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|
Get["KrancThorn`"];
SetEnhancedTimes[False];
(**************************************************************************************)
(* 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],
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]),
PDplus[i_] -> DPlus[i],
PDminus[i_] -> DMinus[i]
};
PD = PDstandard2nd;
(* PD = PDminus; *)
(**************************************************************************************)
(* Tensors *)
(**************************************************************************************)
(* Register the tensor quantities with the TensorTools package *)
Map[DefineTensor, {w, Frho, Fw, FEn, rho, En, p, dir, v}];
(**************************************************************************************)
(* Groups *)
(**************************************************************************************)
evolvedGroups = Map[CreateGroupFromTensor, {rho, w[uj], En, v[uj] (* This should not be here *) }];
nonevolvedGroups = Map[CreateGroupFromTensor, {Frho[ui], Fw[ui,uj], FEn[ui], p}];
declaredGroups = Join[evolvedGroups, nonevolvedGroups];
declaredGroupNames = Map[First, declaredGroups];
groups = Join[declaredGroups];
(**************************************************************************************)
(* Initial data *)
(**************************************************************************************)
initialSineCalc =
{
Name -> "euler_initial_sine",
Schedule -> {"at CCTK_INITIAL as euler_initial"},
ConditionalOnKeyword -> {"initial_data", "sine"},
Equations ->
{
v1 -> v0,
v2 -> 0,
v3 -> 0,
rho -> 1 + amp Sin[2 Pi x],
En -> 1
}
};
initialShockCalc =
{
Name -> "euler_initial_shock",
Schedule -> {"at CCTK_INITIAL as euler_initial"},
ConditionalOnKeyword -> {"initial_data", "shock"},
Equations ->
{
v1 -> 0.5 + 0.5 UnitStep[x-0.5],
v2 -> 0,
v3 -> 0,
rho -> 1 + amp UnitStep[x-0.5],
En -> 1
}
};
conservedCalc =
{
Name -> "euler_conserved",
Schedule -> {"at INITIAL after euler_initial"},
Equations ->
{
w[ui] -> rho v[ui]
}
};
(**************************************************************************************)
(* Evolution equations *)
(**************************************************************************************)
evolCalc =
{
Name -> "euler_evol",
Schedule -> {"in MoL_CalcRHS"},
Shorthands -> {dir[ui]},
Where -> Interior,
Equations ->
{
dot[rho] -> PD[Frho[ui], li],
dot[w[uj]] -> PD[Fw[uj,ui], li],
dot[En] -> PD[FEn[ui], li]
}
};
primitivesCalc =
{
Name -> "euler_primitives",
Schedule -> {"in MoL_PostStep after Euler_ApplyBCs"}, (* Need BCs *)
Equations ->
{
v[ui] -> w[ui] / rho,
p -> 2/3 (En - 1/2 Euc[li,lj] v[ui] v[uj])
}
};
fluxCalc =
{
Name -> "euler_flux",
Schedule -> {"in MoL_PostStep after euler_primitives"},
Equations ->
{
Frho[ui] -> rho v[ui],
Fw[uj,ui] -> rho v[ui] v[uj] + p Euc[ui,uj],
FEn[ui] -> v[ui] * (En + p)
}
};
realParameters = {sigma, v0, amp};
keywordParameters = {
{
Name -> "initial_data",
Default -> "sine",
AllowedValues -> {"sine", "shock"}
}
};
(**************************************************************************************)
(* Construct the thorn *)
(**************************************************************************************)
calculations =
{
initialSineCalc,
initialShockCalc,
evolCalc,
fluxCalc,
(* pressureCalc, *)
primitivesCalc,
conservedCalc
};
CreateKrancThornTT[groups, ".", "Euler",
Calculations -> calculations,
DeclaredGroups -> declaredGroupNames,
PartialDerivatives -> derivatives,
RealParameters -> realParameters,
KeywordParameters -> keywordParameters];
|
