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SetEnhancedTimes[False];
groups = {{"phi_group", {phi}}};
derivatives =
{
PDstandard[i_] ->
StandardCenteredDifferenceOperator[1,fdOrder/2,i],
PDstandard[i_, i_] ->
StandardCenteredDifferenceOperator[2,fdOrder/2,i],
PDstandard[i_, j_] ->
StandardCenteredDifferenceOperator[1,fdOrder/2,i] StandardCenteredDifferenceOperator[1,fdOrder/2,j]
};
PD = PDstandard;
initialCalc =
{
Name -> "Laplace_initial",
Schedule -> {"AT INITIAL"},
Where -> Interior,
Equations ->
{
phi -> phi0 Sum[4/(Pi n) Sin[n Pi x/Lx] Sinh[n Pi y/Lx]/Sinh[n Pi Ly/Lx], {n, 1, 1, 2}]
}
};
initialBoundaryCalc =
{
Name -> "Laplace_initial_boundary",
Schedule -> {"AT INITIAL after Laplace_initial"},
Where -> Boundary,
Equations ->
{
phi -> IfThen[Abs[y-Ly]<10^-10, phi0, 0]
}
};
evolveCalc =
{
Name -> "Laplace_relax",
Schedule -> {"in MoL_CalcRHS", "AT ANALYSIS"},
Where -> Interior,
Equations ->
{
dot[phi] -> mu Euc[ui,uj] PD[phi,li,lj]
}
};
boundaryCalc =
{
Name -> "Laplace_boundary",
Schedule -> {"in MoL_RHSBoundaries", "AT ANALYSIS"},
Where -> Boundary,
Equations ->
{
dot[phi] -> 0
}
};
CreateKrancThornTT[
groups, ".",
"Laplace",
Calculations -> {initialCalc, initialBoundaryCalc, evolveCalc, boundaryCalc},
PartialDerivatives -> derivatives,
ZeroDimensions -> {3},
RealParameters -> {Lx,Ly,phi0,mu},
IntParameters -> {{Name -> fdOrder, Default -> 2, AllowedValues -> {2, 4}}},
DeclaredGroups -> {"phi_group"}];
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