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tex/upwind-flux.tex
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......@@ -167,6 +167,11 @@ to nonlinear systems of conservation laws and derive a
numerical flux function that is consistent with the PDE flux.
\todo{\cite{fontThreedimensionalNumericalGeneral2000} discusses flux limiting methods
for GRHD. The upwinding discussion there is similar to the one done here.
In particular, they also point out the assumption about homogenity of the fluxes,
is satisfied only for particular equation of states.}
\section{Basics}
\todo{
......
zotero.bib
+ 201
− 12
View file @ 4fba1395
......@@ -25,6 +25,24 @@
file = {/home/flo/Zotero/storage/97XTGQI3/Abbott - 2017 - Multi-messenger observations of a binary neutron s.pdf}
}
@article{alcubierreStableNumericalEvolution2000,
title = {Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: {{The}} Conformal Treatments},
shorttitle = {Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity},
author = {Alcubierre, Miguel and Brügmann, Bernd and Dramlitsch, Thomas and Font, José A. and Papadopoulos, Philippos and Seidel, Edward and Stergioulas, Nikolaos and Takahashi, Ryoji},
date = {2000-07-24},
journaltitle = {Physical Review D},
shortjournal = {Phys. Rev. D},
volume = {62},
number = {4},
pages = {044034},
issn = {0556-2821, 1089-4918},
doi = {10.1103/PhysRevD.62.044034},
url = {https://link.aps.org/doi/10.1103/PhysRevD.62.044034},
urldate = {2024-06-18},
langid = {english},
file = {/home/flo/Zotero/storage/326YRDNA/Alcubierre et al. - 2000 - Towards a stable numerical evolution of strongly g.pdf}
}
@article{alcubierreSymmetrySymmetryNumerical2001,
title = {Symmetry without Symmetry: {{Numerical}} Simulation of Axisymmetric Systems Using {{Cartesian}} Grids},
shorttitle = {{{SYMMETRY WITHOUT SYMMETRY}}},
......@@ -96,7 +114,7 @@
volume = {144},
number = {2},
eprint = {astro-ph/0206265},
eprinttype = {arxiv},
eprinttype = {arXiv},
pages = {243--257},
issn = {0067-0049, 1538-4365},
doi = {10.1086/344723},
......@@ -165,6 +183,23 @@
file = {/home/flo/Zotero/storage/3K49L6I9/Baiotti - 2004 - Numerical relativity simulations of non-vacuum spa.pdf;/home/flo/Zotero/storage/J2H5M7DL/Baiotti - 2004 - Numerical relativity simulations of non-vacuum spa.pdf}
}
@article{baiottiThreedimensionalRelativisticSimulations2005,
title = {Three-Dimensional Relativistic Simulations of Rotating Neutron-Star Collapse to a {{Kerr}} Black Hole},
author = {Baiotti, Luca and Hawke, Ian and Montero, Pedro J. and Löffler, Frank and Rezzolla, Luciano and Stergioulas, Nikolaos and Font, José A. and Seidel, Ed},
date = {2005-01-27},
journaltitle = {Physical Review D},
shortjournal = {Phys. Rev. D},
volume = {71},
number = {2},
pages = {024035},
issn = {1550-7998, 1550-2368},
doi = {10.1103/PhysRevD.71.024035},
url = {https://link.aps.org/doi/10.1103/PhysRevD.71.024035},
urldate = {2024-06-10},
langid = {english},
file = {/home/flo/Zotero/storage/5EGWUS6N/Baiotti et al. - 2005 - Three-dimensional relativistic simulations of rota.pdf}
}
@article{banyulsNumericalGeneralRelativistic1997,
title = {Numerical \{3+ 1\} General Relativistic Hydrodynamics: {{A}} Local Characteristic Approach},
shorttitle = {Numerical \{3+ 1\} General Relativistic Hydrodynamics},
......@@ -277,7 +312,8 @@
