From e325ec8ea02357f9e1d382a0363fe28a887a7f7a Mon Sep 17 00:00:00 2001
From: Ian Hinder <ian.hinder@aei.mpg.de>
Date: Wed, 29 Sep 2010 00:52:47 +0100
Subject: Advect.m: Add advection equation

---
 Examples/Advect.m | 153 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 153 insertions(+)
 create mode 100644 Examples/Advect.m

diff --git a/Examples/Advect.m b/Examples/Advect.m
new file mode 100644
index 0000000..2bbb334
--- /dev/null
+++ b/Examples/Advect.m
@@ -0,0 +1,153 @@
+
+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], *)
+  (* ShiftPlus[i_] -> EPlus, *)
+  (* ShiftMinus[i_] -> EMinus *)
+};
+
+(* PD = PDstandard2nd; *)
+PD = PDplus;
+
+(**************************************************************************************)
+(* Tensors *)
+(**************************************************************************************)
+
+(* Register the tensor quantities with the TensorTools package *)
+Map[DefineTensor, {Frho, F2rho, rho, v, dir}];
+
+(**************************************************************************************)
+(* Groups *)
+(**************************************************************************************)
+
+evolvedGroups = Map[CreateGroupFromTensor, {rho}];
+nonevolvedGroups = Map[CreateGroupFromTensor, {Frho[ui], F2rho[ui], v[ui]}];
+
+declaredGroups = Join[evolvedGroups, nonevolvedGroups];
+declaredGroupNames = Map[First, declaredGroups];
+
+groups = Join[declaredGroups];
+
+(**************************************************************************************)
+(* Initial data *)
+(**************************************************************************************)
+
+initialSineCalc =
+{
+  Name -> "advect_initial_sine",
+  Schedule -> {"at CCTK_INITIAL as advect_initial"},
+  ConditionalOnKeyword -> {"initial_data", "sine"},
+  Equations ->
+  {
+    v1 -> v0,
+    v2 -> 0,
+    v3 -> 0,
+    rho -> 1 + amp Sin[2 Pi x]
+  }
+};
+
+initialShockCalc =
+{
+  Name -> "advect_initial_shock",
+  Schedule -> {"at CCTK_INITIAL as advect_initial"},
+  ConditionalOnKeyword -> {"initial_data", "shock"},
+  Equations ->
+  {
+    v1 -> v0,
+    v2 -> 0,
+    v3 -> 0,
+    rho -> amp UnitStep[x-0.5]
+  }
+};
+
+(**************************************************************************************)
+(* Evolution equations *)
+(**************************************************************************************)
+
+evolCalc =
+{
+  Name -> "advect_evol",
+  Schedule -> {"in MoL_CalcRHS"},
+  Shorthands -> {},
+  Where -> Interior,
+  Equations -> 
+  {
+    (* dot[rho]   -> PDplus[F2rho[ui], li] *)
+    dot[rho]   -> PDstandard2nd[Frho[ui],li]
+                  (* alpha PDstandard2nd[rho,li,lj] Euc[ui,uj] *)
+  }
+};
+
+fluxCalc =
+{
+  Name -> "advect_flux",
+  Schedule -> {"in MoL_PostStep after Advect_ApplyBCs"},
+  Equations -> 
+  {
+    Frho[ui] -> rho v[ui]
+  }
+};
+
+(* flux2Calc = *)
+(* { *)
+(*   Name -> "advect_flux2", *)
+(*   Schedule -> {"in MoL_PostStep after advect_flux"}, *)
+(*   Equations ->  *)
+(*   { *)
+(*     F2rho[ui] -> 1/2(ShiftMinus[Frho[ui], lj] Euc[uj,ui] + Frho[ui] +  *)
+(*                      alpha(ShiftMinus[rho, lj] Euc[uj,ui] - rho)) *)
+(*   } *)
+(* }; *)
+
+realParameters = {sigma, v0, amp};
+
+keywordParameters = {
+  {
+    Name -> "initial_data",
+    Default -> "sine",
+    AllowedValues -> {"sine", "shock"}
+  }
+};
+
+(**************************************************************************************)
+(* Construct the thorn *)
+(**************************************************************************************)
+
+calculations = 
+{
+  initialSineCalc,
+  initialShockCalc,
+  evolCalc,
+  fluxCalc
+  (* flux2Calc *)
+};
+
+CreateKrancThornTT[groups, ".", "Advect", 
+  Calculations -> calculations,
+  DeclaredGroups -> declaredGroupNames,
+  PartialDerivatives -> derivatives,
+  RealParameters -> realParameters,
+  KeywordParameters -> keywordParameters];
-- 
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