ vhat = min(mu * r, v0)
+ return 1.0 / sqrt(1.0 - vhat^2)
+ end
+ end
+
+ # setup bracket
+ mu_a = 0.0
+ # with no EM fields we can find the root of (49) analytically, because r = const.
+ mu_plus = 1.0 / sqrt(h02 + r2)
+ mu_b = r < h0 ? 1.0 / h0 : mu_plus
+
+ What_a = fn_What(mu_a)
+ What_b = fn_What(mu_b)
+ if D / What_b > Ïmax
+ error("Invalid state encountered!")
+ end
+
+ if D < Ïmin
+
+ @assert eos isa EquationOfState.Polytrope
+ @unpack K, Gamma = eos
+
+ # employ atmosphere values by taking the zero temperature limit
+ # for an ideal gas eos, we have that eos.Gamma becomes the Gamma for
+ # a polytrope, see grhd notes for derivation
+
+ Ï = Ïatm
+ vr = 0.0
+ W = 1.0
+ p = K * Ï^Gamma
+ ϵ = p / ((Gamma-1)*Ï)
+ h = 1 + ϵ + p/Ï
+ D = W*Ï
+ Sr = W^2*Ï*h*vr
+ Ï„ = W^2*Ï*h - p - D
+
+ else
+
+ # root bracket adjustment, cf. Appendix
+ if D / What_b < Ïmax < D
+ # infamous closure bug ...
+ # https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-captured
+ fn_Ïmax = let D = D, Ïmax = Ïmax
+ mu -> D / fn_What(mu) - Ïmax
+ end
+ mu_b = find_zero(fn_Ïmax, (mu_a, mu_plus), Roots.A42())
+ if isnan(mu_b)
+ error("Failed to correct upper interval bound")
+ end
+ end
+
+ if D / What_b < Ïmin < D # yes, we need What_b here
+ # infamous closure bug ...
+ # https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-captured
+ fn_Ïmin = let D = D, Ïmin = Ïmin
+ mu -> D / fn_What(mu) - Ïmin
+ end
+ mu_a = find_zero(fn_Ïmin, (mu_a, mu_b), Roots.A42())
+ if isnan(mu_b)
+ error("Failed to correct lower interval bound")
+ end
+ end
+
+ # infamous closure bug ...
+ # https://docs.julialang.org/en/v1/manual/performance-tips/#man-performance-captured
+ master_fn = let D = D, v0 = v0, r = r, q = q, r2 = r2
+ mu -> begin # eq (44)
+
+ _vhat = min(mu * r, v0)
+ _What = 1.0 / sqrt(1.0 - _vhat^2)
+ Ïhat = D / _What
+
+ # eq (42)
+ ϵhat = _What * (q - mu * r2) + _vhat^2 * _What^2 / (1.0 + _What)
+
+ # TODO enforce EOS bounds - needed?
+
+ # compute thermodynamic vars
+ phat = eos(Pressure, Density, Ïhat, InternalEnergy, ϵhat)
+ # hhat = eos(Enthalpy, Density, Ïhat, InternalEnergy, ϵhat)
+ ahat = phat / (Ïhat * (1.0 + ϵhat))
+
+ # eq (46)-(48)
+ nu_A = (1.0 + ahat) * (1.0 + ϵhat) / _What
+ nu_B = (1.0 + ahat) * (1.0 + q - mu * r2)
+ nu = max(nu_A, nu_B)
+
+ # eq (44)
+ f = mu - 1.0 / (nu + r2 * mu)
+ return f
+ end
+ end
+
+ # verify if there is a solution inside bracket
+ mf_a = master_fn(mu_a)
+ mf_b = master_fn(mu_b)
+ mf_ab = mf_a*mf_b
+ mu = find_zero(master_fn, (mu_a, mu_b), Roots.A42() #= =^= algorithm 748 =#)
+ if isnan(mu)
+ error("Failed to find root")
+ end
+
+ #### evaluate primitives
+
+ # eq (36) [Kastaun] : h*W = 1/mu
+ # eq (15) [Kastaun] : Ï*W = D
+ # ÏhW2 = D / mu
+
+ # regularize velocity according to Dumbser et al arxiv:2307.06629
+ # eqs (82)-(84)
+ # y, y0 = ÏhW2, 1e-4
+ # if y > y0
+ # v = S / mu
+ # compute v accoriding to eq (68) or (40) [Kasτn]
+ # vr = sign(Sr) * min(mu * r, v0)
+ # vr = sign(Sr) * min(abs(mu * rr), abs(v0))
+ # else
+ # # @warn "limiting v"
+ # # limit velocity ratio v/S
+ # fy = 2.0 * (y/y0)^3 - 3.0 * (y/y0)^2 + 1.0
+ # v = Si * y / (y^2 + fy * 5e-9)
+ # end
+
+ v = sqrt(mu^2 * γuurr*rr*rr)
+ v = min(v, v0)
+ v2 = v^2
+ vr = sign(Sr) * sqrt(v2/γuurr)
+
+ # eq (68) or (40)
+ W = 1.0 / sqrt(1.0 - v2)
+ # eq (41)
+ Ï = D / W
+ # eq (42)
+ ϵ = W * (q - mu * r2) + v2 * W^2 / (1.0 + W)
+ # eq (38)
+ # ϵ2 = W * (q - mu * r2) + W - 1
+
+ # enforce EOS bounds
+
+ if Ï < Ïmin
+ # atmosphere II
+
+ @assert eos isa EquationOfState.Polytrope
+ @unpack K, Gamma = eos
+
+ # employ atmosphere values by taking the zero temperature limit
+ # for an ideal gas eos, we have that eos.Gamma becomes the Gamma for
+ # a polytrope, see grhd notes for derivation
+
+ Ï = Ïatm
+ vr = 0.0
+ W = 1.0
+ p = K * Ï^Gamma
+ ϵ = p / ((Gamma-1)*Ï)
+ h = 1 + ϵ + p/Ï
+ D = W*Ï
+ Sr = W^2*Ï*h*vr
+ Ï„ = W^2*Ï*h - p - D
+
+ elseif ϵ < ϵmin
+ # error()
+ # adjusting Ï„ such that energy density is within bounds
+ # cf. 3rd paragraph in sec. III.A in Kastaun paper
+ ϵ = ϵmin
+ # invert this for τ: ϵ = W * (q - mu * r2) + v^2 * W^2 / (1.0 + W), q = τ / D
+ τ = (ϵ / W - v2 * W / (1.0 + W) + mu * r2) * D
+ end
+
+ # compute thermodynamic vars
+ p = eos(Pressure, Density, Ï, InternalEnergy, ϵ)
+ if p < 0
+ error((Ï,ϵ))
+ end
+
+ end
+
+ return D, Sr, Ï„, Ï, vr, ϵ, p
+end
diff --git a/src/GRHD/cons2prim_implementations.jl b/src/GRHD/cons2prim_implementations.jl
deleted file mode 100644
index 32c930cb..00000000
--- a/src/GRHD/cons2prim_implementations.jl
+++ /dev/null
@@ -1,319 +0,0 @@
-@with_signature function cons2prim(equation::Equation{<:HotEquationOfState})
- @accepts D, Sr, tau, p, r, B
- # S2 = (Sr/B)^2
- # @unpack eos, cons2prim_newtonsolver, cons2prim_bisection = equation
- # p, converged = find_pressure_insane(D, S2, tau, p, r, eos,
- # cons2prim_newtonsolver, cons2prim_bisection)
- # if !converged && eltype(equation) == HybridEoS
- # rho, success = find_density_insane(D, S2, p, r, equation, eos,
- # cons2prim_newtonsolver, cons2prim_bisection)
- # if !success
- # error()
- # end
- # p = eos(Pressure, Density, rho)
- # vr = Formulae.vr(B, D, Sr, tau, p)
- # eps = Formulae.ϵ(B, D, Sr, tau, p)
- # else
- # rho = Formulae.Ï(B, D, Sr, tau, p)
- # vr = Formulae.vr(B, D, Sr, tau, p)
- # eps = Formulae.ϵ(B, D, Sr, tau, p)
- # end
-
- D, Sr, tau = conservative_fixing(D, Sr, tau, B, equation)
- rho, vr, eps, p = cons2prim_kastaun((D, Sr, tau, p, r, B), equation)
- # rho, vr, eps, p, D, Sr, tau = atmosphering(rho, vr, eps, p, D, Sr, tau)
- @returns rho, vr, eps, p, D, Sr, tau
-end
-
-
-@with_signature function cons2prim(equation::Equation{<:ColdEquationOfState})
- @accepts D, Sr, tau, p, r, B
- S2 = (Sr/B)^2
- rho, success = find_density_insane(D, S2, p, equation)
- @unpack eos = equation
- p = eos(Pressure, Density, rho)
- vr = Formulae.vr(B, D, Sr, tau, p)
- eps = Formulae.ϵ(B, D, Sr, tau, p)
- @returns rho, vr, eps, p
-end
-
-
-#######################################################################
-# Insane version - bail out if anything is wrong #
-#######################################################################
-
-
-function find_pressure_insane(D, S2, tau, p, r, eos::HotEquationOfState,
- cons2prim_newtonsolver, cons2prim_bisection)
-
- # upper limit on particle velocity
- # omv2 = 1e-3 # = 1 - v^2
-
- # pmin1 = - (tau + D) + sqrt(S2 + omv2) # √((τ + D + p)^2 - S^2) >= √(1 - vmax^2)
- pmin1 = - (tau + D) + sqrt(S2) + 1e-10 # √((τ + D + p)^2 - S^2) >= √(1 - vmax^2)
- pmin2 = 1e-10 # physical constraint
- pmin = max(pmin1, pmin2)
-
- floor_pressure(pnew) = max(pnew, pmin)
- # p0 = 0.5 * (eos.gamma - 1) * (tau + D)
- p0 = p
-
- f = pp -> pressure_equation_insane(D, S2, tau, pp, r, eos)
- p, err, converged, tol = find_root(f, p0, cons2prim_newtonsolver, sanitize=floor_pressure)
- if !converged
- # reset to guess
- p = p0
- end
- p = max(pmin, p0)
-
- return p, converged
-end
-
-
-function pressure_equation_insane(D, S2, tau, p, r, eos)
-
- a = tau + p + D
- a2mS2 = a^2 - S2
- if a2mS2 < 0
- return NaN
- end
- W = a / sqrt(a2mS2)
- rho = D / W
- # if rho < 0 #1e-15
- # # return NaN
- # # rho = 1e-10
- # end
- eps_rho = (a - W^2 * p) / W^2 - rho
- if eps_rho < 0
- # in low temperature limit we should switch to one parameter EoS
- return NaN
- end
- eps = eps_rho / rho
- eos_p = eos(Pressure, Density, rho, InternalEnergy, eps) + 1e-10
- f = eos_p - p
- return f
-end
-
-
-function find_density_insane(D, S2, rho, eos,
- cons2prim_newtonsolver, cons2prim_bisection)
-
- rhomin = 1e-10
- rho_init = rho
-
- floor_density(rhonew) = max(rhonew, rhomin)
- g = rho -> density_equation(D, S2, rho, eos)
- rho, err, converged, tol = find_root(g, rho_init, cons2prim_newtonsolver,
- sanitize=floor_density)
- if !converged
- # try bisection
- # Figure out brackets for a bisection method.
- # if bisection failed reset
- rho = rho_init
- end
-
- success = converged
-
- return rho, success
-end
-
-
-function density_equation(D, S2, rho, eos)
- D2 = D^2
- h = eos(Enthalpy, Density, rho)
- W = sqrt(1 + S2 / (D2 * h^2))
- chi = eos(Derivative{Pressure,Density}, Density, rho)
- g = W * rho - D
- # assuming zero temperature limit: deps/drho = P / rho^2
- dg = W - S2 * chi / (W * D2 * h^3)
- return g, dg
-end
-
-
-#######################################################################
-# cons2prim a la Kastaun et al 2021 #
-#######################################################################
-
-
-@with_signature function cons2prim_kastaun(equation::AbstractEquation)
- @accepts D, Sr, tau, p, r, B
-
- @unpack eos, atm_density, atm_threshold = equation
- rhomin, rhomax = atm_density * atm_threshold, Inf
- fn_epsmin, fn_epsmax = rho -> -(1-1e-10), rho -> Inf
- h0 = 1e-3
- rhoatm = atm_density
-
- q = tau / D
- S2 = (Sr/B)^2
- s = sqrt(S2) / D # =^= r in paper, r already denotes radius here
- z0 = s / h0
- v0 = z0 / sqrt(1 + z0^2)
- h02 = h0^2
- s2 = s^2
-
- # What is not a question but rather W^hat, cf. (40)
- function fn_What(mu)
- _vhat = min(mu * s, v0)
- if _vhat < 0
- error()
- println((; q, _vhat, s, mu, v0))
- end
- return 1 / sqrt(1 - _vhat^2)
- end
-
- # setup bracket
- mu_a = 0.0
- # with no EM fields we can find the root of (49) analytically, because s = const.
- mu_plus = 1 / sqrt(h02 + s2)
- mu_b = r < h0 ? 1 / h0 : mu_plus
-
- What_b = fn_What(mu_b)
- if D / What_b > rhomax
- error("Invalid state encountered at @ r = $(r)!")
- end
- if D < rhomin
- # @info "Invalid state encountered at @ r = $(r)!"
- # @info "Atmosphering ..."
- # println((; D, rhomax, rhomin))
- rho = rhoatm
- eps = eos.cold_eos(InternalEnergy, Density, rho)
- vr = 0.0
- p = eos.cold_eos(Pressure, Density, rho)
- # p = eos(Pressure, Density, rho, InternalEnergy, eps)
- else
-
- # do we have to adjust the bracket?