date = {2021},
publisher = {Cambridge University Press},
url = {https://books.google.de/books?hl=de&lr=&id=YPQgEAAAQBAJ&oi=fnd&pg=PR9&dq=baumgarte+from+scratch&ots=7EmVHj1xd5&sig=gmoocRPFQFMQlw8-Ky3kGzY9Ue4},
urldate = {2024-05-02}
urldate = {2024-05-02},
file = {/home/flo/Zotero/storage/84CVGU5J/Baumgarte and Shapiro - 2021 - Numerical relativity starting from scratch.pdf}
}
@article{bemficaCausalityExistenceSolutions2018,
......@@ -348,6 +384,15 @@
file = {/home/flo/Zotero/storage/LGGB9KIF/Bernuzzi et al. - 2012 - Tidal effects in binary neutron star coalescence.pdf}
}
@article{bezaresExoticCompactObjects2024,
title = {Exotic Compact Objects: A Recent Numerical-Relativity Perspective},
shorttitle = {Exotic Compact Objects},
author = {Bezares, Miguel and Sanchis-Gual, Nicolas},
date = {2024-06},
keywords = {binary,black hole,boson star,collapse,dark matter,gravitation,gravitational radiation,neutron star equation of state,new physics,singularity formation},
file = {/home/flo/Zotero/storage/EUP9BQWZ/Bezares and Sanchis-Gual - 2024 - Exotic compact objects a recent numerical-relativ.pdf}
}
@article{bezaresKdynamicsWellposedEvolutions2021,
title = {K-Dynamics: Well-Posed 1+ 1 Evolutions in {{K-essence}}},
shorttitle = {K-Dynamics},
......@@ -407,7 +452,7 @@
volume = {72},
number = {10},
eprint = {gr-qc/0509092},
eprinttype = {arxiv},
eprinttype = {arXiv},
pages = {104009},
issn = {1550-7998, 1550-2368},
doi = {10.1103/PhysRevD.72.104009},
......@@ -469,6 +514,17 @@
file = {/home/flo/Zotero/storage/VT2ECGHZ/Bona et al. - 2004 - Symmetry-breaking mechanism for the Z4 general-cov.pdf}
}
@article{bondiSphericallySymmetricalAccretion1952,
title = {On Spherically Symmetrical Accretion},
author = {Bondi, H.},
date = {1952},
journaltitle = {Mon. Not. Roy. Astron. Soc.},
volume = {112},
pages = {195},
doi = {10.1093/mnras/112.2.195},
file = {/home/flo/Zotero/storage/NHF4FT7Y/Bondi - 1952 - On spherically symmetrical accretion.pdf}
}
@book{boydChebyshevFourierSpectral2001,
title = {Chebyshev and {{Fourier}} Spectral Methods},
author = {Boyd, John P.},
......@@ -493,6 +549,19 @@
file = {/home/flo/Zotero/storage/Q6WJA5TE/Boyd - 1982 - The optimization of convergence for Chebyshev poly.pdf}
}
@article{brentAlgorithmGuaranteedConvergence1971,
title = {An Algorithm with Guaranteed Convergence for Finding a Zero of a Function},
author = {Brent, Richard P.},
date = {1971},
journaltitle = {The computer journal},
volume = {14},
number = {4},
pages = {422--425},
publisher = {Oxford University Press},
url = {https://academic.oup.com/comjnl/article-abstract/14/4/422/325237},
urldate = {2024-05-24}
}
@misc{brugmannNotesCartoonMethod2019,
title = {Notes on the Cartoon Method for Bamps},
author = {Brügmann, Bernd},
......@@ -758,7 +827,7 @@
volume = {72},
number = {2},
eprint = {astro-ph/0503420},
eprinttype = {arxiv},
eprinttype = {arXiv},
pages = {024028},
issn = {1550-7998, 1550-2368},
doi = {10.1103/PhysRevD.72.024028},
......@@ -774,7 +843,7 @@
author = {Dumbser, Michael and Zanotti, Olindo and Gaburro, Elena and Peshkov, Ilya},
date = {2024-02-21},
eprint = {2307.06629},
eprinttype = {arxiv},
eprinttype = {arXiv},
eprintclass = {gr-qc},
doi = {10.48550/arXiv.2307.06629},
url = {http://arxiv.org/abs/2307.06629},
......@@ -879,6 +948,21 @@
