GRHydro: Fixing Con2PrimM to call the proper point-wise routines

This re-introduces routines that work for hybrid/hot EOS and
corresponding changes in pointwise routines for hot EOS error checking
and temperature treatment by adding old EOSOmni pointwise routine.

From: Philipp Moesta <pmoesta@tapir.caltech.edu>

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinEvolve/GRHydro/trunk@511 c83d129a-5a75-4d5a-9c4d-ed3a5855bf45

1 files changed, 1056 insertions, 0 deletions

diff --git a/src/GRHydro_Con2PrimM_pt_EOSOmniold.c b/src/GRHydro_Con2PrimM_pt_EOSOmniold.c
new file mode 100644
index 0000000..0eb4845
--- /dev/null
+++ b/src/GRHydro_Con2PrimM_pt_EOSOmniold.c
@@ -0,0 +1,1056 @@
+/***********************************************************************************
+    Copyright 2006 Scott C. Noble, Charles F. Gammie, Jonathan C. McKinney, 
+                   and Luca Del Zanna.
+
+                        PVS_GRMHD
+
+    This file was derived from PVS_GRMHD.  The authors of PVS_GRMHD include 
+    Scott C. Noble, Charles F. Gammie, Jonathan C. McKinney, and Luca Del Zanna.
+    PVS_GRMHD is available under the GPL from:
+    http://rainman.astro.uiuc.edu/codelib/  
+
+    You are morally obligated to cite the following  paper in his/her 
+    scientific literature that results from use of this file:
+
+    [1] Noble, S. C., Gammie, C. F., McKinney, J. C., \& Del Zanna, L. \ 2006, 
+        Astrophysical Journal, 641, 626.
+
+    PVS_GRMHD is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    PVS_GRMHD is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with PVS_GRMHD; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
+
+    If the user has any questions, please direct them to Scott C. Noble at 
+    scn@astro.rit.edu  . 
+
+***********************************************************************************/
+
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdarg.h>
+#include <string.h>
+#include <math.h>
+#include <float.h>
+#include <complex.h>
+
+#include "cctk.h"
+#include "cctk_Parameters.h"
+
+/* Set this to be 1 if you want debug output */
+#define DEBUG_CON2PRIMM (0)
+
+
+/* Adiabatic index used for the state equation */
+
+#define MAX_NEWT_ITER   (30)       /* Max. # of Newton-Raphson iterations for find_root_2D(); */
+#define NEWT_TOL        (1.0e-10)  /* Min. of tolerance allowed for Newton-Raphson iterations */
+#define MIN_NEWT_TOL    (1.0e-10)  /* Max. of tolerance allowed for Newton-Raphson iterations */
+#define EXTRA_NEWT_ITER (2)
+
+#define NEWT_TOL2       (1.0e-15)  /* TOL of new 1D^*_{v^2} gnr2 method */
+#define MIN_NEWT_TOL2   (1.0e-10)  /* TOL of new 1D^*_{v^2} gnr2 method */
+
+#define W_TOO_BIG       (1.e20)    /* \gamma^2 (\rho_0 + u + p) is assumed
+                                      to always be smaller than this.  This
+                                      is used to detect solver failures */
+
+#define FAIL_VAL        (1.e30)    /* Generic value to which we set variables when a problem arises */
+
+/**************************************************
+  The following functions assume a Gamma-law EOS:
+***************************************************/
+
+/* Local Globals */
+struct LocGlob {
+  CCTK_REAL Bsq,QdotBsq,Qtsq,Qdotn,D,half_Bsq ;
+} ;
+
+struct eosomnivars {
+  CCTK_INT eoshandle,eoskeytemp;
+  CCTK_REAL prec,eosprec,eos_y_e[1],eos_temp[1];
+  CCTK_INT eoskeyerr[1],eosanyerr[1];