- debug = false
- # if D / What_b < rhomax < D
- if rhomax < D
- pblm_rhomax = Roots.ZeroProblem(mu -> D / fn_What(mu) - rhomax, (mu_a, mu_b))
- mu_b = Roots.solve(pblm_rhomax, Roots.A42())
- if isnan(mu_b)
- error("Failed to correct upper interval bound")
- end
- debug = true
- end
- # if D / What_b < rhomin < D
- if D / What_b < rhomin
- mu_rng = collect(LinRange(mu_a, mu_b, 1000))
- fn = @. D / fn_What(mu_rng) - rhomin
- data = hcat(mu_rng, fn)
- # display(data)
- # display(D / What_b)
- # display(D)
- # display(rhomin)
- pblm_rhomin = Roots.ZeroProblem(mu -> D / fn_What(mu) - rhomin, (mu_a, mu_b))
- mu_b = Roots.solve(pblm_rhomin, Roots.A42())
- if isnan(mu_b)
- error("Failed to correct lower interval bound")
- end
- println("New interval: ($mu_a, $mu_b) @ r = $r")
- debug = false
- end
-
- function master_fn(mu)
- vhat = min(mu * s, v0)
- What = 1 / sqrt(1 - vhat^2)
- rhohat = D / What
- eps_plus_one_over_What = What * (q - mu * s2)
- epshat = eps_plus_one_over_What + vhat^2 * What^2 / (1 + What)
- # enforce EOS bounds
- _epsmin, _epsmax = fn_epsmin(rhohat), fn_epsmax(rhohat)
- if rhohat < rhomin || epshat < _epsmin
- # TODO Should we reset What here?
- rhohat, epshat = rhomin, _epsmin
- elseif rhohat > rhomax || epshat > _epsmax
- rhohat, epshat = rhomax, _epsmax
- end
- # compute thermodynamic vars
- phat = eos(Pressure, Density, rhohat, InternalEnergy, epshat)
- ahat = phat / (rhohat * (1 + epshat))
- hhat = eos(Enthalpy, Density, rhohat, InternalEnergy, epshat)
- # compute master function
- # extracted from (35), see hint in paragraph after (46)-(48)
- nu_A = (1 + ahat) * eps_plus_one_over_What
- nu_B = (1 + ahat) * (1 + q - mu * s2)
- nu = max(nu_A, nu_B)
- f = mu - 1 / (nu + s2 * mu)
- return f
- end
-
- if debug
- mu_rng = collect(LinRange(mu_a, mu_b, 1000))
- fn = @. master_fn(mu_rng)
- data = hcat(mu_rng, fn)
- display(data)
- end
-
- mf_a = master_fn(mu_a)
- mf_b = master_fn(mu_b)
- if mf_a * mf_b >= 0
- println((; D, Sr, tau, p, r, B, mf_a, mf_b, mu_a, mu_b))
- error("Master function is ill conditioned, @ r = $(r)!")
- end
- pblm = Roots.ZeroProblem(master_fn, (mu_a, mu_b))
- mu = Roots.solve(pblm, Roots.A42() #= =^= algorithm 748 =#)
- if isnan(mu)
- error("failed to find root")
- end
-
- # evaluate primitives
- v = min(mu * s, v0)
- W = 1 / sqrt(1 - v^2)
- rho = D / W
- eps_plus_one_over_W = W * (q - mu * s2)
- eps = eps_plus_one_over_W + v^2 * W^2 / (1 + W)
- # enforce EOS bounds
- epsmin, epsmax = fn_epsmin(rho), fn_epsmax(rho)
- if rho < rhomin || eps < epsmin
- rho, eps = rhomin, epsmin
- elseif rho > rhomax || eps > epsmax
- rho, eps = rhomax, epsmax
- end
- # compute thermodynamic vars
- p = eos(Pressure, Density, rho, InternalEnergy, eps)
-
- vr = Sr*mu/D
-
- end
-
- @returns rho, vr, eps, p
-end
-
-
-#######################################################################
-# Conservative variable fixing #
-#######################################################################
-
-
-function conservative_fixing(D, Sr, tau, B, equation)
-
- @unpack eos, atm_density, atm_threshold = equation
- rhomin = atm_density * atm_threshold
- rhoatm = atm_density
-
- if D < rhomin
- D = rhoatm
- end
-
- if tau < 0
- tau = 1e-12
- end
-
- # (48)-(50) in Deppe paper where we put B=0
- # that = tau / D
- # muhat = 0
- # Solution to (52) when B=0
- What = 1 + tau / D
-
- # in spherical symmetry: S^2 = S_r^2 / B^2
- # Hence, Smax^2/S^2 = Srmax^2 / Sr^2
- S2 = Sr^2 / B^2
- factor = sqrt( (1-1e-12) * (What^2-1) * D^2 / (S2 + D^2 * 1e-16) )
- if factor > 1
- Sr /= factor * (1 + 1e-8)
- end
-
- return D, Sr, tau
-end
diff --git a/src/GRHD/equation.jl b/src/GRHD/equation.jl
index a5081108..ccdd108e 100644
--- a/src/GRHD/equation.jl
+++ b/src/GRHD/equation.jl
@@ -1,240 +1,472 @@
-### TODO Move include to GRHD.jl or merge with this file?
-include("cons2prim_implementations.jl")
+function make_Equation(eos, prms, m::Mesh)
+ @unpack atm_factor, atm_threshold_factor = prms
+ if m isa Mesh1d
+ return Equation(eos, -1.0, atm_factor, atm_threshold_factor)
+ elseif m isa Mesh2d
+ TODO()
+ else
+ error("unknown mesh type encountered")
+ end
+end
-module Formulae
- ### Auxilary functions
+#######################################################################
+# "spherical1d" #
+# Spherical symmetry (1d) + spherical coordinates #
+#######################################################################
- # Lorentz factor
- Wprim(B, Ï, vr, ϵ, p) = 1.0 / sqrt(1.0 - B^2 * vr^2)
- Wcons(B, D, Sr, Ï„, p) = (Ï„ + p + D) / sqrt((Ï„ + p + D)^2 - (Sr / B)^2)
- ### Primitive variables
- # in terms of conservative ones
+@with_signature function flux_source_spherical1d(eq::Equation)
+ @accepts D, Sr, Ï„, ϵ, Ï, p, vr
+ @accepts α, ∂αr, βru, ∂βrrdu,
+ γrr, γθθ, γϕϕ, ∂γrrr, ∂γrθθ, ∂γrϕϕ, ∂γθϕϕ,
+ Γrrr, Γrθθ, Γrϕϕ, Γθrθ, Γθϕϕ, Γϕθϕ, Γϕrϕ,
+ Krr, Kθθ, Kϕϕ
+ @accepts flr_D, flr_Sr, flr_Ï„
+
+ γuurr = 1/γrr
+ γuuθθ = 1/γθθ
+ γuuϕϕ = 1/γϕϕ
+ Γkrk = Γrrr + Γθrθ + Γϕrϕ
+
+ gtt = -α^2 + γrr*βru*βru
+ gtr = γrr*βru
+ grr = γrr
+ guutt = -1/α^2
+ guutr = βru/α^2
+ guurr = γuurr - βru*βru/α^2
+ guuθθ = γuuθθ
+ guuϕϕ = γuuϕϕ
+
+ vru = γuurr*vr
+ v2 = vru*vr
+ W = 1/sqrt(1-v2)
+ ut = W/α
+ ur = W*(vru - βru/α)
+
+ h = 1 + ϵ + p/Ï
+ Tuutt = Ï*h*ut*ut + p*guutt
+ Tuutr = Ï*h*ut*ur + p*guutr
+ Tuurr = Ï*h*ur*ur + p*guurr
+ Tuuθθ = p*guuθθ
+ Tuuϕϕ = p*guuϕϕ
+ Tudtr = Tuutt*gtr + Tuutr*grr
+
+ flr_D = α*D*(vru - βru/α)
+ flr_Sr = α*( Sr*(vru - βru/α) + p )
+ flr_τ = α*( τ*(vru - βru/α) + p*vru )
+
+ src_D = - flr_D*Γkrk
+
+ # tmp1 = 1/2*(Tuutt*βru*βru + 2*Tuutr*βru + Tuurr) * (∂γrrr - 2*Γrrr*γrr)
+ tmp1 = 0 # because Dj γik = 0 (Levi-Civita connection)
+ tmp2 = Tudtr*(∂βrrdu + Γrrr*βru)
+ tmp3 = -Tuutt*α*∂αr
+ flθ_Sθ = α*p
+ flϕ_Sϕ = α*p
+ src_Sr = α*(tmp1 + tmp2 + tmp3) - flr_Sr*Γkrk + flr_Sr*Γrrr + flθ_Sθ*Γθrθ + flϕ_Sϕ*Γϕrϕ
+
+ src_τ = Tuutt*(βru*βru*Krr - βru*∂αr) + Tuutr*(2*βru*Krr - ∂αr) + Tuurr*Krr + Tuuθθ*Kθθ + Tuuϕϕ*Kϕϕ
+ src_τ *= α
+ src_τ += - flr_τ*Γkrk
+
+ @returns src_D, src_Sr, src_Ï„, flr_D, flr_Sr, flr_Ï„
+end
- Ï(B, D, Sr, Ï„, p) = D / Wcons(B, D, Sr, Ï„, p)
- vr(B, D, Sr, Ï„, p) = Sr / (B^2 * (Ï„ + D + p))
- ϵ(B, D, Sr, τ, p) = (sqrt((τ + p + D)^2 - (Sr/B)^2) - Wcons(B, D, Sr, τ, p) * p) / D - 1
- ### Conservative variables
- # in terms of primitive variables
+@with_signature function maxspeed(equation::Equation)
+ @accepts vr, Ï, ϵ
+ @accepts α, βru, γrr
+ @unpack eos = equation
+ cs2 = eos(SquareSpeedOfSound, Density, Ï, InternalEnergy, ϵ)
+ cs = sqrt(abs(cs2))
+ γuurr = 1/γrr
+ vru = γuurr * vr
+ v2 = vru*vr
+ λ0 = α*vru - βru
+ W = 1/sqrt(1-v2)
+ λp = α/(1-v2)*(vru*(1-cs2)+cs/W*sqrt((1-v2*cs2)*γuurr-vru^2*(1-cs2)))
+ λm = α/(1-v2)*(vru*(1-cs2)-cs/W*sqrt((1-v2*cs2)*γuurr-vru^2*(1-cs2)))
+ max_v = absmax(λm, λ0, λp)
+ @returns max_v
+end
- D(B, Ï, vr, ϵ, p) = Ï * Wprim(B, Ï, vr, ϵ, p)
- Sr(B, Ï, vr, ϵ, p) = Ï * (1 + ϵ + p / Ï) * Wprim(B, Ï, vr, ϵ, p)^2 * B^2 * vr
- Ï„(B, Ï, vr, ϵ, p) = Ï * (1 + ϵ + p / Ï) * Wprim(B, Ï, vr, ϵ, p)^2 - p - Ï * Wprim(B, Ï, vr, ϵ, p)
- ### Fluxes
- # in terms of primitive variables
+@with_signature function llf(equation::Equation)
+ @accepts D, flr_D, Sr, flr_Sr, Ï„, flr_Ï„, max_v, p
+ @accepts α, βru, γrr
+ @accepts [bdry] bdry_D, bdry_Sr, bdry_Ï„, bdry_max_v, bdry_Ï, bdry_vr, bdry_ϵ, bdry_p
+ @accepts [bdry] nx
- fD(B, Ï, vr, ϵ, p) = D(B, Ï, vr, ϵ, p) * vr
- fSr(B, Ï, vr, ϵ, p) = Sr(B, Ï, vr, ϵ, p) * vr + p
- fÏ„(B, Ï, vr, ϵ, p) = (Ï„(B, Ï, vr, ϵ, p) + p) * vr
+ vmax = absmax(max_v, bdry_max_v)
+ γuurr = 1/γrr
+ bdry_vru = γuurr * bdry_vr
- #### Sources
+ bdry_flr_D = α * bdry_D * (bdry_vru - βru/α)
+ bdry_flr_Sr = α * ( bdry_Sr * (bdry_vru - βru/α) + bdry_p )
+ bdry_flr_τ = α * ( bdry_τ * (bdry_vru - βru/α) + bdry_p * bdry_vru )
- function sD(r, A, A_r, B, B_r, Ï, vr, ϵ, p)
- val = - A * B^3 * D(B, Ï, vr, ϵ, p) * vr
- return val
- end
+ nflr = nx*flr_D
+ bdry_nflr = nx*bdry_flr_D
+ nflr_D = LLF(nflr, bdry_nflr, D, bdry_D, vmax)
- function sSr(r, A, A_r, B, B_r, Ï, vr, ϵ, p)
- h = 1 + ϵ + p / Ï
- Sr = Formulae.Sr(B, Ï, vr, ϵ, p)
- W = Wprim(B, Ï, vr, ϵ, p)
- v2 = B^2 * vr^2
- ÏhW2 = Ï * h * W^2
- val = - (ÏhW2 - p) * r * B^3 * A_r
- val += A * B^4 * (r * B_r + B / 3) * (ÏhW2 * vr^2 + 3 * p / B^2)
- val += - 4 / 3 * A * B^3 * Sr * vr
- return val
- end
+ nflr = nx*flr_Sr
+ bdry_nflr = nx*bdry_flr_Sr
+ nflr_Sr = LLF(nflr, bdry_nflr, Sr, bdry_Sr, vmax)
- function sÏ„(r, A, A_r, B, B_r, Ï, vr, ϵ, p)
- Ï„ = Formulae.Ï„(B, Ï, vr, ϵ, p)
- h = 1 + ϵ + p / Ï
- W = Wprim(B, Ï, vr, ϵ, p)
- ÏhW2 = Ï * h * W^2
- val = - r * B^3 * ÏhW2 * vr * A_r - A * B^3 * (Ï„ + p) * vr
- return val
- end
+ nflr = nx*flr_Ï„
+ bdry_nflr = nx*bdry_flr_Ï„
+ nflr_Ï„ = LLF(nflr, bdry_nflr, Ï„, bdry_Ï„, vmax)
+
+ @returns [bdry] nflr_D, nflr_Sr, nflr_Ï„
end
-@with_signature function flux(equation::Equation)
- @accepts State(sD, sSr, stau), p, rho, vr, eps, A, B, r
- rAB3 = r * A * B^3
- flx_sD, flx_sSr, flx_stau = 0, 0, 0
- try
- flx_sD = rAB3 * Formulae.fD(B, rho, vr, eps, p)
- flx_sSr = rAB3 * Formulae.fSr(B, rho, vr, eps, p)
- flx_stau = rAB3 * Formulae.fτ(B, rho, vr, eps, p)
- catch e
- println("failed @ r = $r")
- rethrow(e)
- end
- @returns flx_sD, flx_sSr, flx_stau
+@with_signature function bdryllf(equation::Equation)
+ @accepts D, flr_D, Sr, flr_Sr, Ï„, flr_Ï„, max_v, vr, p
+ @accepts init_D, init_Sr, init_Ï„, init_vr, init_max_v, init_p
+ @accepts α, βru, γrr
+ @accepts [bdry] nx
+
+ vmax = absmax(max_v, init_max_v)
+ γuurr = 1/γrr
+ init_vru = γuurr * init_vr
+ vru = γuurr * vr
+
+ # enforce dirichlet/neumann conditions following stability analysis
+ # see dg-notes/tex/evm.pdf
+ # Hesthaven, Numerical Methods for Conservation Laws uses same logic
+
+ # Dirichlet conditions
+ # ## if block for hand-tweaked outflow condition for bondi accretion at inner radius
+ # if nx > 0
+ bdry_D = -D + 2*init_D
+ bdry_Sr = -Sr + 2*init_Sr
+ bdry_Ï„ = -Ï„ + 2*init_Ï„
+ bdry_vru = -vru + 2*init_vru
+ bdry_p = -p + 2*init_p
+ # else
+ # bdry_D = D
+ # bdry_Sr = Sr
+ # bdry_Ï„ = Ï„
+ # bdry_vru = vru
+ # bdry_p = p
+ # end
+
+ # Neumann conditions
+ # bdry_D = D
+ # bdry_Sr = Sr
+ # bdry_Ï„ = Ï„
+
+ bdry_flr_D = α * bdry_D * (bdry_vru - βru/α)
+ bdry_flr_Sr = α * ( bdry_Sr * (bdry_vru - βru/α) + bdry_p )
+ bdry_flr_τ = α * ( bdry_τ * (bdry_vru - βru/α) + bdry_p * bdry_vru )
+
+ nflr = nx*flr_D
+ bdry_nflr = nx*bdry_flr_D
+ nflr_D = LLF(nflr, bdry_nflr, D, bdry_D, vmax)
+
+ nflr = nx*flr_Sr
+ bdry_nflr = nx*bdry_flr_Sr
+ nflr_Sr = LLF(nflr, bdry_nflr, Sr, bdry_Sr, vmax)
+
+ nflr = nx*flr_Ï„
+ bdry_nflr = nx*bdry_flr_Ï„
+ nflr_Ï„ = LLF(nflr, bdry_nflr, Ï„, bdry_Ï„, vmax)
+
+ @returns [bdry] nflr_D, nflr_Sr, nflr_Ï„
end
-
-@with_signature function speed(equation::Equation)
- @accepts State(sD, sSr, stau), p, rho, vr, eps, A, B, r
- # TODO Implement characteristics and derive maxiumum wave speeds.