file = {/home/flo/Zotero/storage/88HTIQIM/Font et al. - 1994 - Multidimensional relativistic hydrodynamics chara.pdf}
}
@article{fontNonlinearHydrodynamicalEvolution2000,
title = {Non-Linear Hydrodynamical Evolution of Rotating Relativistic Stars: Numerical Methods and Code Tests},
shorttitle = {Non-Linear Hydrodynamical Evolution of Rotating Relativistic Stars},
author = {Font, Jose A. and Stergioulas, Nikolaos and Kokkotas, Kostas D.},
date = {2000},
journaltitle = {Monthly Notices of the Royal Astronomical Society},
volume = {313},
number = {4},
pages = {678--688},
publisher = {Blackwell Science Ltd Oxford, UK},
url = {https://academic.oup.com/mnras/article-abstract/313/4/678/1084948},
urldate = {2024-06-12},
file = {/home/flo/Zotero/storage/BLEXWTID/Font et al. - 2000 - Non-linear hydrodynamical evolution of rotating re.pdf}
}
@article{fontNumericalHydrodynamicsMagnetohydrodynamics2008,
title = {Numerical {{Hydrodynamics}} and {{Magnetohydrodynamics}} in {{General Relativity}}},
author = {Font, José A.},
......@@ -897,6 +981,24 @@
file = {/home/flo/Zotero/storage/VXVDDASB/Font - 2008 - Numerical Hydrodynamics and Magnetohydrodynamics i.pdf}
}
@article{fontThreedimensionalNumericalGeneral2000,
title = {Three-Dimensional Numerical General Relativistic Hydrodynamics: {{Formulations}}, Methods, and Code Tests},
shorttitle = {Three-Dimensional Numerical General Relativistic Hydrodynamics},
author = {Font, José A. and Miller, Mark and Suen, Wai-Mo and Tobias, Malcolm},
date = {2000-01-25},
journaltitle = {Physical Review D},
shortjournal = {Phys. Rev. D},
volume = {61},
number = {4},
pages = {044011},
issn = {0556-2821, 1089-4918},
doi = {10.1103/PhysRevD.61.044011},
url = {https://link.aps.org/doi/10.1103/PhysRevD.61.044011},
urldate = {2024-06-18},
langid = {english},
file = {/home/flo/Zotero/storage/PX75FJSU/Font et al. - 2000 - Three-dimensional numerical general relativistic h.pdf}
}
@article{fontThreedimensionalNumericalGeneral2002,
title = {Three-Dimensional Numerical General Relativistic Hydrodynamics. {{II}}. {{Long-term}} Dynamics of Single Relativistic Stars},
author = {Font, José A. and Goodale, Tom and Iyer, Sai and Miller, Mark and Rezzolla, Luciano and Seidel, Edward and Stergioulas, Nikolaos and Suen, Wai-Mo and Tobias, Malcolm},
......@@ -1002,6 +1104,17 @@
file = {/home/flo/Zotero/storage/MBQ79ZDS/Gautschi - 2011 - Numerical analysis.pdf}
}
@book{gautschiOrthogonalPolynomialsComputation2004,
title = {Orthogonal Polynomials: Computation and Approximation},
shorttitle = {Orthogonal Polynomials},
author = {Gautschi, Walter},
date = {2004},
publisher = {OUP Oxford},
url = {https://books.google.de/books?hl=de&lr=&id=fhRREAAAQBAJ&oi=fnd&pg=PR5&dq=gautschi+orthogonal+polynomials&ots=akvaLbeMVs&sig=7sxY-TKzL154-lDnLEwx0ZZKzIY},
urldate = {2024-06-17},
file = {/home/flo/Zotero/storage/8H2JDDNQ/Gautschi - 2004 - Orthogonal polynomials computation and approximat.pdf}
}
@book{glaubitzShockCapturingHighorder2020,
title = {Shock Capturing and High-Order Methods for Hyperbolic Conservation Laws},
author = {Glaubitz, Jan},
......@@ -1174,7 +1287,7 @@
shortjournal = {Journal of Computational Physics},
volume = {426},
eprint = {2008.12044},
eprinttype = {arxiv},
eprinttype = {arXiv},
eprintclass = {physics},
pages = {109935},
issn = {00219991},
