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Get["KrancThorn`"];
(*SetDebugLevel[InfoFull];*)
SetEnhancedTimes[False];
SetSourceLanguage["C"];
(****************************************************************************
Derivatives
****************************************************************************)
derivatives =
{
PDstandard2nd[i_] -> StandardCenteredDifferenceOperator[1,1,i],
PDstandard2nd[i_, i_] -> StandardCenteredDifferenceOperator[2,1,i],
PDstandard2nd[i_, j_] -> StandardCenteredDifferenceOperator[1,1,i] *
StandardCenteredDifferenceOperator[1,1,j],
PDstandard4th[i_] -> StandardCenteredDifferenceOperator[1,2,i],
PDstandard4th[i_, i_] -> StandardCenteredDifferenceOperator[2,2,i],
PDstandard4th[i_, j_] -> StandardCenteredDifferenceOperator[1,2,i] *
StandardCenteredDifferenceOperator[1,2,j],
PDplus[i_] -> DPlus[i],
PDminus[i_] -> DMinus[i],
PDplus[i_,j_] -> DPlus[i] DPlus[j],
PDonesided2nd[1] -> dir[1] (-shift[1]^(2 dir[1]) + 4 shift[1]^dir[1] - 3 )/
(2 spacing[1]),
PDonesided2nd[2] -> dir[2] (-shift[2]^(2 dir[2]) + 4 shift[2]^dir[2] - 3 )/
(2 spacing[2]),
PDonesided2nd[3] -> dir[3] (-shift[3]^(2 dir[3]) + 4 shift[3]^dir[3] - 3 )/
(2 spacing[3])
};
(*PD = PDstandard2nd;*)
(****************************************************************************
Tensors
****************************************************************************)
(* Register all the tensors that will be used with TensorTools *)
Map[DefineTensor,
{
rho, vel, eps, press,
dens, mom, tau
}];
(* Register the TensorTools symmetries (this is very simplistic) *)
Map[AssertSymmetricDecreasing,
{
}];
(* Determinants of the metrics in terms of their components
(Mathematica symbolic expressions) *)
gDet = Det[MatrixOfComponents[g[la,lb]]];
(****************************************************************************
Groups
****************************************************************************)
SetGroupTimelevels[g_,tl_] = Join[g, {Timelevels -> tl}];
evolvedGroups =
{CreateGroupFromTensor [dens ], (* mass density *)
CreateGroupFromTensor [mom[la]], (* momentum density *)
CreateGroupFromTensor [tau ]}; (* energy density *)
evaluatedGroups =
{CreateGroupFromTensor [rho ], (* mass density *)
CreateGroupFromTensor [vel[ua]], (* velocity *)
CreateGroupFromTensor [eps ], (* specific internal energy *)
CreateGroupFromTensor [press ]}; (* pressure *)
declaredGroups = Join [evolvedGroups, evaluatedGroups];
declaredGroupNames = Map [First, declaredGroups];
groups = Join[declaredGroups];
(******************************************************************************)
(* Initial data *)
(******************************************************************************)
initialCalc =
{
Name -> BSSN <> "_vacuum",
Schedule -> {"IN ADMBase_InitialData"},
ConditionalOnKeyword -> {"my_initial_data", "vacuum"},
Equations ->
{
rho -> 0,
vel[ua] -> 0,
eps -> 0
}
};
(******************************************************************************)
(* Convert from primitive to conserved variables *)
(******************************************************************************)
prim2conCalc =
{
Name -> BSSN <> "_con2prim",
Schedule -> {"AT initial AFTER ADMBase_PostInitial"},
Equations ->
{
dens -> rho,
mom[la] -> rho vel[ua],
tau -> (1/2) rho vel[ua] vel[la] + rho eps
}
};
(******************************************************************************)
(* Convert from conserved to primitive variables *)
(******************************************************************************)
con2primCalc =
{
Name -> BSSN <> "_con2prim",
Schedule -> {"IN " <> BSSN <>"_con2primGroup"},
Equations ->
{
rho -> dens,
vel[ua] -> mom[la] / dens,
eps -> tau / dens - (1/2) vel[ua] vel[la],
press -> Gamma rho eps +
alpha PD[vel[ua],la]
}
};
(******************************************************************************)
(* Evolution equations *)
(******************************************************************************)
evolCalc =
{
Name -> BSSN <> "_RHS",
Schedule -> {"IN " <> BSSN <>"_evolCalcGroup"},
Shorthands -> {rhov[ua], momv[la,ub], tauv[ua]},
Equations ->
{
(* dt rho + div rho v = 0 *)
rhov[ua] -> mom[la],
dot[dens] -> - PD[rhov[ua],la],
(* dt pi + div (pi v + P) = 0 *)
momv[la,ub] -> mom[la] vel[ub] + KD[la,ub] press,
dot[mom[la]] -> - PD[momv[la,ub],lb],
(* dt tau + div (tauv + P) = 0 *)
tauv[ua] -> tau vel[ua] + press vel[ua],
dot[tau] -> - PD[tauv[ua],la]
}
};
|