- # Might be as simple as adding a missing factor for the auxiliary metric to the
- # eigenvalues, since ts is the only thing the generalized Valencia formulation adds
- # to the principal part.
- # for now we use speed of light
- max_v = 0.999
- @returns max_v
+@with_signature function fv_bdry_flux(equation::Equation)
+ @accepts D, Sr, Ï„, vr, p
+ @accepts init_D, init_Sr, init_Ï„, init_vr, init_p
+ @accepts α, βru, γrr
+ @accepts [bdry] nx
+
+ γuurr = 1/γrr
+ init_vru = γuurr * init_vr
+ vru = γuurr * vr
+
+ # Dirichlet conditions
+ # if nx < 0
+ bdry_D = -D + 2*init_D
+ bdry_Sr = -Sr + 2*init_Sr
+ bdry_Ï„ = -Ï„ + 2*init_Ï„
+ bdry_vru = -vru + 2*init_vru
+ bdry_p = -p + 2*init_p
+ # else
+ # bdry_D = D
+ # bdry_Sr = Sr
+ # bdry_Ï„ = Ï„
+ # bdry_vru = vru
+ # bdry_p = p
+ # end
+
+ nflr_D = α * bdry_D * (bdry_vru - βru/α)
+ nflr_Sr = α * ( bdry_Sr * (bdry_vru - βru/α) + bdry_p )
+ nflr_τ = α * ( bdry_τ * (bdry_vru - βru/α) + bdry_p * bdry_vru )
+
+ @returns [bdry] bdry_D, bdry_Sr, bdry_Ï„, nflr_D, nflr_Sr, nflr_Ï„
end
-# @with_signature function impose_atmosphere(equation::Equation)
-# @accepts rho, p, eps, v, D, S, tau
-# @unpack atmosphere = equation
-#
-# Ïatm = atmosphere.rho
-# patm = 0.0
-# ϵatm = tau / Ïatm
-# sm = 1.0
-# Watm = 1.0
-# vatm = 1.0
-#
-# if rho < atmosphere.rho * atmosphere.threshold
-# rho = rhoatm
-# p = patm
-# eps = epsatm
-# v = vatm
-# D = Formulae.D(rhoatm, vatm, epsatm, patm)
-# S = Formulae.S(rhoatm, vatm, epsatm, patm)
-# tau = Formulae.Ï„(rhoatm, vatm, epsatm, patm)
-# end
-#
-# @returns rho, p, eps, v, D, S, tau
-# end
-
-
-@with_signature function primitives(equation::Equation)
- @accepts D, Sr, tau, p, B
- rho = Formulae.Ï(B, D, Sr, tau, p)
- vr = Formulae.vr(B, D, Sr, tau, p)
- eps = Formulae.ϵ(B, D, Sr, tau, p)
- @returns rho, vr, eps
-end
+#######################################################################
+# "rescaled_spherical1d" #
+# Spherical symmetry (1d) + spherical coordinates #
+#######################################################################
-@with_signature function prim2cons(equation::Equation)
- @accepts rho, vr, eps, p, B
- D = Formulae.D(B, rho, vr, eps, p)
- Sr = Formulae.Sr(B, rho, vr, eps, p)
- tau = Formulae.Ï„(B, rho, vr, eps, p)
- @returns D, Sr, tau
-end
+@with_signature function flux_source_rescaled_spherical1d(eq::Equation)
+ @accepts D, Sr, Ï„, p, vr
+ @accepts A, ∂Ar, B, ∂Br, r
+
+ γuurr = 1/B^2
+ vru = γuurr * vr
+ B3 = B^3
+ flr_rD = r*A*B3 * D * vru
+ flr_rSr = r*A*B3 * (Sr*vru + p)
+ flr_rτ = r*A*B3 * (τ + p) * vru
-@with_signature function entropy_variables(equation::Equation{EquationOfState.IdealGas})
- @accepts rho, p, E, flx_E
- TODO(entropy_variables)
- # @unpack eos = equation
- # γ = eos.gamma
- # E = rho / (γ - 1) * log(p / rho^γ)
- # flx_E = q * E / rho
- @returns E, flx_E
+ src_rD = - A*B3 * D * vru
+ # src_rSr = -(τ+p)*r*B3*∂Ar + A*B^2*(r*∂Br+B/3)*(Sr*vru+3*p) - 4/3*A*B3*Sr*vru
+ # src_rSr = -(τ+p)*r*B3*∂Ar + A*B^2*(r*∂Br+B/3)*(Sr*vru/A^2+3*p) - 4/3*A*B3*Sr*vru
+ src_rSr = -(τ+p)*r*B3*∂Ar + A*B^2*(r*∂Br+B/3)*(Sr*vru/A^2+3*p) - 4/3*A*B3*Sr*vru
+ # src_rτ = -r*B*Sr*∂Ar - A*B3*(τ+p)*vru
+ src_rτ = -r*B*Sr*∂Ar/A - A*B3*(τ+p)*vru
+
+ @returns src_rD, src_rSr, src_rτ, flr_rD, flr_rSr, flr_rτ
end
+@with_signature function maxspeed_rescaled_spherical1d(equation::Equation)
+ @accepts vr, Ï, ϵ
+ @accepts B, A
+ @unpack eos = equation
+ cs2 = eos(SquareSpeedOfSound, Density, Ï, InternalEnergy, ϵ)
+ cs = sqrt(abs(cs2))
+ γuurr = 1/B^2
+ vru = γuurr * vr
+ v2 = vru*vr
+ λ0 = A*vru
+ W = 1/sqrt(1-v2)
+ λp = A/(1-v2)*(vru*(1-cs2)+cs/W*sqrt((1-v2*cs2)*γuurr-vru^2*(1-cs2)))
+ λm = A/(1-v2)*(vru*(1-cs2)-cs/W*sqrt((1-v2*cs2)*γuurr-vru^2*(1-cs2)))
+ max_v = absmax(λm, λ0, λp)
+ @returns max_v
+end
+
+@with_signature function llf_rescaled_spherical1d(equation::Equation)
+ @accepts D, flr_rD, Sr, flr_rSr, τ, flr_rτ, max_v, p
+ @accepts A, B, r
+ @accepts [bdry] bdry_D, bdry_Sr, bdry_Ï„, bdry_max_v, bdry_vr, bdry_p
+ @accepts [bdry] nx
+
+ vmax = absmax(max_v, bdry_max_v)
+ γuurr = 1/B^2
+ bdry_vru = γuurr * bdry_vr
+ B3 = B^3
+
+ rD = r*B3*D
+ rSr = r*B3*Sr
+ rτ = r*B3*τ
+ bdry_rD = r*B3*bdry_D
+ bdry_rSr = r*B3*bdry_Sr
+ bdry_rτ = r*B3*bdry_τ
+
+ bdry_flr_rD = r*A*B3 * bdry_D * bdry_vru
+ bdry_flr_rSr = r*A*B3 * ( bdry_Sr * bdry_vru + bdry_p )
+ bdry_flr_rτ = r*A*B3 * ( (bdry_τ + bdry_p) * bdry_vru )
+
+ nflr = nx*flr_rD
+ bdry_nflr = nx*bdry_flr_rD
+ nflr_rD = LLF(nflr, bdry_nflr, rD, bdry_rD, vmax)
+
+ nflr = nx*flr_rSr
+ bdry_nflr = nx*bdry_flr_rSr
+ nflr_rSr = LLF(nflr, bdry_nflr, rSr, bdry_rSr, vmax)
+
+ nflr = nx*flr_rτ
+ bdry_nflr = nx*bdry_flr_rτ
+ nflr_rτ = LLF(nflr, bdry_nflr, rτ, bdry_rτ, vmax)
+
+ @returns [bdry] nflr_rD, nflr_rSr, nflr_rτ
+end
-@with_signature function sources(equation::Equation)
- @accepts rho, vr, p, eps, r, A, A_r, B, B_r
- src_sD = Formulae.sD(r, A, A_r, B, B_r, rho, vr, eps, p)
- src_sSr = Formulae.sSr(r, A, A_r, B, B_r, rho, vr, eps, p)
- src_stau = Formulae.sτ(r, A, A_r, B, B_r, rho, vr, eps, p)
- @returns src_sD, src_sSr, src_stau
+@with_signature function bdryllf_rescaled_spherical1d(equation::Equation)
+ @accepts D, flr_rD, Sr, flr_rSr, τ, flr_rτ, max_v, vr, p
+ @accepts init_D, init_Sr, init_Ï„, init_vr, init_max_v, init_p
+ @accepts A, B, r
+ @accepts [bdry] nx
+
+ vmax = absmax(max_v, init_max_v)
+ γuurr = 1/B^2
+ init_vru = γuurr * init_vr
+ vru = γuurr * vr
+ B3 = B^3
+
+ # Dirichlet conditions
+ bdry_D = -D + 2*init_D
+ bdry_Sr = -Sr + 2*init_Sr
+ bdry_Ï„ = -Ï„ + 2*init_Ï„
+ bdry_vru = -vru + 2*init_vru
+ bdry_p = -p + 2*init_p
+
+ # Neumann conditions
+ # bdry_D = D
+ # bdry_Sr = Sr
+ # bdry_Ï„ = Ï„
+
+ rD = r*B3*D
+ rSr = r*B3*Sr
+ rτ = r*B3*τ
+ bdry_rD = r*B3*bdry_D
+ bdry_rSr = r*B3*bdry_Sr
+ bdry_rτ = r*B3*bdry_τ
+
+ bdry_flr_rD = r*A*B3 * bdry_D * bdry_vru
+ bdry_flr_rSr = r*A*B3 * ( bdry_Sr * bdry_vru + bdry_p )
+ bdry_flr_rτ = r*A*B3 * (bdry_τ + bdry_p) * bdry_vru
+
+ nflr = nx*flr_rD
+ bdry_nflr = nx*bdry_flr_rD
+ nflr_rD = LLF(nflr, bdry_nflr, rD, bdry_rD, vmax)
+
+ nflr = nx*flr_rSr
+ bdry_nflr = nx*bdry_flr_rSr
+ nflr_rSr = LLF(nflr, bdry_nflr, rSr, bdry_rSr, vmax)
+
+ nflr = nx*flr_rτ
+ bdry_nflr = nx*bdry_flr_rτ
+ nflr_rτ = LLF(nflr, bdry_nflr, rτ, bdry_rτ, vmax)
+
+ @returns [bdry] nflr_rD, nflr_rSr, nflr_rτ
end
-@with_signature function cons2scaledcons(equations::Equation)
- @accepts D, Sr, tau, B, r
- sD = r * B^3 * D
- sSr = r * B^3 * Sr
- stau = r * B^3 * tau
- @returns sD, sSr, stau
+@with_signature function unscale_conservatives(equation::Equation)
+ @accepts rD, rSr, rτ
+ @accepts r, B
+ B3 = B^3
+ D = rD/(r*B3)
+ Sr = rSr/(r*B3)
+ τ = rτ/(r*B3)
+ @returns D, Sr, Ï„
end
-@with_signature function scaledcons2cons(equations::Equation)
- @accepts sD, sSr, stau, B, r
- D = sD / (r * B^3)
- Sr = sSr / (r * B^3)
- tau = stau / (r * B^3)
- @returns D, Sr, tau
+@with_signature function fv_bdry_flux_rescaled_spherical1d(equation::Equation)
+ @accepts D, Sr, Ï„, vr, p
+ @accepts init_D, init_Sr, init_Ï„, init_vr, init_p
+ @accepts A, B, ∂Br, r
+ @accepts [bdry] nx
+
+ γuurr = 1/B^2
+ init_vru = γuurr * init_vr
+ vru = γuurr * vr
+ B3 = B^3
+
+ # # Dirichlet conditions
+ bdry_D = -D + 2*init_D
+ bdry_Sr = -Sr + 2*init_Sr
+ bdry_Ï„ = -Ï„ + 2*init_Ï„
+ bdry_vru = -vru + 2*init_vru
+ bdry_p = -p + 2*init_p
+ # bdry_D = init_D
+ # bdry_Sr = init_Sr
+ # bdry_Ï„ = init_Ï„
+ # bdry_vru = init_vru
+ # bdry_p = init_p
+
+ @show init_D, D
+
+ nflr_rD = r*A*B3* bdry_D * bdry_vru
+ nflr_rSr = r*A*B3* (bdry_Sr * bdry_vru + bdry_p)
+ nflr_rτ = r*A*B3* (bdry_τ + bdry_p) * bdry_vru
+
+ # FIXME We are abusing the bdry_D,Sr,Ï„ buffers to store the rescaled bdry values
+ bdry_D *= r*B3
+ bdry_Sr *= r*B3
+ bdry_Ï„ *= r*B3
+
+ @returns [bdry] bdry_D, bdry_Sr, bdry_τ, nflr_rD, nflr_rSr, nflr_rτ
end
-"""
-Postprocess points where we divided by zero in `scaledcons2cons`.
