fix source term in dg and fv rhs computation

src/dg_rhs.jl

@@ -26,7 +26,7 @@ function compute_rhs_weak_form!(rhs, f, nf, mesh::Mesh1d{SpectralElement})
 end
 function compute_rhs_weak_form!(rhs, f, s, nf, mesh::Mesh1d{SpectralElement})
   compute_rhs_weak_form!(rhs, f, nf, mesh)
-  rhs .+= s
+  rhs .-= s
   return
 end
 
@@ -229,6 +229,6 @@ function compute_rhs_weak_form!(rhs, _::Real, fy, nf, mesh::Mesh2d{SpectralEleme
 end
 function compute_rhs_weak_form!(rhs, fx, fy, s, nf, mesh::Mesh2d{SpectralElement})
   compute_rhs_weak_form!(rhs, fx, fy, nf, mesh)
-  rhs .+= s
+  rhs .-= s
   return
 end

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