......@@ -1388,7 +1501,7 @@
author = {Kastaun, Wolfgang and Ohme, Frank},
date = {2024-04-17},
eprint = {2404.11346},
eprinttype = {arxiv},
eprinttype = {arXiv},
eprintclass = {gr-qc},
url = {http://arxiv.org/abs/2404.11346},
urldate = {2024-04-26},
......@@ -1455,7 +1568,7 @@
volume = {2},
number = {1},
eprint = {gr-qc/9909058},
eprinttype = {arxiv},
eprinttype = {arXiv},
pages = {2},
issn = {2367-3613, 1433-8351},
doi = {10.12942/lrr-1999-2},
......@@ -1496,6 +1609,27 @@
file = {/home/flo/Zotero/storage/SF5QKFC8/Kovtun - 2019 - First-order relativistic hydrodynamics is stable.pdf}
}
@article{kovtunLecturesHydrodynamicFluctuations2012,
title = {Lectures on Hydrodynamic Fluctuations in Relativistic Theories},
author = {Kovtun, Pavel},
date = {2012-11-30},
journaltitle = {Journal of Physics A: Mathematical and Theoretical},
shortjournal = {J. Phys. A: Math. Theor.},
volume = {45},
number = {47},
eprint = {1205.5040},
eprinttype = {arXiv},
eprintclass = {hep-th},
pages = {473001},
issn = {1751-8113, 1751-8121},
doi = {10.1088/1751-8113/45/47/473001},
url = {http://arxiv.org/abs/1205.5040},
urldate = {2024-05-29},
abstract = {These are pedagogical lecture notes on hydrodynamic fluctuations in normal relativistic fluids. The lectures discuss correlation functions of conserved densities in thermal equilibrium, interactions of the hydrodynamic modes, an effective action for viscous fluids, and the breakdown of the derivative expansion in hydrodynamics.},
keywords = {High Energy Physics - Theory},
file = {/home/flo/Zotero/storage/3LSB8UWN/Kovtun - 2012 - Lectures on hydrodynamic fluctuations in relativis.pdf;/home/flo/Zotero/storage/R9Y99WL4/1205.html}
}
@book{landauFluidMechanicsLandau2013,
title = {Fluid Mechanics: {{Landau And Lifshitz}}: Course of Theoretical Physics, {{Volume}} 6},
shorttitle = {Fluid Mechanics},
......@@ -1622,7 +1756,7 @@
author = {Marouda, Krinio and Cors, Daniela and Rüter, Hannes R. and Atteneder, Florian and Hilditch, David},
date = {2024-02-09},
eprint = {2402.06724},
eprinttype = {arxiv},
eprinttype = {arXiv},
eprintclass = {gr-qc},
url = {http://arxiv.org/abs/2402.06724},
urldate = {2024-03-22},
......@@ -1741,7 +1875,7 @@
author = {Mielke, Eckehard W. and Schunck, Franz E.},
date = {1998-01-19},
eprint = {gr-qc/9801063},
eprinttype = {arxiv},
eprinttype = {arXiv},
doi = {10.48550/arXiv.gr-qc/9801063},
url = {http://arxiv.org/abs/gr-qc/9801063},
urldate = {2024-05-08},
......@@ -1931,6 +2065,23 @@
file = {/home/flo/Zotero/storage/82YCW9FY/Pilz - 2015 - A New ADER-DG Scheme based on a Local Continuous R.pdf}
}
@article{poudelIncreasingAccuracyBinary2020,
title = {Increasing the Accuracy of Binary Neutron Star Simulations with an Improved Vacuum Treatment},
author = {Poudel, Amit and Tichy, Wolfgang and Brügmann, Bernd and Dietrich, Tim},
date = {2020-11-06},
journaltitle = {Physical Review D},
shortjournal = {Phys. Rev. D},
volume = {102},
number = {10},
pages = {104014},
issn = {2470-0010, 2470-0029},
doi = {10.1103/PhysRevD.102.104014},
url = {https://link.aps.org/doi/10.1103/PhysRevD.102.104014},
urldate = {2024-06-10},
langid = {english},
file = {/home/flo/Zotero/storage/96MFQN87/Poudel et al. - 2020 - Increasing the accuracy of binary neutron star sim.pdf}
}
@article{pretoriusNumericalRelativityUsing2005,