-Do so by interpolating value where x = 0 using symmetry/anti-symmetry
-"""
-function postprocess_scaledcons2cons!(cache::Cache, equations::Equation, mesh::Mesh)
+#######################################################################
+# helpers to resolve coordinate singularities #
+# by imposing symmetry conditions at r=0 #
+#######################################################################
- @unpack x = mesh
- Npts, K = layout(mesh)
- if isodd(Npts) && isodd(K)
- error("Cannot yet handle case where r = 0 falls into symmetric cell with even polynomial!")
- end
+function impose_symmetry!(P::Project{:rescaled_spherical1d}, mesh::Mesh)
- # find points where x coordinate is zero
- idxs = findall(xi->abs(xi) < 1e-14, mesh.x)
+ @unpack cache = mesh
+ @unpack D, Sr, Ï„ = get_static_variables(cache)
+ L = layout(mesh)
+ Npts, _ = L
- @unpack D, Sr, tau = get_static_variables(cache)
+ vD = dg1d.vreshape(D, L)
+ vSr = dg1d.vreshape(Sr, L)
+ vτ = dg1d.vreshape(τ, L)
- for con in (D, tau) # symmetric variables need to be interpolated
- mat_con = reshape(view(con, :), (Npts, K))
- for idx in idxs
- i, j = Tuple(idx)
- mat_con[i,j] = 0 # remove nan, because we are computing inplace
- Di = mesh.element.D[i,:] # derivative weights for ith point
- Dii = Di[i]
- mat_con[i,j] = - dot(Di, mat_con[:,j]) / Dii
- end
- end
- for con in (Sr,) # asymmetric variables need to be set to zero
- for idx in idxs
- i, j = Tuple(idx)
- con[i+(j-1)*Npts] = 0
+ # even variables are interpolated such that derivative vanishes at r=0
+ for var in (vD, vτ)
+ tmp = 0
+ for j = 2:Npts
+ tmp += mesh.element.D[1,j] * var[j,1]
end
+ var[1,1] = -tmp/mesh.element.D[1,1]
end
+ # odd variables are set to zero at r=0
+ Sr[1] = 0
+
+ return
end
-#######################################################################
-# LDG #
-#######################################################################
+function impose_symmetry!(P::Project{:rescaled_spherical1d}, mesh::Mesh{FVElement})
+ @unpack cache = mesh
+ @unpack rD = get_dynamic_variables(cache)
+ @unpack D, Sr, Ï„, r = get_static_variables(cache)
+ L = layout(mesh)
+ Npts, _ = L
-@with_signature function ldg_flux(equations::Equation)
- @accepts State(sD, sSr, stau)
- flx_ldg_sD, flx_ldg_sSr, flx_ldg_stau = sD, sSr, stau
- @returns flx_ldg_sD, flx_ldg_sSr, flx_ldg_stau
-end
-
+ @show rD[1], rD[2]
-@with_signature function ldg_speed(equations::Equation)
- @accepts State(sD, sSr, stau)
- v_ldg_sD, v_ldg_sSr, v_ldg_stau = 1, 1, 1
- @returns v_ldg_sD, v_ldg_sSr, v_ldg_stau
-end
+ # symmetric variables are interpolated such that derivative vanishes at r=0
+ for var in (D, Ï„)
+ tmp = 0
+ # use quadratic interpolation around origin
+ var2, var3, r2, r3 = var[2], var[3], r[2], r[3]
+ var[1] = (r3^2*var2-r2^2*var3)/(r3^2-r2^2)
+ end
+ # asymmetric variables are set to zero at r=0
+ Sr[1] = 0
+ @show D[1], D[2]
-@with_signature function av_flux(equations::Equation)
- @accepts State(ldg_sD, ldg_sSr, ldg_stau), smoothed_mu
- flx_ldg_sD, flx_ldg_sSr, flx_ldg_stau =
- smoothed_mu * ldg_sD, smoothed_mu * ldg_sSr, smoothed_mu * ldg_stau
- @returns flx_ldg_sD, flx_ldg_sSr, flx_ldg_stau
+ return
end
-@with_signature function av_speed(equations::Equation)
- @accepts State(ldg_sD, ldg_sSr, ldg_stau), smoothed_mu
- flx_ldg_sD, flx_ldg_sSr, flx_ldg_stau = smoothed_mu, smoothed_mu, smoothed_mu
- @returns v_flx_ldg_sD, v_flx_ldg_sSr, v_flx_ldg_stau
+function impose_symmetry_sources!(P::Project{:spherical1d}, mesh::Mesh)
+ @unpack r = get_static_variables(mesh.cache)
+ r[1] ≈ 0.0 || return
+ @unpack src_D, src_Sr, src_Ï„ = get_static_variables(mesh.cache)
+ L = layout(mesh)
+ Npts, _ = L
+ v_src_D = dg1d.vreshape(src_D, L)
+ v_src_Ï„ = dg1d.vreshape(src_Ï„, L)
+ # even variables are interpolated such that derivative vanishes at r=0
+ for var in (v_src_D, v_src_Ï„)
+ tmp = 0
+ for j = 2:Npts
+ tmp += mesh.element.D[1,j] * var[j,1]
+ end
+ var[1,1] = -tmp/mesh.element.D[1,1]
+ end
+ # odd variables are set to zero at r=0
+ src_Sr[1] = 0
+ return
end
diff --git a/src/GRHD/initialdata.jl b/src/GRHD/initialdata.jl
index d473ee1d..c73c8f9d 100644
--- a/src/GRHD/initialdata.jl
+++ b/src/GRHD/initialdata.jl
@@ -1,14 +1,9 @@
function initialdata!(env, P::Project, prms)
@unpack id = prms
- let
- @unpack r = get_static_variables(env.cache)
- @. r = env.mesh.x[:]
- end
initialdata_equation!(Val(Symbol(id)), env, P, prms)
- return
- # initialdata_entropy_variables!(id, P, prms)
- initialdata_hrsc!(Val(Symbol(id)), env, P, P.hrsc, prms)
- initialdata_tci!(Val(Symbol(id)), env, P, P.tci, prms)
+ # # initialdata_entropy_variables!(id, P, prms)
+ # initialdata_hrsc!(Val(Symbol(id)), env, P, P.hrsc, prms)
+ # initialdata_tci!(Val(Symbol(id)), env, P, P.tci, prms)
end
@@ -17,291 +12,382 @@ end
#######################################################################
-function initialdata_equation!(::Val{T}, env, P, parameters) where T
- TODO(initialdata_equation!)
-end
-
+function initialdata_equation!(::Val{:bondi_accretion}, env, P::Project{:spherical1d}, prms)
-function initialdata_equation!(::Val{:bondi_accretion}, env, P, prms)
- TODO(initialdata_equation!)
-end
+ @unpack mesh = env
+ @unpack equation = P
+ id_filename = prms["id_filename"]
+ if !isfile(id_filename)
+ error("GRHD: Failed to locate bondi_accretion initial data at $id_filename")
+ end
-function readdata_tov(filename)
- return h5open(filename, "r") do file
- g = file["TOV"]
- Γ = read_attribute(g, "Γ")
- K = read_attribute(g, "K")
+ data = h5open(id_filename, "r") do file
+ g = file["bondi_accretion"]
+ Γ = read_attribute(g, "Γ")
+ K = read_attribute(g, "K")
Ïc = read_attribute(g, "Ïc")
- M = read_attribute(g, "M")
- Ï• = read(g, "Ï•")
- p = read(g, "p")
- m = read(g, "m")
- R = read(g, "R")
- r = read(g, "r")
- (; Γ, K, Ïc, M, Ï•, p, m, R, r)
+ rc = read_attribute(g, "rc")
+ M = read_attribute(g, "M")
+ r = read(g, "r")
+ Ï = read(g, "Ï")
+ p = read(g, "p")
+ ϵ = read(g, "ϵ")
+ vr = read(g, "vr")
+ (; Γ, K, Ïc, rc, M, r, Ï, ϵ, p, vr)
end
+
+ @assert data.K ≈ equation.eos.K
+ @assert data.Γ ≈ equation.eos.Gamma
+
+ @unpack D, Sr, Ï„ = get_dynamic_variables(mesh.cache)
+ @unpack Ï, p, ϵ, vr, r, max_v,
+ init_D, init_Sr, init_Ï„, init_vr, init_p,
+ init_max_v = get_static_variables(mesh.cache)
+ @unpack α, βru, ∂αr, ∂βrrdu,
+ γrr, γθθ, γϕϕ, ∂γrrr, ∂γrθθ, ∂γrϕϕ, ∂γθϕϕ,
+ Γrrr, Γrθθ, Γrϕϕ, Γθrθ, Γθϕϕ, Γϕrϕ, Γϕθϕ,
+ Krr, Kθθ, Kϕϕ = get_static_variables(mesh.cache)
+
+ p .= interpolate(r, data.r, data.p)
+ Ï .= interpolate(r, data.r, data.Ï)
+ ϵ .= interpolate(r, data.r, data.ϵ)
+ vru = interpolate(r, data.r, data.vr)
+
+ equation.atm_density = maximum(Ï) * equation.atm_factor
+ equation.atm_factor = prms["atm_factor"]
+ equation.atm_threshold = prms["atm_threshold_factor"]
+
+ # to avoid problems with 1/sin(θ) etc., this is also done in initialdata/SphericalAccretion.jl
+ θ = π/2
+ @unpack M = data
+
+ @. α = sqrt(r/(r+2*M))
+ @. βru = 2*M/(r+2*M) # = β^r
+ @. ∂αr = M / sqrt(r*(2*M+r)^3)
+ @. ∂βrrdu = - 2*M/(2*M+r)^2
+
+ # γ_ij
+ @. γrr = 1 + 2*M/r
+ @. γθθ = r^2
+ @. γϕϕ = r^2 * sin(θ)^2
+
+ # # γijuu = γ^ij
+ # γrruu = @. 1/γrr
+ # γθθuu = @. 1/γθθ
+ # γϕϕuu = @. 1/γϕϕ
+
+ # ∂iγjk := ∂γijk
+ @. ∂γrrr = -2*M/r^2
+ @. ∂γrθθ = 2*r
+ @. ∂γrϕϕ = 2*r*sin(θ)^2
+ @. ∂γθϕϕ = r^2 * sin(θ)*cos(θ)
+
+ # Γijk := Γ^i_jk wrt γ_ij
+ @. Γrrr = -M/(r*(2*M+r))
+ @. Γrθθ = -r^2/(2*M+r)
+ @. Γrϕϕ = -r^2*sin(θ)^2/(2*M+r)
+ @. Γθrθ = 1/r
+ @. Γθϕϕ = -sin(θ)*cos(θ)
+ @. Γϕrϕ = 1/r
+ @. Γϕθϕ = cos(θ)/sin(θ)
+
+ # Kij := K_ij
+ @. Krr = -2*M*(M+r)/sqrt(r^5*(2*M+r))
+ @. Kθθ = 2*M*sqrt(r/(2*M+r))
+ @. Kϕϕ = 2*M*sqrt(r/(2*M+r))*sin(θ)^2
+
+ # # ∂Kijk = ∂_i K_jk
+ # ∂Krrr = @. 2*M*(5*M^2+2*r^2+6*M*r)/sqrt(r^7*(2*M+r)^3)
+ # ∂Krθθ = @. 2*M^2/sqrt(r*(2*M+r)^3)
+ # ∂Krϕϕ = @. ∂Krθθ * sin(θ)^2
+
+ # # verify trace of K
+ # trK_v1 = @. Krr*γrruu + Kθθ*γθθuu + Kϕϕ*γϕϕuu
+ # trK_v2 = @. 2*M*α^3/r^2*(1+3*M/r)
+ # @show(extrema(trK_v1.-trK_v2))
+
+
+ # from initialdata/SphericalAccretion.jl
+ # also see Papadopoulos and Font 1998, arXiv:gr-qc/9803087, eq (5)
+ v2 = @. γrr*vru^2
+ W = @. 1/sqrt(1-v2) # = αu^t, Lorentz factor
+ @. vr = γrr * vru # = γ_rr v^r
+
+ h = @. 1 + ϵ + p/Ï
+ @. D = W * Ï
+ @. Sr = W^2 * Ï * h * vr
+ @. Ï„ = W^2 * Ï * h - p - D
+
+ broadcast_volume!(cons2prim, equation, mesh)
+ broadcast_volume!(maxspeed, equation, mesh)
+ broadcast_volume!(flux_source_spherical1d, equation, mesh)
+
+ @. init_D = D
+ @. init_Sr = Sr
+ @. init_Ï„ = Ï„
+ @. init_vr = vr
+ @. init_p = p
+ @. init_max_v = max_v
+
+ return
end
-function initialdata_equation!(::Val{:tov}, env, P, prms)
+function initialdata_equation!(::Val{:tov}, env, P::Project{:spherical1d}, prms)
filename = prms["id_filename"]
- if length(filename) == 0
- error("GRHD: Missing filename for TOV output, include with GRHD.id_filename = 'tov'")
- end
- filename = joinpath(get_output_dir(), filename)
-
- # read TOV result from file
- # should only contain solution in star interior
- # output_dir = dg1d.get_output_dir()
- # data = TOV.read_data(joinpath(output_dir, "TOV.h5"))
- data = readdata_tov(filename)
- Ï•int = data.Ï•
- Rint = data.R
- rint = data.r
- pint = data.p
- K = data.K
- Γ = data.Γ
- M = data.M
- Rsurf = Rint[end]
-
- # interpolate data onto our grid
- # we don't assume a special grid layout for the loaded data
-
- @unpack cache, mesh = env
- @unpack Npts = mesh.element
-
- intrp_R = vec(mesh.x) # DG coordinates
- NN = length(intrp_R)
-
- # determine if grid contains r = 0 point
- R_ismirrored = intrp_R[1] ≈ -intrp_R[end]
-
- if !R_ismirrored
- idx_origin = findall(Ri -> isapprox(Ri, 0), intrp_R)
- @assert length(idx_origin) > 0 "Non-symmetric grids must include coordinate origin"
+ if !isfile(filename)
+ error("GRHD: Failed to locate TOV initial data at id_filename = $filename")
end
- # determine our grid setup
- R_includes_origin = (
- !R_ismirrored # LGL grids always contain bdry points
- || (
- iseven(mesh.K) || # origin falls at interface between two cells
- (isodd(mesh.K) && isodd(mesh.element.Npts)) # origin sits in the center
- # of a cell with a point in the center
- )
- )
- R_origin_isdoubled = (
- R_ismirrored && # only happens for mirrored domains
- iseven(mesh.K) # and origin falls at interface between two cells
- )
- # if r = 0 only covered by one point we have to exclude the boundary
- # point when mirroring/refelcting back
- exclude_origin = !R_origin_isdoubled && R_includes_origin
-
- # on a mirrored grid we only do interpolation on one half and then
- # mirror/reflect onto the other
- @show NN
- @show R_ismirrored
- @show R_origin_isdoubled
- @show R_includes_origin
- if R_ismirrored
- idx_innermost_R = if R_origin_isdoubled
- Int64(NN/2) + 1
- elseif R_includes_origin
- Int64((NN+1)/2)
- else
- Int64(NN/2) + 1
- end
- intrp_R = intrp_R[idx_innermost_R:end]
- end
- Rmax = maximum(intrp_R) # star's radius
-
- @info "TOV star surface located at R = $Rsurf"
-
- #### setup metric functions A, B and derivatives in isotropic coordinates
-
- # star interior solution
- Aint = exp.(Ï•int)
- # B := r / R, needs special treatment of coordinate singularity.
