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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],
DiffPlus[i_] -> DiffPlusOp[i],
DiffMinus[i_] -> DiffMinusOp[i],
ShiftMinus[i_] -> 1/shift[i]
};
(* PD = PDstandard2nd; *)
PD = PDplus;
(**************************************************************************************)
(* Tensors *)
(**************************************************************************************)
(* Register the tensor quantities with the TensorTools package *)
Map[DefineTensor, {u, uF, uR, uLeft}];
(**************************************************************************************)
(* Groups *)
(**************************************************************************************)
evolvedGroups = Map[CreateGroupFromTensor, {u}];
nonevolvedGroups = Map[CreateGroupFromTensor, {uF, uLeft, uR}];
declaredGroups = Join[evolvedGroups, nonevolvedGroups];
declaredGroupNames = Map[First, declaredGroups];
groups = Join[declaredGroups];
(**************************************************************************************)
(* Initial data *)
(**************************************************************************************)
initialSineCalc =
{
Name -> "burgers_initial_sine",
Schedule -> {"at CCTK_INITIAL as burgers_initial"},
ConditionalOnKeyword -> {"initial_data", "sine"},
Equations ->
{
u -> 1 + amp Sin[2 Pi x]
}
};
initialShockCalc =
{
Name -> "burgers_initial_shock",
Schedule -> {"at CCTK_INITIAL as burgers_initial"},
ConditionalOnKeyword -> {"initial_data", "shock"},
Equations ->
{
u -> uR0 StepFunction[x-0.5] + uL0 (1-StepFunction[x-0.5])
}
};
(**************************************************************************************)
(* Evolution equations *)
(**************************************************************************************)
(* Burger's equation is dot[u] + PD[F,x] = 0
with F[ui] = 1/2 u^2
*)
burgersFlux[u_] := 1/2 u^2;
zeroRHSCalc[] :=
{
Name -> "burgers_zero_rhs",
Schedule -> {"in MoL_CalcRHS"},
Equations ->
{
dot[u] -> 0
}
};
reconstructCalc[i_] :=
{
Name -> "burgers_reconstruct_" <> ToString[i],
Where -> Interior,
Schedule -> {"in MoL_CalcRHS after " <>
If[i == 1, "burgers_zero_rhs", "burgers_rhs_" <> ToString[i-1]]},
Shorthands -> {slopeL, slopeR, slope},
ApplyBCs -> True,
Equations ->
{
slopeL -> DiffMinus[u, i],
slopeR -> DiffPlus[u, i],
slope -> IfThen[slopeL slopeR < 0, 0, IfThen[Abs[slopeL] < Abs[slopeR], slopeL, slopeR]],
uLeft -> u - 0.5 slope,
uR -> u + 0.5 slope
}
};
fluxCalc[f_, i_] :=
{
Name -> "burgers_flux_" <> ToString[i],
ApplyBCs -> True,
Where -> Interior,
Schedule -> {"in MoL_CalcRHS after burgers_reconstruct_" <> ToString[i]},
Equations ->
{
uF -> 1/2 (f[uLeft] + f[ShiftMinus[uR,i]] + alpha (ShiftMinus[uR,i] - uLeft))
}
};
rhs[i_] :=
{
Name -> "burgers_rhs_" <> ToString[i],
Schedule -> {"in MoL_CalcRHS after burgers_flux_" <> ToString[i]},
Where -> Interior,
Equations ->
{
dot[u] -> dot[u] - PDplus[uF, i]
}
};
makeConservationCalcs[f_] :=
({ zeroRHSCalc[]} ~Join~ Flatten[Table[
{reconstructCalc[i],
fluxCalc[f, i],
rhs[i]}, {i, 1, 1}], 1]);
realParameters = {sigma, v0, amp, uL0, uR0, alpha};
keywordParameters = {
{
Name -> "initial_data",
Default -> "sine",
AllowedValues -> {"sine", "shock"}
}
};
(**************************************************************************************)
(* Construct the thorn *)
(**************************************************************************************)
calculations =
{
initialSineCalc,
initialShockCalc
} ~Join~ makeConservationCalcs[burgersFlux];
CreateKrancThornTT[groups, ".", "Burgers",
Calculations -> calculations,
DeclaredGroups -> declaredGroupNames,
PartialDerivatives -> derivatives,
RealParameters -> realParameters,
KeywordParameters -> keywordParameters];
|