+} ;
+
+// Declarations: 
+static CCTK_REAL vsq_calc(CCTK_REAL W, struct LocGlob *lgp);
+
+static CCTK_INT twod_newton_raphson( CCTK_REAL x[], CCTK_REAL gammaeos, struct LocGlob *lgp,
+                                     void (*funcd) (CCTK_REAL [], CCTK_REAL [], 
+                                                    CCTK_REAL [], CCTK_REAL [][2], 
+                                                    CCTK_REAL *, CCTK_REAL *, CCTK_REAL, struct LocGlob *) );
+
+static CCTK_INT threed_newton_raphson_omni( CCTK_REAL x[], struct eosomnivars *eosvars, struct LocGlob *lgp,
+                                     void (*funcd) (CCTK_REAL [], CCTK_REAL [], 
+                                                    CCTK_REAL [], CCTK_REAL [][3], 
+                                                    CCTK_REAL *, CCTK_REAL *, 
+                                                    struct eosomnivars *eosvars, struct LocGlob *) );
+
+static  void func_vsq( CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], CCTK_REAL [][2], 
+                       CCTK_REAL *f, CCTK_REAL *df, CCTK_REAL gammaeos, struct LocGlob *lgp);
+
+static  void func_vsq_eosomni( CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], CCTK_REAL [][3], 
+                       CCTK_REAL *f, CCTK_REAL *df, struct eosomnivars *eosvars, struct LocGlob *lgp);
+
+static CCTK_REAL x1_of_x0(CCTK_REAL x0, struct LocGlob *lgp ) ;
+
+
+// EOS STUFF:
+static CCTK_REAL eos_info(CCTK_REAL W, CCTK_REAL vsq, CCTK_REAL *dpdw, CCTK_REAL *dpdvsq, CCTK_REAL gammaeos, struct LocGlob *lgp);
+static CCTK_REAL eos_info_eosomni(CCTK_REAL W, CCTK_REAL vsq, CCTK_REAL eps0, struct LocGlob *lgp);
+
+/* pressure as a function of rho0 and u */
+//static CCTK_REAL pressure_rho0_u(CCTK_REAL rho0, CCTK_REAL u, CCTK_REAL gammaeos)
+//{
+//  return((gammaeos - 1.)*u) ;
+//}
+
+static CCTK_REAL pressure_rho0_eps_eosomni(CCTK_REAL rho0, CCTK_REAL eps, CCTK_REAL* dpdrho, CCTK_REAL* dpdeps, struct eosomnivars *eosvars);
+
+/* Pressure as a function of rho0 and w = rho0 + u + p */
+static CCTK_REAL pressure_rho0_w(CCTK_REAL rho0, CCTK_REAL w,CCTK_REAL gammaeos)
+{
+  return((gammaeos-1.)*(w - rho0)/gammaeos) ;
+}
+
+void CCTK_FCALL CCTK_FNAME(GRHydro_Con2PrimM_pt2) (
+    CCTK_INT  *handle, CCTK_INT *keytemp, CCTK_REAL *eos_prec, CCTK_REAL *prec,
+    CCTK_REAL *gamma_eos,
+    CCTK_REAL *dens_in, 
+    CCTK_REAL *sx_in, CCTK_REAL *sy_in, CCTK_REAL *sz_in, 
+    CCTK_REAL *tau_in, CCTK_REAL *Bconsx_in, CCTK_REAL *Bconsy_in, CCTK_REAL *Bconsz_in, 
+    CCTK_REAL *y_e_in, CCTK_REAL *temp_in,
+    CCTK_REAL *rho, 
+    CCTK_REAL *velx, CCTK_REAL *vely, CCTK_REAL *velz,
+    CCTK_REAL *epsilon, CCTK_REAL *pressure,
+    CCTK_REAL *Bx, CCTK_REAL *By, CCTK_REAL *Bz, CCTK_REAL *bsq,
+    CCTK_REAL *w_lorentz, 
+    CCTK_REAL *gxx, CCTK_REAL *gxy, CCTK_REAL *gxz, 
+    CCTK_REAL *gyy, CCTK_REAL *gyz, CCTK_REAL *gzz, 
+    CCTK_REAL *uxx, CCTK_REAL *uxy, CCTK_REAL *uxz,
+    CCTK_REAL *uyy, CCTK_REAL *uyz, CCTK_REAL *uzz,
+    CCTK_REAL *det,
+    CCTK_INT  *epsnegative,
+    CCTK_REAL *retval);
+
+/**********************************************************************/
+/**********************************************************************************
+
+  Con2PrimM_pt():
+  -----------------------------
+
+   -- Attempts an inversion from GRMHD conserved variables to primitive variables assuming a guess.
