From b26044cd0af6066d2169b2beece38c75e2f38099 Mon Sep 17 00:00:00 2001
From: Ian Hinder <ian.hinder@aei.mpg.de>
Date: Wed, 29 Sep 2010 00:53:33 +0100
Subject: Burgers.m: Add Burger's equation with minmod reconstruction and HLLE
 Riemann solver

---
 Examples/Burgers.m | 170 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 170 insertions(+)
 create mode 100644 Examples/Burgers.m

diff --git a/Examples/Burgers.m b/Examples/Burgers.m
new file mode 100644
index 0000000..60ab50a
--- /dev/null
+++ b/Examples/Burgers.m
@@ -0,0 +1,170 @@
+
+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]
+};
+
+(* 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 UnitStep[x-0.5] + uL0 (1-UnitStep[x-0.5])
+  }
+};
+
+(**************************************************************************************)
+(* Evolution equations *)
+(**************************************************************************************)
+
+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[Abs[slopeL] < Abs[slopeR], slopeL, slopeR],
+    uLeft -> u - 0.5 slope,
+    uR -> u + 0.5 slope
+  }
+};
+
+fluxCalc[f_, i_] :=
+{
+  Name -> "burgers_flux_" <> ToString[i],
+  Schedule -> {"in MoL_CalcRHS after burgers_reconstruct_" <> ToString[i]},
+  Equations -> 
+  {
+    uF -> 1/2 (f[uLeft] + f[uR] + alpha (uLeft - uR))
+  }
+};
+
+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];
+
+Print[calculations];
+
+CreateKrancThornTT[groups, ".", "Burgers", 
+  Calculations -> calculations,
+  DeclaredGroups -> declaredGroupNames,
+  PartialDerivatives -> derivatives,
+  RealParameters -> realParameters,
+  KeywordParameters -> keywordParameters];
-- 
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