- Bint = [ (ri == 0) ? 1.0 : ri / Ri for (ri, Ri) in zip(rint, Rint) ]
- # use linear interpolation to obtain value at r = R = 0.
- Bint[1] = (Bint[3] - Bint[2]) / (Rint[3] - Rint[2]) * (0.0 - Rint[2]) + Bint[2]
-
- # derivatives
- dAint = dg1d.FD.central_dx(Aint, Rint)
- dBint = dg1d.FD.central_dx(Bint, Rint)
-
- # star exterior solution =^= Schwarzschild solution
- Npts_ext = 1000 # number of points used for interpolation of exterior solution
- Rext = collect(LinRange(Rsurf, Rmax, Npts_ext))
- Aext, Bext = schwarzschild_solution_isotropic_coordinates(Rext, M)
-
- # merge interior and exterior solutions
- # note: exclude surface point in one of the arrays when merging
- R = cat(Rint, Rext[2:end], dims=1)
- A = cat(Aint, Aext[2:end], dims=1)
- B = cat(Bint, Bext[2:end], dims=1)
-
- # derivatives
- dA = dg1d.FD.central_dx(A, R)
- dB = dg1d.FD.central_dx(B, R)
-
- intrp_A = interpolate(intrp_R[:], R, A)
- intrp_B = interpolate(intrp_R[:], R, B)
- intrp_A_r = interpolate(intrp_R[:], R, dA)
- intrp_B_r = interpolate(intrp_R[:], R, dB)
-
- if R_ismirrored
- intrp_A = mirror(intrp_A, exclude_origin)
- intrp_B = mirror(intrp_B, exclude_origin)
- intrp_A_r = reflect(intrp_A_r, exclude_origin)
- intrp_B_r = reflect(intrp_B_r, exclude_origin)
+ data = h5open(filename, "r") do file
+ g = file["TOV"]
+ Γ = read_attribute(g, "Γ")
+ K = read_attribute(g, "K")
+ Ïc = read_attribute(g, "Ïc")
+ M = read_attribute(g, "M")
+ rsch = read(g, "r") # schwarzschild radius coordinate
+ riso = read(g, "R") # isotropic radius coordinate
+ Ï = read(g, "Ï")
+ p = read(g, "p")
+ ϵ = read(g, "ϵ")
+ Ï• = read(g, "Ï•")
+ m = read(g, "m")
+
+ # metric potentials: ds^2 = -A^2 dt^2 + B^2 γij dx^i dx^j
+ A = @. exp(Ï•)
+ B = @. rsch / riso
+ # B[1] is nan, because rsch = riso = 0 there
+ # use a parabola to interpolate data point at riso = 0
+ # this also ensures that B is symmetric arcoss riso = 0
+ B2, B3, r2, r3 = B[2], B[3], riso[2], riso[3]
+ B[1] = (r3^2*B2-r2^2*B3)/(r3^2-r2^2)
+
+ (; Γ, K, Ïc, M, riso, Ï, ϵ, p, A, B)
end
- @assert all(map(X->all(isfinite.(X)), [intrp_A, intrp_B, intrp_A_r, intrp_B_r])) == true ""
- "Initial data interpolation failed!"
-
- @unpack A, B, A_r, B_r = get_static_variables(cache)
- A .= intrp_A
- B .= intrp_B
- A_r .= intrp_A_r
- B_r .= intrp_B_r
-
- ### setup hydrodynamic variables
@unpack equation = P
- # @unpack atmosphere = equation
- eos = Polytrope(K=K, Gamma=Γ)
-
- # apply atmosphere treatment
- pmax = maximum(pint)
- Ïmax = eos(Density, Pressure, pmax)
- Ïatm = equation.atm_factor * Ïmax
- # initialize atmosphere
- equation.atm_density = Ïatm
- patm = eos(Pressure, Density, Ïatm)
- pint[@.(pint < 0)] .= 0.0 # just to be sure, they will be replace with patm below anyways
- Ïint = @. eos(Density, Pressure, pint)
- idxatm_treatment = @. Ïint < Ïatm * equation.atm_threshold
- pint[idxatm_treatment] .= patm
- Ïint[idxatm_treatment] .= Ïatm
- vint = zeros(size(Rint))
- ϵint = @. eos(InternalEnergy, Density, Ïint)
-
- # star exterior data
- Ïext = Ïatm * ones(size(Rext))
- pext = @. eos(Pressure, Density, Ïext)
- vext = zeros(size(Rext))
- ϵext = @. eos(InternalEnergy, Density, Ïext)
-
- # merge interior and exterior solutions
- p = cat(pint, pext[2:end], dims=1)
- Ï = cat(Ïint, Ïext[2:end], dims=1)
- vr = cat(vint, vext[2:end], dims=1)
- ϵ = cat(ϵint, ϵext[2:end], dims=1)
-
- intrp_p = interpolate(intrp_R[:], R, p)
- intrp_Ï = interpolate(intrp_R[:], R, Ï)
- intrp_vr = interpolate(intrp_R[:], R, vr)
- intrp_ϵ = interpolate(intrp_R[:], R, ϵ)
-
- if R_ismirrored
- intrp_p = mirror(intrp_p, exclude_origin)
- intrp_Ï = mirror(intrp_Ï, exclude_origin)
- intrp_vr = reflect(intrp_vr, exclude_origin)
- intrp_ϵ = mirror(intrp_ϵ, exclude_origin)
- end
-
- @unpack p, vr, rho, eps = get_static_variables(cache)
- @unpack sD, sSr, stau = get_dynamic_variables(cache)
- @unpack D, Sr, tau, = get_static_variables(cache)
-
- p .= intrp_p
- rho .= intrp_Ï
- vr .= intrp_vr
- eps .= intrp_ϵ
-
- broadcast_volume!(prim2cons, equation, cache)
- broadcast_volume!(cons2scaledcons, equation, cache)
-
- @assert all(map(X->all(isfinite.(X)),
- [p, vr, rho, eps, D, Sr, tau, sD, sSr, stau])) == true "Initial data interpolation failed!"
+ @unpack mesh = env
+ @unpack eos = P.equation
+ @assert data.K ≈ eos.K
+ @assert data.Γ ≈ eos.Gamma
+
+ equation.atm_density = data.Ïc * equation.atm_factor
+ equation.atm_factor = prms["atm_factor"]
+ equation.atm_threshold = prms["atm_threshold_factor"]
+
+ @unpack D, Sr, Ï„ = get_dynamic_variables(mesh.cache)
+ @unpack Ï, p, ϵ, vr, r, max_v,
+ init_D, init_Sr, init_Ï„, init_vr, init_p,
+ init_max_v = get_static_variables(mesh.cache)
+ @unpack α, βru, ∂αr, ∂βrrdu,
+ γrr, γθθ, γϕϕ, ∂γrrr, ∂γrθθ, ∂γrϕϕ, ∂γθϕϕ,
+ Γrrr, Γrθθ, Γrϕϕ, Γθrθ, Γθϕϕ, Γϕrϕ, Γϕθϕ,
+ Krr, Kθθ, Kϕϕ = get_static_variables(mesh.cache)
+
+ # need to split initial data into portion that lies inside and outside of star,
+ # because derivatives of the hydro variables are discontinuous at the surface
+ # although metric functions are supposed to be better conditioned there,
+ # we also split them for the interpolation, because of potential contamination
+ # with numerical error from patching
+ rmax = data.riso[end]
+ idx_exterior = findfirst(ri -> ri > rmax, r) |> something
+ @assert idx_exterior > 0
+ interior = 1:idx_exterior-1
+ exterior = idx_exterior:length(mesh)
+
+ rint = view(r, interior)
+ rext = view(r, exterior)
+ A, B, ∂Ar, ∂Br = [ similar(r) for _ in 1:4 ]
+
+ Ï[interior] .= interpolate(rint, data.riso, data.Ï)
+ ϵ[interior] .= interpolate(rint, data.riso, data.ϵ)
+ p[interior] .= interpolate(rint, data.riso, data.p)
+ A[interior] .= interpolate(rint, data.riso, data.A)
+ B[interior] .= interpolate(rint, data.riso, data.B)
+
+ Ï[exterior] .= equation.atm_density
+ p[exterior] .= @. eos(Pressure, Density, Ï[exterior])
+ ϵ[exterior] .= @. eos(InternalEnergy, Density, Ï[exterior])
+ # metric potentials of Schwarzschild solution in isotropic coordinates:
+ # ds^2 = -A^2 dt^2 + B^2 γij dx^i dx^j
+ @unpack M = data
+ A[exterior] .= @. (1-M/(2*rext))/(1+M/(2*rext))
+ B[exterior] .= @. (1+M/(2*rext))^2
+
+ # BasicInterpolators.jl cannot differentiate ... so we diff numerically
+ ∂Ar .= dg1d.differentiate(A, mesh)
+ ∂Br .= dg1d.differentiate(B, mesh)
+
+ θ = π/2
+
+ @. α = A
+ @. βru = 0.0
+ @. ∂αr = ∂Ar
+ @. ∂βrrdu = 0
+
+ @. γrr = B^2
+ @. γθθ = B^2*r^2
+ @. γϕϕ = B^2*r^2*sin(θ)^2
+
+ @. ∂γrrr = 2*B*∂Br
+ @. ∂γrθθ = 2*(r*B^2+B*∂Br*r^2)
+ @. ∂γrϕϕ = ∂γrθθ * sin(θ)^2
+ @. ∂γθϕϕ = 0.0
+
+ @. Γrrr = ∂Br/B
+ @. Γrθθ = (-r^2*B*∂Br-r*B^2)/B^2
+ @. Γrϕϕ = Γrθθ*sin(θ)^2
+ @. Γθrθ = (r^2*B*∂Br+r*B^2)/(r^2*B^2)
+ @. Γθϕϕ = -sin(θ)*cos(θ)
+ @. Γϕrϕ = (r^2*B*∂Br+r*B^2)/(r^2*B^2)
+ @. Γϕθϕ = cos(θ)/sin(θ)
+
+ @. Krr = 0.0
+ @. Kθθ = 0.0
+ @. KÏ•Ï• = 0.0
+
+ @. vr = 0
+ W = 1.0
+ h = @. 1 + ϵ + p/Ï
+ @. D = W * Ï
+ @. Sr = W^2 * Ï * h * vr
+ @. Ï„ = W^2 * Ï * h - p - D
+
+ broadcast_volume!(cons2prim, equation, mesh)
+ broadcast_volume!(maxspeed, equation, mesh)
+ broadcast_volume!(flux_source_spherical1d, equation, mesh)
+ impose_symmetry_sources!(P, mesh)
+
+ @. init_D = D
+ @. init_Sr = Sr
+ @. init_Ï„ = Ï„
+ @. init_vr = vr
+ @. init_p = p
+ @. init_max_v = max_v
- return
-end
-
-
-function schwarzschild_solution_isotropic_coordinates(R, M)
- Rmin = minimum(R)
- @assert 2 * Rmin >= M
- A = @. (1 - 0.5 * M / R) / (1 + 0.5 * M / R)
- B = @. (1 + 0.5 * M / R)^2
- return A, B
end
-function interpolate(x, x_ref, y_ref)
- x_intrp = LinearInterpolation(x_ref, y_ref, extrapolation_bc=Line())
- y = [ x_intrp(xi) for xi in x ]
- return y
-end
+function initialdata_equation!(::Val{:tov}, env, P::Project{:rescaled_spherical1d}, prms)
-
-function mirror(A, exclude_bdry::Bool)
- if exclude_bdry
- return cat(A[end:-1:2], A, dims=1)
- else
- return cat(A[end:-1:1], A, dims=1)
+ filename = prms["id_filename"]
+ if !isfile(filename)
+ error("GRHD: Failed to locate TOV initial data at id_filename = $filename")
end
-end
-
-function reflect(A, exclude_bdry::Bool)
- if exclude_bdry
- return cat(-A[end:-1:2], A, dims=1)
- else
- return cat(-A[end:-1:1], A, dims=1)
+ data = h5open(filename, "r") do file
+ g = file["TOV"]
+ Γ = read_attribute(g, "Γ")
+ K = read_attribute(g, "K")
+ Ïc = read_attribute(g, "Ïc")
+ M = read_attribute(g, "M")
+ rsch = read(g, "r") # schwarzschild radius coordinate
+ riso = read(g, "R") # isotropic radius coordinate
+ Ï = read(g, "Ï")
+ p = read(g, "p")
+ ϵ = read(g, "ϵ")
+ Ï• = read(g, "Ï•")
+ m = read(g, "m")
+
+ # metric potentials: ds^2 = -A^2 dt^2 + B^2 γij dx^i dx^j
+ A = @. exp(Ï•)
+ B = @. rsch / riso
+ # B[1] is nan, because rsch = riso = 0 there
+ # use a parabola to interpolate data point at riso = 0
+ # this also ensures that B is symmetric arcoss riso = 0
+ B2, B3, r2, r3 = B[2], B[3], riso[2], riso[3]
+ B[1] = (r3^2*B2-r2^2*B3)/(r3^2-r2^2)
+
+ (; Γ, K, Ïc, M, riso, Ï, ϵ, p, A, B)
end
-end
-
-function initialdata_equation!(::Val{:atmosphere}, env, P, prms)
-
- @unpack cache, mesh = env
@unpack equation = P
- @unpack Npts = mesh.element
- @unpack eos = equation
- @unpack A, B, A_r, B_r = get_static_variables(P.cache)
- R = vec(mesh.x)
-
- # minkowski metric
- A .= ones(size(R))
- B .= ones(size(R))
- A_r .= zeros(size(R))
- B_r .= zeros(size(R))
+ @unpack mesh = env
+ @unpack eos = P.equation
+ @assert data.K ≈ eos.K
+ @assert data.Γ ≈ eos.Gamma
+
+ equation.atm_density = data.Ïc * equation.atm_factor
+ equation.atm_factor = prms["atm_factor"]
+ equation.atm_threshold = prms["atm_threshold_factor"]
+
+ @unpack rD, rSr, rτ = get_dynamic_variables(mesh.cache)
+ @unpack Ï, p, ϵ, vr, r, max_v,
+ D, Sr, Ï„,
+ init_D, init_Sr, init_Ï„,
+ init_vr, init_p, init_max_v = get_static_variables(mesh.cache)
+ @unpack A, ∂Ar, B, ∂Br = get_static_variables(mesh.cache)
+