+
+   -- Uses the 2D method of Noble et al. (2006): 
+       -- Solves for two independent variables (W,v^2) via a 2D
+          Newton-Raphson method 
+       -- Can be used (in principle) with a general equation of state. 
+
+   -- Minimizes two residual functions using a homemade Newton-Raphson routine. 
+       -- It is homemade so that it can catch exceptions and handle them correctly, plus it is 
+          optimized for this particular  problem. 
+
+  -- Note that the notation used herein is that of Noble et al. (2006) except for the argument 
+     list. 
+
+
+INPUT:  (using GRHydro variable defintions)
+
+   s[x,y,z]   =  scons[0,1,2]  = \alpha \sqrt(\gamma) T^0_i 
+   dens, tau  =  as defined in GRHydro and are assumed to be densitized (i.e. with sqrt(\gamma))   
+   dens       =  D = \sqrt(\gamma) W \rho    
+   tau        =  \alpha^2 \sqrt(\gamma) T^{00} - D 
+   g[x,y,z][x,y,x] = spatial metric corresponding to \gamma 
+   u[x,y,z][x,y,z] = inverse of the spatial metric, g[x,y,z][x,y,x]
+   det        =  sqrt(\gamma)
+   B[x,y,z]   =  Bvec[0,1,2] 
+   bsq        = b^\mu b_\mu  
+
+   epsnegative = (integer)
+               = 0  if rho and epsilon are positive
+              != 0  otherwise 
+
+
+  --  (users should set B[x,y,z] = 0  for hydrodynamic runs) 
+
+
+OUTPUT:  (using GRHydro variable defintions)
+   rho, eps   =  as defined in GRHydro, primitive variables
+   vel[x,y,z] =  as defined in GRHydro, primitive variables
+
+
+RETURN VALUE: of retval = (i*100 + j)  where 
+         i = 0 ->  Newton-Raphson solver either was not called (yet or not used) 
+                   or returned successfully;
+             1 ->  Newton-Raphson solver did not converge to a solution with the 
+                   given tolerances;
+             2 ->  Newton-Raphson procedure encountered a numerical divergence 
+                   (occurrence of "nan" or "+/-inf" ;
+             
+         j = 0 -> success 
+             1 -> failure: some sort of failure in Newton-Raphson; 
+             2 -> failure: unphysical vsq = v^2  value at initial guess;
+             3 -> failure: W<0 or W>W_TOO_BIG
+             4 -> failure: v^2 > 1 
+             ( used to be  5 -> failure: rho,uu <= 0   but now sets epsnegative to non-zero )
+
+**********************************************************************************/
+
+
+void CCTK_FCALL CCTK_FNAME(GRHydro_Con2PrimM_pt2)  ( 
+    CCTK_INT  *handle, CCTK_INT *keytemp, CCTK_REAL *eos_prec, CCTK_REAL *prec,
+    CCTK_REAL *gamma_eos,
+    CCTK_REAL *dens_in, 
+    CCTK_REAL *sx_in, CCTK_REAL *sy_in, CCTK_REAL *sz_in, 
+    CCTK_REAL *tau_in,     
+    CCTK_REAL *Bconsx_in, CCTK_REAL *Bconsy_in, CCTK_REAL *Bconsz_in, 
+    CCTK_REAL *y_e_in, CCTK_REAL* temp_in,
+    CCTK_REAL *rho, 
+    CCTK_REAL *velx, CCTK_REAL *vely, CCTK_REAL *velz,
+    CCTK_REAL *epsilon, CCTK_REAL *pressure,
+    CCTK_REAL *Bx, CCTK_REAL *By, CCTK_REAL *Bz, 
+    CCTK_REAL *bsq,
+    CCTK_REAL *w_lorentz, 
+    CCTK_REAL *gxx, CCTK_REAL *gxy, CCTK_REAL *gxz, 