title = {Numerical Relativity Using a Generalized Harmonic Decomposition},
author = {Pretorius, Frans},
......@@ -2045,6 +2196,20 @@
file = {/home/flo/Zotero/storage/YG3YQPXU/00329037.pdf}
}
@article{rosswogAstrophysicalSmoothParticle2009,
title = {Astrophysical Smooth Particle Hydrodynamics},
author = {Rosswog, Stephan},
date = {2009},
journaltitle = {New Astronomy Reviews},
volume = {53},
number = {4-6},
pages = {78--104},
publisher = {Elsevier},
url = {https://www.sciencedirect.com/science/article/pii/S1387647309000487?casa_token=jPHbzND_TncAAAAA:ml1btRYHPb1zwZ1a3L_8Z2WVWJzs1JkU8axdwPdGgaebD__vUMXOOlDMa3PSzjZiVVps3ikf},
urldate = {2024-06-10},
file = {/home/flo/Zotero/storage/YKZVDM3A/Rosswog - 2009 - Astrophysical smooth particle hydrodynamics.pdf;/home/flo/Zotero/storage/5WC4AA95/S1387647309000487.html}
}
@article{ruterHyperbolicRelaxationMethod2018,
title = {Hyperbolic Relaxation Method for Elliptic Equations},
author = {Rüter, Hannes R. and Hilditch, David and Bugner, Marcus and Brügmann, Bernd},
......@@ -2232,6 +2397,17 @@
file = {/home/flo/Zotero/storage/4LGIQ38X/Tolman - 1939 - Static Solutions of Einstein's Field Equations for.pdf}
}
@article{toroRiemannSolversNumerical1999,
title = {Riemann {{Solvers}} and {{Numerical Methods}} for {{Fluid Dynamics}}},
author = {Toro, Eleuterio F.},
date = {1999},
journaltitle = {Riemann Solvers and Numerical Methods for Fluid Dynamics},
publisher = {Springer Berlin Heidelberg},
url = {https://cir.nii.ac.jp/crid/1363670320418146048},
urldate = {2024-05-23},
file = {/home/flo/Zotero/storage/ZZ4V7H5N/Toro E.F. - Riemann Solvers and Numerical Methods for Fluid Dynamics-Springer (1999).djvu}
}
@book{toroRiemannSolversNumerical2013,
title = {Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction},
shorttitle = {Riemann Solvers and Numerical Methods for Fluid Dynamics},
......@@ -2239,8 +2415,7 @@
date = {2013},
publisher = {Springer Science \& Business Media},
url = {https://books.google.de/books?hl=de&lr=&id=zkLtCAAAQBAJ&oi=fnd&pg=PR5&dq=toro+riemann+solvers+and+numerical+methods+for+fluid&ots=SH5Etp-ZQ-&sig=6CQ-UsevIBNZNXA2QJG7NR-CNko},
urldate = {2024-02-27},
file = {/home/flo/Zotero/storage/ZZ4V7H5N/Toro E.F. - Riemann Solvers and Numerical Methods for Fluid Dynamics-Springer (1999).djvu}
urldate = {2024-02-27}
}
@article{valdez-alvaradoDynamicalEvolutionFermionboson2013,
......@@ -2341,6 +2516,20 @@
file = {/home/flo/Zotero/storage/NXVQCVCS/1972ApJ...173..431W.html}
}
@article{woodwardNumericalSimulationTwodimensional1984,
title = {The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks},
author = {Woodward, Paul and Colella, Phillip},
date = {1984},
journaltitle = {Journal of computational physics},
volume = {54},
number = {1},
pages = {115--173},
publisher = {Elsevier},
url = {https://www.sciencedirect.com/science/article/pii/0021999184901426},
urldate = {2024-05-23},
file = {/home/flo/Zotero/storage/YGK7LJU6/Woodward and Colella - 1984 - The numerical simulation of two-dimensional fluid .pdf}
}
@article{yuEffectsArtificialViscosity2018,
title = {Effects of Artificial Viscosity and Upwinding on Spectral Properties of the Discontinuous {{Galerkin}} Method},
author = {Yu, Jian and Yan, Chao and Jiang, Zhenhua},
......
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