+ # need to split initial data into portion that lies inside and outside of star,
+ # because derivatives of the hydro variables are discontinuous at the surface
+ # although metric functions are supposed to be better conditioned there,
+ # we also split them for the interpolation, because of potential contamination
+ # with numerical error from patching
+ rmax = data.riso[end]
+ idx_exterior = findfirst(ri -> ri > rmax, r) |> something
+ @assert idx_exterior > 0
+ interior = 1:idx_exterior-1
+ exterior = idx_exterior:length(mesh)
+
+ rint = view(r, interior)
+ rext = view(r, exterior)
+
+ Ï[interior] .= interpolate(rint, data.riso, data.Ï)
+ ϵ[interior] .= interpolate(rint, data.riso, data.ϵ)
+ p[interior] .= interpolate(rint, data.riso, data.p)
+ A[interior] .= interpolate(rint, data.riso, data.A)
+ B[interior] .= interpolate(rint, data.riso, data.B)
+
+ Ï[exterior] .= equation.atm_density
+ p[exterior] .= @. eos(Pressure, Density, Ï[exterior])
+ ϵ[exterior] .= @. eos(InternalEnergy, Density, Ï[exterior])
+ # metric potentials of Schwarzschild solution in isotropic coordinates:
+ # ds^2 = -A^2 dt^2 + B^2 γij dx^i dx^j
+ @unpack M = data
+ A[exterior] .= @. (1-M/(2*rext))/(1+M/(2*rext))
+ B[exterior] .= @. (1+M/(2*rext))^2
+
+ # BasicInterpolators.jl cannot differentiate ... so we diff numerically
+ ∂Ar .= dg1d.differentiate(A, mesh)
+ ∂Br .= dg1d.differentiate(B, mesh)
+
+ @. vr = 0
+ W = 1.0
+ h = @. 1 + ϵ + p/Ï
+ @. D = W * Ï
+ @. Sr = W^2 * Ï * h * vr
+ @. Ï„ = W^2 * Ï * h - p - D
+ @. rD = r*B^3*D
+ @. rSr = r*B^3*Sr
+ @. rτ = r*B^3*τ
+
+ broadcast_volume!(unscale_conservatives, equation, mesh)
+ impose_symmetry!(P, mesh)
+ broadcast_volume!(cons2prim_rescaled_spherical1d, equation, mesh)
+ broadcast_volume!(flux_source_rescaled_spherical1d, equation, mesh)
+ broadcast_volume!(maxspeed_rescaled_spherical1d, equation, mesh)
+
+ @. init_D = D
+ @. init_Sr = Sr
+ @. init_Ï„ = Ï„
+ @. init_vr = vr
+ @. init_p = p
+ @. init_max_v = max_v
- # low density atmosphere
- # rho_atm = query(prms, "density", default=1e-11)
- rho_atm = prms["id_atmosphere_density"]
- @assert rho_atm > 0.0
- @assert eos isa Polytrope "Require model for cold atmosphere"
-
- @unpack rho, vr, p, eps = get_static_variables(P.cache)
+end
- NN = length(mesh)
- @. rho = rho_atm * $ones(NN)
- @. p = eos(Pressure, Density, rho, InternalEnergy, eps)
- @. eps = eos(InternalEnergy, Density, rho, Pressure, p)
- @. vr = $zeros(NN)
- @assert all(map(X->all(isfinite.(X)), [rho, p, eps, vr])) == true ""
- "Invalid initial data encountered!"
+function interpolate(x, x_ref, y_ref)
+ intrp = CubicSplineInterpolator(x_ref, y_ref)
+ return intrp.(x)
+end
- broadcast_volume!(prim2cons, equation, P.cache)
- broadcast_volume!(cons2scaledcons, equation, P.cache)
- return
+function interpolate_derivative(x, x_ref, y_ref)
+ intrp = CubicSplineInterpolator(x_ref, y_ref)
+ return intrp.(x)
end
diff --git a/src/GRHD/parameters.jl b/src/GRHD/parameters.jl
deleted file mode 100644
index e69de29b..00000000
diff --git a/src/GRHD/rhs.jl b/src/GRHD/rhs.jl
index ffa15f28..6f6d8532 100644
--- a/src/GRHD/rhs.jl
+++ b/src/GRHD/rhs.jl
@@ -2,49 +2,51 @@
# Timestep #
#######################################################################
+function compute_maxspeed(::Project{:spherical1d}, equation, mesh)
+ broadcast_volume!(maxspeed, equation, mesh)
+end
+function compute_maxspeed(::Project{:rescaled_spherical1d}, equation, mesh)
+ broadcast_volume!(maxspeed_rescaled_spherical1d, equation, mesh)
+end
-function timestep(env, P::Project, hrsc::Maybe{HRSC.AbstractHRSC})
- @unpack cache, mesh = env
- @unpack equation = P
- @unpack max_v = get_static_variables(cache)
-
- broadcast_volume!(cons2prim, equation, cache)
- broadcast_volume!(speed, equation, cache)
- vmax = dg1d.absolute_maximum(max_v)
- vmax_limit = 0.9999
+function get_maxspeed(mesh, equation)
+ @unpack max_v = get_static_variables(mesh.cache)
+ vmax = maximum(abs, max_v)
+ vmax_limit = 0.99999999999
if vmax > vmax_limit
@warn "Limiting timestep due to maximum speed exceeding $vmax_limit"
vmax = vmax_limit
end
+ return vmax
+end
- @unpack dl, x, element = mesh
- @unpack N = element
-
- dt = dl / (N^2 * vmax)
+function timestep(mesh, P::Project, hrsc::Maybe{HRSC.AbstractHRSC})
+ compute_maxspeed(P, P.equation, mesh)
+ vmax = get_maxspeed(mesh, P.equation)
+ dl = min_grid_spacing(mesh)
+ dt = dl / (vmax * dtfactor(mesh))
return dt
end
+dtfactor(mesh::Mesh1d{FVElement}) = 2
+dtfactor(mesh::Mesh1d{SpectralElement}) = mesh.element.N
-function timestep(env, P::Project, hrsc::HRSC.AbstractArtificialViscosity)
- @unpack cache, mesh = env
+function timestep(mesh, P::Project, hrsc::HRSC.AbstractArtificialViscosity)
+ @unpack cache = mesh
@unpack equation = P
- broadcast_volume!(cons2prim, equation, cache)
- broadcast_volume!(speed, equation, cache)
- max_v = get_variable(cache, :max_v)
- vmax = dg1d.absolute_maximum(view(max_v,:))
- vmax_limit = 0.9999
- if vmax > vmax_limit
- @warn "Limiting timestep due to maximum speed exceeding $vmax_limit"
- vmax = vmax_limit
- end
- smoothed_mu = get_variable(cache, :smoothed_mu)
- mumax = dg1d.absolute_maximum(view(smoothed_mu, :))
+ compute_maxspeed(P, P.equation, mesh)
+ vmax = get_maxspeed(mesh, P.equation)
+ @unpack mu = get_static_variables
+ mumax = maximum(abs, mu)
- @unpack dl, x, element = mesh
+ @unpack element = mesh
@unpack N = element
+ L, = dg1d.widths(mesh)
+ K, = mesh.tree.dims
+ dL = L/K
- dt = 1 / (vmax * N / dl + mumax * N^3 / dl^2)
+ dt = 1 / (vmax * N / dL + mumax * N^3 / dL^2)
dt_limit = 1e-7
if dt < dt_limit
@warn "Limiting timestep due to dt being smaller than $dt_limit"
@@ -59,38 +61,140 @@ end
#######################################################################
-function rhs!(env, P::Project, hrsc::Nothing, bdryconds, ldg_bdryconds, av_bdryconds)
+function rhs!(mesh::Mesh1d{FVElement}, P::Project{:spherical1d}, hrsc::Nothing)
- @unpack cache, mesh = env
- @unpack equation, rsolver = P
+ @unpack cache = mesh
+ @unpack equation = P
- @unpack sD, sSr, stau = get_dynamic_variables(cache)
- @unpack flx_sD, flx_sSr, flx_stau = get_static_variables(cache)
- @unpack rhs_sD, rhs_sSr, rhs_stau = get_rhs_variables(cache)
- @unpack lhs_numflx_sD, rhs_numflx_sD,
- lhs_numflx_sSr, rhs_numflx_sSr,
- lhs_numflx_stau, rhs_numflx_stau = get_bdry_variables(cache)
+ @unpack D, Sr, Ï„ = get_dynamic_variables(cache)
+ @unpack flr_D, flr_Sr, flr_Ï„,
+ max_v, Ï, ϵ, vr, p,
+ src_D, src_Sr, src_Ï„ = get_static_variables(cache)
+ @unpack rhs_D, rhs_Sr, rhs_Ï„ = get_rhs_variables(cache)
+ @unpack nflr_D, nflr_Sr, nflr_Ï„,
+ bdry_D, bdry_Sr, bdry_Ï„ = get_bdry_variables(cache)
- broadcast_volume!(scaledcons2cons, equation, cache)
- postprocess_scaledcons2cons!(cache, equation, mesh)
- broadcast_volume!(cons2prim, equation, cache)
- broadcast_volume!(flux, equation, cache)
- broadcast_volume!(sources, equation, cache)
- broadcast_faces!(lax_friedrich_flux, rsolver, cache, mesh)
- broadcast_boundaryconditions!(lax_friedrich_flux, bdryconds, cache, mesh, 0.0)
+ broadcast_volume!(cons2prim, equation, mesh)
+ broadcast_volume!(maxspeed, equation, mesh)
+ broadcast_volume!(flux_source_spherical1d, equation, mesh)
+ broadcast_bdry!(fv_bdry_flux, equation, mesh)
- @unpack p, vr, rho, eps = get_static_variables(cache)
+ dt = timestep(mesh, P, hrsc)
+ fv_update_step!(rhs_D, D, flr_D, src_D, bdry_D, nflr_D, dt, mesh)
+ fv_update_step!(rhs_Sr, Sr, flr_Sr, src_Sr, bdry_Sr, nflr_Sr, dt, mesh)
+ fv_update_step!(rhs_Ï„, Ï„, flr_Ï„, src_Ï„, bdry_Ï„, nflr_Ï„, dt, mesh)
+
+ return
+end
+
+
+function rhs!(mesh::Mesh1d, P::Project{:spherical1d}, hrsc::Nothing)
+
+ @unpack cache = mesh
+ @unpack equation = P
+
+ @unpack D, Sr, Ï„ = get_dynamic_variables(cache)
+ @unpack rhs_D, rhs_Sr, rhs_Ï„ = get_rhs_variables(cache)
+ @unpack flr_D, flr_Sr, flr_Ï„,
+ max_v, vr, p,
+ src_D, src_Sr, src_Ï„ = get_static_variables(cache)
+ @unpack nflr_D, nflr_Sr, nflr_Ï„,
+ bdry_D, bdry_Sr, bdry_Ï„,
+ bdry_max_v, bdry_vr, bdry_p = get_bdry_variables(cache)
+
+ broadcast_volume!(cons2prim, equation, mesh)
+ broadcast_volume!(maxspeed, equation, mesh)
+
+ dg1d.interpolate_face_data!(mesh, D, bdry_D)
+ dg1d.interpolate_face_data!(mesh, Sr, bdry_Sr)
+ dg1d.interpolate_face_data!(mesh, Ï„, bdry_Ï„)
+ dg1d.interpolate_face_data!(mesh, max_v, bdry_max_v)
+ dg1d.interpolate_face_data!(mesh, vr, bdry_vr)
+ dg1d.interpolate_face_data!(mesh, p, bdry_p)
+
+ broadcast_volume!(flux_source_spherical1d, equation, mesh)
+ impose_symmetry_sources!(P, mesh)
+ broadcast_faces!(llf, equation, mesh)
+ broadcast_bdry!(bdryllf, equation, mesh)
+
+ compute_rhs_weak_form!(rhs_D, flr_D, src_D, nflr_D, mesh)
+ compute_rhs_weak_form!(rhs_Sr, flr_Sr, src_Sr, nflr_Sr, mesh)
+ compute_rhs_weak_form!(rhs_Ï„, flr_Ï„, src_Ï„, nflr_Ï„, mesh)
+
+ return
+end
- compute_rhs_weak_form!(rhs_sD, flx_sD, lhs_numflx_sD, rhs_numflx_sD, mesh)
- compute_rhs_weak_form!(rhs_sSr, flx_sSr, lhs_numflx_sSr, rhs_numflx_sSr, mesh)
- compute_rhs_weak_form!(rhs_stau, flx_stau, lhs_numflx_stau, rhs_numflx_stau, mesh)
+
+function rhs!(mesh::Mesh1d{FVElement}, P::Project{:rescaled_spherical1d}, hrsc::Nothing)
+
+ @unpack cache = mesh
+ @unpack equation = P
+
+ @unpack rD, rSr, rτ = get_dynamic_variables(cache)
+ @unpack flr_rD, flr_rSr, flr_rτ,
+ D, Sr, Ï„,
+ src_rD, src_rSr, src_rτ = get_static_variables(cache)
+ @unpack rhs_rD, rhs_rSr, rhs_rτ = get_rhs_variables(cache)
+ @unpack nflr_rD, nflr_rSr, nflr_rτ,
+ bdry_D, bdry_Sr, bdry_Ï„ = get_bdry_variables(cache)
+
+ broadcast_volume!(unscale_conservatives, equation, mesh)
+ impose_symmetry!(P, mesh)
+ broadcast_volume!(cons2prim_rescaled_spherical1d, equation, mesh)
+ broadcast_volume!(maxspeed_rescaled_spherical1d, equation, mesh)
+ broadcast_volume!(flux_source_rescaled_spherical1d, equation, mesh)