+    CCTK_REAL *gyy, CCTK_REAL *gyz, CCTK_REAL *gzz, 
+    CCTK_REAL *uxx, CCTK_REAL *uxy, CCTK_REAL *uxz,
+    CCTK_REAL *uyy, CCTK_REAL *uyz, CCTK_REAL *uzz,
+    CCTK_REAL *det,
+    CCTK_INT  *epsnegative,
+    CCTK_REAL *retval)
+
+{
+  CCTK_REAL x_3d[3];
+  CCTK_REAL sx, sy, sz;
+  CCTK_REAL usx, usy, usz;
+  CCTK_REAL tau, dens, gammaeos;
+  CCTK_REAL QdotB;
+  CCTK_REAL rho0,u,p,w,gammasq,gamma,gtmp,W_last,W,vsq;
+  CCTK_REAL g_o_WBsq, QdB_o_W;
+  CCTK_REAL detg = (*det);
+  CCTK_REAL sqrt_detg = sqrt(detg);
+  CCTK_REAL inv_sqrt_detg = 1./sqrt_detg; 
+  CCTK_INT i,j, i_increase ;
+
+  DECLARE_CCTK_PARAMETERS;
+  
+  struct LocGlob lg; 
+  struct eosomnivars eosvars;
+
+  eosvars.eoshandle = *handle;
+  //printf("handle = %i\n",*handle);
+  eosvars.eoskeytemp = *keytemp;
+  eosvars.eosprec = *eos_prec;
+  eosvars.prec = *prec;
+  eosvars.eos_y_e[0] = *y_e_in;
+  eosvars.eos_temp[0] = *temp_in;
+  eosvars.eoskeyerr[0] = 0;
+  eosvars.eosanyerr[0] = 0;
+
+  gammaeos = *gamma_eos;
+
+  /* Assume ok initially: */
+  *retval = 0.;
+  *epsnegative = 0; 
+
+#if(DEBUG_CON2PRIMM)
+  fprintf(stdout," *dens        = %26.16e \n", *dens_in         );
+  fprintf(stdout," *sx          = %26.16e \n", *sx_in     );    
+  fprintf(stdout," *sy          = %26.16e \n", *sy_in     );    
+  fprintf(stdout," *sz          = %26.16e \n", *sz_in     );    
+  fprintf(stdout," *tau         = %26.16e \n", *tau_in    );    
+  fprintf(stdout," *Bconsx      = %26.16e \n", *Bconsx_in );    
+  fprintf(stdout," *Bconsy      = %26.16e \n", *Bconsy_in );    
+  fprintf(stdout," *Bconsz      = %26.16e \n", *Bconsz_in );    
+  fprintf(stdout," *rho         = %26.16e \n", *rho       );    
+  fprintf(stdout," *velx        = %26.16e \n", *velx      );    
+  fprintf(stdout," *vely        = %26.16e \n", *vely      );    
+  fprintf(stdout," *velz        = %26.16e \n", *velz      );    
+  fprintf(stdout," *epsilon     = %26.16e \n", *epsilon     );
+  fprintf(stdout," *temp_in     = %26.16e \n", *temp_in     );
+  fprintf(stdout," *y_e_in     = %26.16e \n", *y_e_in     );
+  fprintf(stdout," *pressure    = %26.16e \n", *pressure    );
+  fprintf(stdout," *Bx          = %26.16e \n", *Bx        );    
+  fprintf(stdout," *By          = %26.16e \n", *By        );    
+  fprintf(stdout," *Bz          = %26.16e \n", *Bz        );    
+  fprintf(stdout," *bsq         = %26.16e \n", *bsq       );    
+  fprintf(stdout," *w_lorentz   = %26.16e \n", *w_lorentz   );
+  fprintf(stdout," *gxx         = %26.16e \n", *gxx       );    
+  fprintf(stdout," *gxy         = %26.16e \n", *gxy       );    
+  fprintf(stdout," *gxz         = %26.16e \n", *gxz       );    
+  fprintf(stdout," *gyy         = %26.16e \n", *gyy       );    
+  fprintf(stdout," *gyz         = %26.16e \n", *gyz       );    
+  fprintf(stdout," *gzz         = %26.16e \n", *gzz       );    
+  fprintf(stdout," *uxx         = %26.16e \n", *uxx       );    
+  fprintf(stdout," *uxy         = %26.16e \n", *uxy       );    
