From 0178eeab9d99ba38794b38da86b88a589d2b48a8 Mon Sep 17 00:00:00 2001
From: Erik Schnetter <schnetter@cct.lsu.edu>
Date: Mon, 27 Apr 2009 11:07:39 -0500
Subject: Add experiment towards a hydro code

---
 m/grhydro.m | 154 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 154 insertions(+)
 create mode 100644 m/grhydro.m

(limited to 'm/grhydro.m')

diff --git a/m/grhydro.m b/m/grhydro.m
new file mode 100644
index 0000000..a71a28b
--- /dev/null
+++ b/m/grhydro.m
@@ -0,0 +1,154 @@
+Get["KrancThorn`"];
+
+(*SetDebugLevel[InfoFull];*)
+
+SetEnhancedTimes[False];
+SetSourceLanguage["C"];
+
+(****************************************************************************
+ 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],
+
+ PDplus[i_] -> DPlus[i],
+ PDminus[i_] -> DMinus[i],
+ PDplus[i_,j_] -> DPlus[i] DPlus[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])
+};
+
+(*PD = PDstandard2nd;*)
+
+(****************************************************************************
+ Tensors 
+****************************************************************************)
+
+(* Register all the tensors that will be used with TensorTools *)
+Map[DefineTensor, 
+{
+  rho, vel, eps, press,
+  dens, mom, tau
+}];
+
+(* Register the TensorTools symmetries (this is very simplistic) *)
+Map[AssertSymmetricDecreasing, 
+{
+}];
+
+(* Determinants of the metrics in terms of their components
+  (Mathematica symbolic expressions) *)
+gDet = Det[MatrixOfComponents[g[la,lb]]];
+
+(****************************************************************************
+ Groups
+****************************************************************************)
+
+SetGroupTimelevels[g_,tl_] = Join[g, {Timelevels -> tl}];
+
+evolvedGroups =
+  {CreateGroupFromTensor [dens   ],             (* mass density *)
+   CreateGroupFromTensor [mom[la]],             (* momentum density *)
+   CreateGroupFromTensor [tau    ]};            (* energy density *)
+evaluatedGroups =
+  {CreateGroupFromTensor [rho    ],             (* mass density *)
+   CreateGroupFromTensor [vel[ua]],             (* velocity *)
+   CreateGroupFromTensor [eps    ],             (* specific internal energy *)
+   CreateGroupFromTensor [press  ]};            (* pressure *)
+
+declaredGroups = Join [evolvedGroups, evaluatedGroups];
+declaredGroupNames = Map [First, declaredGroups];
+
+groups = Join[declaredGroups];
+
+(******************************************************************************)
+(* Initial data *)
+(******************************************************************************)
+
+initialCalc =
+{
+  Name -> BSSN <> "_vacuum",
+  Schedule -> {"IN ADMBase_InitialData"},
+  ConditionalOnKeyword -> {"my_initial_data", "vacuum"},
+  Equations -> 
+  {
+    rho     -> 0,
+    vel[ua] -> 0,
+    eps     -> 0
+  }
+};
+
+(******************************************************************************)
+(* Convert from primitive to conserved variables *)
+(******************************************************************************)
+
+prim2conCalc =
+{
+  Name -> BSSN <> "_con2prim",
+  Schedule -> {"AT initial AFTER ADMBase_PostInitial"},
+  Equations -> 
+  {
+    dens    -> rho,
+    mom[la] -> rho vel[ua],
+    tau     -> (1/2) rho vel[ua] vel[la] + rho eps
+  }
+};
+
+(******************************************************************************)
+(* Convert from conserved to primitive variables *)
+(******************************************************************************)
+
+con2primCalc =
+{
+  Name -> BSSN <> "_con2prim",
+  Schedule -> {"IN " <> BSSN <>"_con2primGroup"},
+  Equations -> 
+  {
+    rho     -> dens,
+    vel[ua] -> mom[la] / dens,
+    eps     -> tau / dens - (1/2) vel[ua] vel[la],
+    
+    press   -> Gamma rho eps +
+               alpha PD[vel[ua],la]
+  }
+};
+
+(******************************************************************************)
+(* Evolution equations *)
+(******************************************************************************)
+
+evolCalc =
+{
+  Name -> BSSN <> "_RHS",
+  Schedule -> {"IN " <> BSSN <>"_evolCalcGroup"},
+  Shorthands -> {rhov[ua], momv[la,ub], tauv[ua]},
+  Equations -> 
+  {
+    (* dt rho + div rho v = 0 *)
+    rhov[ua]  -> mom[la],
+    dot[dens] -> - PD[rhov[ua],la],
+    
+    (* dt pi + div (pi v + P) = 0 *)
+    momv[la,ub]  -> mom[la] vel[ub] + KD[la,ub] press,
+    dot[mom[la]] -> - PD[momv[la,ub],lb],
+    
+    (* dt tau + div (tauv + P) = 0 *)
+    tauv[ua] -> tau vel[ua] + press vel[ua],
+    dot[tau] -> - PD[tauv[ua],la]
+  }
+};
-- 
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