+ broadcast_bdry!(fv_bdry_flux_rescaled_spherical1d, equation, mesh)
+
+ dt = timestep(mesh, P, hrsc)
+ fv_update_step!(rhs_rD, rD, flr_rD, src_rD, bdry_D, nflr_rD, dt, mesh)
+ fv_update_step!(rhs_rSr, rSr, flr_rSr, src_rSr, bdry_Sr, nflr_rSr, dt, mesh)
+ fv_update_step!(rhs_rτ, rτ, flr_rτ, src_rτ, bdry_τ, nflr_rτ, dt, mesh)
+
+ return
+end
+
+
+function rhs!(mesh::Mesh1d, P::Project{:rescaled_spherical1d}, hrsc::Nothing)
+
+ @unpack cache = mesh
+ @unpack equation = P
+
+ @unpack rD, rSr, rτ = get_dynamic_variables(cache)
+ @unpack rhs_rD, rhs_rSr, rhs_rτ = get_rhs_variables(cache)
+ @unpack flr_rD, flr_rSr, flr_rτ,
+ max_v, vr, p, D, Sr, Ï„,
+ src_rD, src_rSr, src_rτ = get_static_variables(cache)
+ @unpack nflr_rD, nflr_rSr, nflr_rτ,
+ bdry_D, bdry_Sr, bdry_Ï„,
+ bdry_max_v, bdry_vr, bdry_p = get_bdry_variables(cache)
+
+ broadcast_volume!(unscale_conservatives, equation, mesh)
+ impose_symmetry!(P, mesh)
+ broadcast_volume!(cons2prim_rescaled_spherical1d, equation, mesh)
+ broadcast_volume!(maxspeed_rescaled_spherical1d, equation, mesh)
+
+ dg1d.interpolate_face_data!(mesh, D, bdry_D)
+ dg1d.interpolate_face_data!(mesh, Sr, bdry_Sr)
+ dg1d.interpolate_face_data!(mesh, Ï„, bdry_Ï„)
+ dg1d.interpolate_face_data!(mesh, max_v, bdry_max_v)
+ dg1d.interpolate_face_data!(mesh, vr, bdry_vr)
+ dg1d.interpolate_face_data!(mesh, p, bdry_p)
+
+ broadcast_volume!(flux_source_rescaled_spherical1d, equation, mesh)
+ broadcast_faces!(llf_rescaled_spherical1d, equation, mesh)
+ broadcast_bdry!(bdryllf_rescaled_spherical1d, equation, mesh)
+
+ compute_rhs_weak_form!(rhs_rD, flr_rD, src_rD, nflr_rD, mesh)
+ compute_rhs_weak_form!(rhs_rSr, flr_rSr, src_rSr, nflr_rSr, mesh)
+ compute_rhs_weak_form!(rhs_rτ, flr_rτ, src_rτ, nflr_rτ, mesh)
return
end
-function rhs!(env, P::Project, hrsc::HRSC.AbstractReconstruction,
- bdryconds, ldg_bdryconds, av_bdryconds)
+function rhs!(env, P::Project, hrsc::HRSC.AbstractReconstruction)
+
+ TODO()
@unpack cache, mesh = env
@unpack equation, rsolver = P
@@ -122,8 +226,9 @@ function rhs!(env, P::Project, hrsc::HRSC.AbstractReconstruction,
end
-function rhs!(env, P::Project, hrsc::HRSC.AbstractArtificialViscosity,
- bdryconds, ldg_bdryconds, av_bdryconds)
+function rhs!(env, P::Project, hrsc::HRSC.AbstractArtificialViscosity)
+
+ TODO()
@unpack cache, mesh = env
@unpack equation, rsolver, ldg_rsolver, av_rsolver = P
diff --git a/src/GRHD/setup.jl b/src/GRHD/setup.jl
index 92c0a10f..f46e1199 100644
--- a/src/GRHD/setup.jl
+++ b/src/GRHD/setup.jl
@@ -2,87 +2,28 @@ function Project(env::Environment, prms)
# construct Project
eos = EquationOfState.make_EquationOfState(prms["EquationOfState"])
- equation = Equation(eos, prms["GRHD"])
+ equation = make_Equation(eos, prms["GRHD"], env.mesh)
tci = TCI.make_TCI(env.mesh, prms["TCI"])
hrsc = HRSC.make_HRSC(env.mesh, prms["HRSC"])
- rsolver = ApproxRiemannSolver(flux, speed, equation)
- ldg_rsolver, av_rsolver = if hrsc isa AbstractArtificialViscosity
- ApproxRiemannSolver(ldg_flux, ldg_speed, equation),
- ApproxRiemannSolver(av_flux, av_flux, equation)
- else
- nothing, nothing
- end
- P = Project(equation, hrsc, tci, rsolver, ldg_rsolver, av_rsolver)
+ fixedprms = (;)
+ formulation = prms["GRHD"]["formulation"]
+ P = Project(Symbol(formulation), equation, hrsc, tci, fixedprms)
# register variables
- # TODO add a ::Nothing overload for register_variables!
- # TODO Somehow replace _register_variables! with register_variables!
@unpack cache = env
- _register_variables!(cache, P)
- register_variables!(cache, rsolver)
- !isnothing(ldg_rsolver) && register_variables!(cache, ldg_rsolver)
- !isnothing(av_rsolver) && register_variables!(cache, av_rsolver, dont_register=true)
+ register!(cache, P)
display(cache)
# setup initial data
initialdata!(env, P, prms["GRHD"])
- # TODO Bdry conditions should be moved to project and should only be just a 'lightweight'
- # descriptor. Furthermore, they should also register variables in cache themselves.
- # Note: Atm, only the 'from_initial_data' option would require a place to store the data
- # somewhere. For periodic BCs we don't need extra storage at all.
- # But what other types of boundary conditions will be needed in the future?
-
- # setup boundary conditions
- bdryconds = make_BoundaryConditions(env, equation, rsolver, prms)
- ldg_bdryconds, av_bdryconds = if hrsc isa AbstractArtificialViscosity
- make_BoundaryConditions_LDG(env, equation, ldg_rsolver, prms),
- make_BoundaryConditions_LDG(env, equation, av_rsolver, prms)
- else
- nothing, nothing
- end
-
# setup callbacks
- projectcb = make_callback(env, P, bdryconds)
-
- # artificially smooth initial data
- # TODO Move this into make_callback
- smoother_called = false
- function id_smoother_fn(u, t)
- if !smoother_called
- println("Smoothing initial data...")
- @unpack sD, sSr, stau = get_dynamic_variables(cache)
- @unpack flag = get_cell_variables(cache)
- id_hrsc = HRSC.BernsteinReconstruction(env.mesh)
- HRSC.reconstruct!(sD, flag, id_hrsc, isperiodic=isperiodic(bdryconds))
- HRSC.reconstruct!(sSr, flag, id_hrsc, isperiodic=isperiodic(bdryconds))
- HRSC.reconstruct!(stau, flag, id_hrsc, isperiodic=isperiodic(bdryconds))
- smoother_called = true
- broadcast_volume!(cons2prim, equation, cache)
- end
- end
- id_smoother_cb = FunctionCallback(id_smoother_fn,
- CallbackTiming(every_iteration=1))
-
- append!(env.callbacks, CallbackSet(projectcb.callbacks..., id_smoother_cb))
-
- return P, (bdryconds, ldg_bdryconds, av_bdryconds)
-end
+ projectcb = make_callback(env, P, isperiodic(env.mesh))
+ append!(env.callbacks, CallbackSet(projectcb.callbacks...))
-function Equation(eos, prms)
- @unpack atm_factor, atm_threshold_factor = prms
- if atm_factor < 0
- error("GRHD: atm_factor must be positive, found 'atm_factor = $atm_factor'")
- end
- if atm_threshold_factor < 0
- error("GRHD: atm_threshold_factor must be positive, found 'atm_threshold_factor = $atm_threshold_factor'")
- end
- cons2prim_newtonsolver = dg1d.NewtonSolver(approx_derivative=true)
- cons2prim_bisection = dg1d.Bisection()
- return Equation(eos, -1.0, atm_factor, atm_threshold_factor,
- cons2prim_newtonsolver, cons2prim_bisection)
+ return P, nothing
end
@@ -91,64 +32,113 @@ end
#######################################################################
-# Julia limitation/bug: Overloading imported functions without their Module prefix shadows their
-# definition in this module without a warning or error. This does not happen for methods
-# defined in Base.
-# Because of that we prefix with _ below.
-# Cf. https://github.com/JuliaLang/julia/issues/15510
-function _register_variables!(cache, P::Project)
+function register!(cache, P::Project)
+ register_evolution!(cache, P)
+ register_metricvars!(cache, P)
+ register_hrsc!(cache, P, P.hrsc)
+ register_tci!(cache, P, P.tci)
+end
+
+
+function register_evolution!(cache, P::Project{:spherical1d})
+ register_variables!(cache,
+ dynamic_variablenames = (:D, :Sr, :Ï„,),
+ rhs_variablenames = (:rhs_D, :rhs_Sr, :rhs_Ï„), # rhs of conservatives
+ static_variablenames = (:flr_D, :flr_Sr, :flr_Ï„, # conservatives' fluxes
+ :src_D, :src_Sr, :src_Ï„, # sources
+ :Ï, :vr, :p, :ϵ, # primitives
+ :max_v, :r, # maximum charactersitic speed, radius
+ :init_D, :init_Sr, :init_Ï„, :init_max_v, :init_vr, :init_p),
+ bdry_variablenames = (:bdry_D, :bdry_Sr, :bdry_Ï„,
+ :bdry_Ï, :bdry_ϵ, :bdry_vr, :bdry_p,
+ :bdry_max_v,
+ :nflr_D, :nflr_Sr, :nflr_Ï„),
+ cell_variablenames = (:cellmax_v,),
+ global_variablenames = (:t, :tm1) # time steps
+ )
+ @unpack r, x = get_static_variables(cache)
+ r .= x
+end
+function register_evolution!(cache, P::Project{:rescaled_spherical1d})
register_variables!(cache,
- dynamic_variablenames = (:sD, :sSr, :stau,), # 'scaled' conservatives
- rhs_variablenames = (:rhs_sD, :rhs_sSr, :rhs_stau), # rhs of conservatives
- static_variablenames = (:flx_sD, :flx_sSr, :flx_stau, # conservatives' fluxes
- :src_sD, :src_sSr, :src_stau, # sources
- :D, :Sr, :tau, # true hydrodynamic conservatives
- :rho, :vr, :p, :eps, # primitives
- :max_v, :r, # maximum charactersitic speed, grid
- :E, :Em1, # entropy
- :flx_E, :flx_Em1, # entropy flux
- :A, :B, :A_r, :B_r), # metric fields and derivatives
+ dynamic_variablenames = (:rD, :rSr, :rτ,), # we evolve rescaled variables
+ rhs_variablenames = (:rhs_rD, :rhs_rSr, :rhs_rτ), # rhs of conservatives
+ static_variablenames = (:flr_rD, :flr_rSr, :flr_rτ, # conservatives' fluxes
+ :src_rD, :src_rSr, :src_rτ, # sources
+ :D, :Sr, :Ï„, # conserved variables
+ :Ï, :vr, :p, :ϵ, # primitives
+ :max_v, :r, # maximum charactersitic speed, radius
+ :init_D, :init_Sr, :init_Ï„, :init_max_v, :init_vr, :init_p),
+ bdry_variablenames = (:bdry_D, :bdry_Sr, :bdry_Ï„,
+ :bdry_Ï, :bdry_ϵ, :bdry_vr, :bdry_p,
+ :bdry_max_v,
+ :nflr_rD, :nflr_rSr, :nflr_rτ),
cell_variablenames = (:cellmax_v,),
global_variablenames = (:t, :tm1) # time steps
)
- _register_variables!(cache, P.hrsc)
- _register_variables!(cache, P.tci)
- # @unpack r = get_static_variables(cache)
+ @unpack r, x = get_static_variables(cache)
+ r .= x
end
-function _register_variables!(P, tci_or_hrsc::Nothing) end
+function register_metricvars!(cache, P::Project{:spherical1d})
+ register_variables!(cache,
+ static_variablenames = (:α, :βru,
+ :γrr, :γθθ, :γϕϕ,
+ :Krr, :Kθθ, :Kϕϕ,
+ :Γrrr, :Γrθθ, :Γrϕϕ, :Γθrθ, :Γθϕϕ, :Γϕrϕ, :Γϕθϕ,
+ :∂αr, :∂βrrdu,
+ :∂γrrr, :∂γrθθ, :∂γrϕϕ, :∂γθϕϕ,)
+ )
+end
+function register_metricvars!(cache, P::Project{:rescaled_spherical1d})
+ register_variables!(cache,
+ static_variablenames = (:A, :∂Ar, :B, :∂Br)
+ )
+end
-_register_variables!(P, hrsc::AbstractHRSC) =
- error("_register_variables: Not implemented for hrsc of type '$(typeof(hrsc))'")
+# TODO Where to put these? Can be needed by either HRSC or TCI.