+  fprintf(stdout," *uxz         = %26.16e \n", *uxz       );    
+  fprintf(stdout," *uyy         = %26.16e \n", *uyy       );    
+  fprintf(stdout," *uyz         = %26.16e \n", *uyz       );    
+  fprintf(stdout," *uzz         = %26.16e \n", *uzz       );    
+  fprintf(stdout," *det         = %26.16e \n", *det       );    
+  fprintf(stdout," *epsnegative = %10d    \n", *epsnegative );
+  fprintf(stdout," *retval      = %26.16e \n", *retval      );
+  fflush(stdout);
+#endif
+
+  /* First undensitize all conserved variables : */
+  sx   = (  *sx_in)   * inv_sqrt_detg;
+  sy   = (  *sy_in)   * inv_sqrt_detg;
+  sz   = (  *sz_in)   * inv_sqrt_detg;
+  tau  = ( *tau_in)   * inv_sqrt_detg;
+  dens = (*dens_in)   * inv_sqrt_detg;
+
+  usx  =  (*uxx)*sx + (*uxy)*sy + (*uxz)*sz;
+  usy  =  (*uxy)*sx + (*uyy)*sy + (*uyz)*sz;
+  usz  =  (*uxz)*sx + (*uyz)*sy + (*uzz)*sz;
+
+  *Bx = (*Bconsx_in) * inv_sqrt_detg;
+  *By = (*Bconsy_in) * inv_sqrt_detg;
+  *Bz = (*Bconsz_in) * inv_sqrt_detg;
+
+  // Calculate various scalars (Q.B, Q^2, etc)  from the conserved variables:
+  
+  lg.Bsq = 
+    (*gxx) * (*Bx) * (*Bx) + 
+    (*gyy) * (*By) * (*By) + 
+    (*gzz) * (*Bz) * (*Bz) + 
+    2*( 
+       (*gxy) * (*Bx) * (*By) +
+       (*gxz) * (*Bx) * (*Bz) +
+       (*gyz) * (*By) * (*Bz) );
+    
+  QdotB = (sx * (*Bx) + sy * (*By) + sz * (*Bz)) ;
+  lg.QdotBsq = QdotB*QdotB ;
+
+  lg.Qdotn = -(tau + dens) ;
+
+  lg.Qtsq = (usx * sx  +  usy * sy  +  usz * sz) ;
+
+  lg.D = dens;
+
+  lg.half_Bsq = 0.5*lg.Bsq;
+
+  /* calculate W from last timestep and use for guess */
+  vsq = 
+    (*gxx) * (*velx) * (*velx) + 
+    (*gyy) * (*vely) * (*vely) + 
+    (*gzz) * (*velz) * (*velz) + 
+    2*( 
+       (*gxy) * (*velx) * (*vely) +
+       (*gxz) * (*velx) * (*velz) +
+       (*gyz) * (*vely) * (*velz) );
+
+  if( (vsq < 0.) && (fabs(vsq) < 1.0e-13) ) { 
+    vsq = fabs(vsq);
+  }
+  if(vsq < 0. || vsq > 1. ) {
+    *retval = 2.;
+    fprintf(stdout," *retval      = %26.16e \n", *retval      );
+    return;
+  }
+
+  gammasq = 1. / (1. - vsq);
+  gamma  = sqrt(gammasq);
+        
+  // Always calculate rho from D and gamma so that using D in EOS remains consistent
+  //   i.e. you don't get positive values for dP/d(vsq) . 
+  rho0 = lg.D / gamma ;
+  u = (*epsilon) * rho0;
+  CCTK_REAL uold = u; 
+ 
+  CCTK_REAL dum1,dum2;
+  p = pressure_rho0_eps_eosomni(rho0,*epsilon,&dum1,&dum2,&eosvars) ;  // EOSOMNI
+  //  p = pressure_rho0_u(rho0,u,gammaeos) ;  // EOS
+  w = rho0 + u + p ;
+
+  W_last = w*gammasq ;
+
+  //fprintf(stdout," p                  = %26.16e \n", p                );
+
+  // Make sure that W is large enough so that v^2 < 1 : 
+  i_increase = 0;
+  while( (( W_last*W_last*W_last * ( W_last + 2.*lg.Bsq ) 
+            - lg.QdotBsq*(2.*W_last + lg.Bsq) ) <= W_last*W_last*(lg.Qtsq-lg.Bsq*lg.Bsq))
+         && (i_increase < 10) ) {
+    W_last *= 10.;
+    i_increase++;
+  }
+  
+  // Calculate W and vsq: 
+  x_3d[0] =  fabs( W_last );
+  x_3d[1] = x1_of_x0( W_last, &lg ) ;
+
+  //Use 2d NR for polytropes!