+# :E, :Em1, # entropy
+# :flx_E, :flx_Em1, # entropy flux
-_register_variables!(P, hrsc::HRSC.AbstractReconstruction) = nothing
+#######################################################################
+# HRSC #
+#######################################################################
-function _register_variables!(cache, hrsc::HRSC.AbstractArtificialViscosity)
+
+register_hrsc!(cache, P, hrsc::Nothing) = nothing
+register_hrsc!(cache, P, hrsc::AbstractHRSC) = TODO(hrsc)
+function register_hrsc!(cache, P, hrsc::HRSC.AbstractArtificialViscosity)
+ TODO(hrsc)
register_variables!(cache,
static_variablenames = (:ldg_sD, :ldg_sSr, :ldg_stau, # local DG variable
:flx_ldg_sD, :flx_ldg_sSr, :flx_ldg_stau), # local DG flux
cell_variablenames = (:mu,), # 'one viscosity to rule them all'
)
end
-
-
-function _register_variables!(cache, hrsc::HRSC.SmoothedArtificialViscosity)
- _register_variables!(cache, hrsc.av)
+function register_hrsc!(cache, P, hrsc::HRSC.SmoothedArtificialViscosity)
+ TODO(hrsc)
+ register_hrsc!(cache, P, hrsc.av)
register_variables!(cache,
static_variablenames = (:smoothed_mu,)
)
end
-function _register_variables!(cache, tci::TCI.AbstractTCI)
- register_variables!(cache, cell_variablenames = (:flag,:sD_flag,:sSr_flag,:stau_flag))
-end
+#######################################################################
+# TCI #
+#######################################################################
-function _register_variables!(cache, tci::TCI.EntropyProduction)
+register_tci!(cache, P, tci::Maybe{HRSC.AbstractReconstruction}) = nothing
+function register_tci!(cache, P, tci::TCI.AbstractTCI)
+ TODO(tci)
+ register_variables!(cache, cell_variablenames = (:flag,:sD_flag,:sSr_flag,:stau_flag))
+end
+function register_tci!(cache, P, tci::TCI.EntropyProduction)
+ TODO(tci)
register_variables!(cache,
cell_variablenames = (:flag,),
static_variablenames = (:EP,), # entropy production
diff --git a/src/GRHD/types.jl b/src/GRHD/types.jl
index 06831cc3..d22aeed2 100644
--- a/src/GRHD/types.jl
+++ b/src/GRHD/types.jl
@@ -3,21 +3,20 @@ mutable struct Equation{T_EoS<:AbstractEquationOfState} <: AbstractEquation
atm_density::Float64
atm_factor::Float64
atm_threshold::Float64
- cons2prim_newtonsolver::dg1d.NewtonSolver
- cons2prim_bisection::dg1d.Bisection
end
-struct Project{T_HRSC <:Maybe{HRSC.AbstractHRSC},
- T_TCI <:Maybe{TCI.AbstractTCI},
- T_RSolver <:AbstractRiemannSolver,
- T_LDG_RSolver <:Maybe{AbstractRiemannSolver},
- T_AV_RSolver <:Maybe{AbstractRiemannSolver}} <: dg1d.AbstractProject
-
- equation::Equation
+struct Project{Formulation,
+ T_Eq <:AbstractEquation,
+ T_HRSC <:Maybe{HRSC.AbstractHRSC},
+ T_TCI <:Maybe{TCI.AbstractTCI},
+ T_Prms}
+ equation::T_Eq
hrsc::T_HRSC
tci::T_TCI
- rsolver::T_RSolver
- ldg_rsolver::T_LDG_RSolver
- av_rsolver::T_AV_RSolver
+ prms::T_Prms
end
+Project(formulation, fields...) = Project{formulation,typeof.(fields)...}(fields...)
+
+
+formulation(::Project{F}) where F = F
diff --git a/src/SRHD/SRHD.jl b/src/SRHD/SRHD.jl
index bb48cc90..4e60be28 100644
--- a/src/SRHD/SRHD.jl
+++ b/src/SRHD/SRHD.jl
@@ -1,3 +1,4 @@
+export SRHD
module SRHD
diff --git a/src/dg1d.jl b/src/dg1d.jl
index e237e337..fe3ecd54 100644
--- a/src/dg1d.jl
+++ b/src/dg1d.jl
@@ -151,7 +151,7 @@ include("ScalarEq/ScalarEq.jl")
include("HeatEq/HeatEq.jl")
include("EulerEq/EulerEq.jl")
include("SRHD/SRHD.jl")
-# include("GRHD/GRHD.jl")
+include("GRHD/GRHD.jl")
end # module
diff --git a/src/fv_rhs.jl b/src/fv_rhs.jl
index 3c30ffca..f0c7f514 100644
--- a/src/fv_rhs.jl
+++ b/src/fv_rhs.jl
@@ -27,20 +27,7 @@ function fv_update_step!(up1, u, f, bdry_u, bdry_f, dt, mesh::Mesh1d{FVElement})
end
-function fv_update_step!(up1, u, f, s, bdry_u, bdry_f, bdry_s, dt, mesh::Mesh1d{FVElement})
- TODO()
- @unpack invjac = mesh
- @unpack K = mesh
- dl = widths(mesh)[1] / K
- dtdl = dt/dl
- @turbo for j = 2:K-1
- up1[j] = (u[j+1] + 2*u[j] + u[j-1])/4 - dtdl/2 * (f[j+1] - f[j-1]) + s[j]
- end
- if mesh.tree.periodic[1]
- up1[1] = (u[2] + 2*u[1] + u[end])/4 - dtdl/2 * (f[2] - f[end]) + s[1]
- up1[end] = (u[1] + 2*u[end] + u[end-1])/4 - dtdl/2 * (f[1] - f[end-1]) + s[end]
- else
- TODO()
- end
- return
+function fv_update_step!(up1, u, f, s, bdry_u, bdry_f, dt, mesh::Mesh1d{FVElement})
+ fv_update_step!(up1, u, f, bdry_u, bdry_f, dt, mesh)
+ up1 .+= s
end
diff --git a/src/mesh.jl b/src/mesh.jl
index 3420cedc..7c57d21f 100644
--- a/src/mesh.jl
+++ b/src/mesh.jl
@@ -404,6 +404,41 @@ norm_L2(u, mesh::Mesh) = sqrt(broken_inner_product(u, u, mesh))
norm_L1(u, mesh::Mesh) = broken_inner_product(abs.(u), ones(Float64, size(u)), mesh)
+function differentiate!(du, u, mesh::Mesh1d)
+ @unpack invdetJ = get_static_variables(mesh.cache)
+ for (duk,uk,invdetJk) in zip(eachcell(mesh,du),eachcell(mesh,u),eachcell(mesh,invdetJ))
+ differentiate!(duk, uk, mesh.element)
+ duk .*= invdetJk
+ end
+end
+function differentiate!(du, u, mesh::Mesh1d{FVElement})
+ @unpack x, invdetJ = get_static_variables(mesh.cache)
+ K, = mesh.tree.dims
+ for k in 2:K-1
+ du[k] = (u[k+1]-u[k-1])/(x[k+1]-x[k-1])
+ end
+ x1, x2, x3 = x[1], x[2], x[3]
+ M = [ 1 x1 x1^2;
+ 1 x2 x2^2;
+ 1 x3 x3^2 ]
+ uu = u[1:3]
+ b = M \ uu
+ du[1] = b[2] + 2*b[3]*x1
+ x1, x2, x3 = x[end], x[end-1], x[end-2]
+ M = [ 1 x1 x1^2;
+ 1 x2 x2^2;
+ 1 x3 x3^2 ]
+ uu = u[end:-1:end-2]
+ b = M \ uu
+ du[end] = b[2] + 2*b[3]*x1
+end
+function differentiate(u, mesh)
+ du = similar(u)
+ differentiate!(du, u, mesh)
+ return du
+end
+
+
"""
find_nearest(xi, mesh::Mesh)
@@ -571,7 +606,7 @@ end
struct CellDataIterator{M<:AbstractMesh,A<:AbstractArray}
mesh::M
- data::A
+ data::A # TODO Replace with NTuple{N,A} to allow iterating multiple arrays at once
function CellDataIterator(m::AbstractMesh, a::AbstractArray)
@toggled_assert length(m) == length(a)
return new{typeof(m),typeof(a)}(m,a)
diff --git a/src/sandbox.jl b/src/sandbox.jl
index 403fd0a1..c748c9b7 100644
--- a/src/sandbox.jl
+++ b/src/sandbox.jl
@@ -6,6 +6,8 @@ const BLACKLISTED_TOKENS = [ "function", "using", "import", "struct", "mutable",
"if", "else", "elseif", "try", "catch", "Main", "module",
"dg1d", "println", "print", "display", "show" ]
+const ROOTDIR = joinpath(@__DIR__, "..")
+
# rudimentary protection against arbitrary code execution
function has_blacklisted_tokens(str)
diff --git a/src/spectralelement.jl b/src/spectralelement.jl
index 66170c38..ded604c1 100644
--- a/src/spectralelement.jl
+++ b/src/spectralelement.jl
@@ -93,3 +93,12 @@ end
return GLGL.integrate(el.w, el.v, el.D, u)
end
end
+
+
+@inline function differentiate(u, el::SpectralElement)
+ return el.D * u
+end
+
+@inline function differentiate!(du, u, el::SpectralElement)
+ mul!(du, el.D, u)
+end
diff --git a/test/IntegrationTests/refs/grhd_bondi_accretion/grhd_bondi_accretion.toml b/test/IntegrationTests/refs/grhd_bondi_accretion/grhd_bondi_accretion.toml
new file mode 100644
index 00000000..1a2307c9
--- /dev/null
+++ b/test/IntegrationTests/refs/grhd_bondi_accretion/grhd_bondi_accretion.toml
@@ -0,0 +1,25 @@
+[EquationOfState]
+eos = "polytrope"
+polytrope_k = 0.02143872868864732
+polytrope_gamma = "$(4/3)"
+
+[GRHD]
+bc = "from_id"
+id = "bondi_accretion"
+id_filename = "$(joinpath(ROOTDIR,\"initialdata\",\"bondi_accretion.h5\"))"
+
+[Mesh]
+range = [ 1.8, 10.0 ]
+n = 4
+k = 35
+basis = "lgl"
+periodic = false
+
+[Output]
+variables = [ "D", "Sr", "Ï„", "p", "Ï", "ϵ", "vr" ]
+aligned_ts = "$(collect(range(0.5,5.0,step=0.5)))"
+enable1d = true
+
+[Evolution]
+cfl = 0.8
+tend = 5.0
diff --git a/test/IntegrationTests/refs/grhd_bondi_accretion/output.h5 b/test/IntegrationTests/refs/grhd_bondi_accretion/output.h5
new file mode 100644
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GIT binary patch
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HcmV?d00001
diff --git a/test/IntegrationTests/refs/grhd_tov_spherical1d/grhd_tov_spherical1d.toml b/test/IntegrationTests/refs/grhd_tov_spherical1d/grhd_tov_spherical1d.toml
new file mode 100644
index 00000000..7f8831e0
--- /dev/null
+++ b/test/IntegrationTests/refs/grhd_tov_spherical1d/grhd_tov_spherical1d.toml
@@ -0,0 +1,27 @@
+[EquationOfState]
+eos = "polytrope"
+polytrope_k = 100.0
+polytrope_gamma = 2.0
+
+[GRHD]
+bc = "from_id"
+id = "tov"
+id_filename = "$(joinpath(ROOTDIR,\"initialdata\",\"TOV_stable.h5\"))"
+atm_factor = 1e-8
+formulation = "spherical1d"
+
+[Mesh]
+range = [ 0.0, 20.0 ]
+n = 4
+k = 124
+basis = "lgl"
+periodic = false
+
+[Output]
+variables = [ "D", "Sr", "Ï„" ]
+aligned_ts = "$(collect(range(2.5,10.0,step=2.5)))"
+enable1d = true
+
+[Evolution]
+cfl = 0.4
+tend = 10.0
diff --git a/test/IntegrationTests/refs/grhd_tov_spherical1d/output.h5 b/test/IntegrationTests/refs/grhd_tov_spherical1d/output.h5
new file mode 100644
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literal 0
HcmV?d00001
diff --git a/test/IntegrationTests/refs/testconfig.toml b/test/IntegrationTests/refs/testconfig.toml
index 68dda7e2..e3f1893e 100644
--- a/test/IntegrationTests/refs/testconfig.toml
+++ b/test/IntegrationTests/refs/testconfig.toml
@@ -76,6 +76,14 @@ reltol = 1e-6
variables = [ "D", "S", "tau" ]
reltol = 1e-6
+[grhd_bondi_accretion]
+# runs into discontinuity
+variables = [ "D", "Sr", "Ï„", "p", "Ï", "ϵ", "vr" ]
+
+[grhd_tov_spherical1d]
+# test does not use any hrsc method, so we can encounter garbage
+# but we are happy when it runs
+variables = []
# 2D tests
--
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