+  if (*handle==1 || *handle==2) {    
+    *retval = 1.0*twod_newton_raphson( x_3d, gammaeos, &lg, func_vsq ) ;  
+
+  } else {
+    //USE 3d NR for non-polytropes!
+    x_3d[2] = u;
+    *retval = 1.0*threed_newton_raphson_omni( x_3d, &eosvars, &lg, func_vsq_eosomni ) ;  
+  }
+  
+  W = x_3d[0];
+  vsq = x_3d[1];
+        
+  /* Problem with solver, so return denoting error before doing anything further */
+  if( ((*retval) != 0.) || (W == FAIL_VAL) ) {
+    *retval = *retval*100.+1.;
+    fprintf(stdout," *retval      = %26.16e \n", *retval      );
+    return;
+  }
+  else{
+    if(W <= 0. || W > W_TOO_BIG) {
+      *retval = 3.;
+      fprintf(stdout," *retval      = %26.16e \n", *retval      );
+      return;
+    }
+  }
+
+  // Calculate v^2:
+  if( vsq >= 1. ) {
+    *retval = 4.;
+    fprintf(stdout," *retval      = %26.16e \n", *retval      );
+    return;
+  }
+
+  // Recover the primitive variables from the scalars and conserved variables:
+  gtmp = sqrt(1. - vsq);
+  gamma = 1./gtmp ;
+  rho0 = lg.D * gtmp;
+
+  w = W * (1. - vsq) ;
+ 
+  if (*handle==1 || *handle==2) {     
+    p = pressure_rho0_w(rho0,w,gammaeos) ;  // EOS
+    u = w - (rho0 + p) ;
+    *epsilon = u / rho0;
+  } else {
+    u=x_3d[2];
+    *epsilon = u/rho0;
+    p = pressure_rho0_eps_eosomni(rho0,*epsilon,&dum1,&dum2,&eosvars) ;  // EOSOMNI
+   // printf("%g %g %g %g\n",rho0,u,*epsilon,p);
+  }
+
+  // User may want to handle this case differently, e.g. do NOT return upon 
+  // a negative rho/u, calculate v^i so that rho/u can be floored by other routine:
+  if( (rho0 <= 0.) || (u <= 0.) ) { 
+    *epsnegative = 1; 
+    fprintf(stdout," *epsnegative = %10d    \n", *epsnegative );
+    fprintf(stdout," rho0       = %26.16e \n", rho0             ); 
+    fprintf(stdout," u                  = %26.16e \n", u                );
+    fprintf(stdout," W                  = %26.16e \n", W                );
+    fprintf(stdout," vsq                = %26.16e \n", vsq              );
+    fprintf(stdout," uold               = %26.16e \n", uold             );
+    return;
+  }
+
+  *rho = rho0;
+  *w_lorentz = gamma; 
+  *pressure = p ; 
+
+  g_o_WBsq = 1./(W+lg.Bsq);
+  QdB_o_W  = QdotB / W; 
+  *bsq = lg.Bsq * (1.-vsq) + QdB_o_W*QdB_o_W;
+
+  *velx = g_o_WBsq * ( usx + QdB_o_W*(*Bx) ) ;
+  *vely = g_o_WBsq * ( usy + QdB_o_W*(*By) ) ;
+  *velz = g_o_WBsq * ( usz + QdB_o_W*(*Bz) ) ;
+
+  if (*rho <= rho_abs_min*(1.0+GRHydro_atmo_tolerance) ) {
+    *rho = rho_abs_min;
+    *velx = 0.0;
+    *vely = 0.0;
+    *velz = 0.0;
+    *w_lorentz = 1.0;
+  }
+
+#if(DEBUG_CON2PRIMM)
+  fprintf(stdout,"rho          = %26.16e \n",*rho      );
+  fprintf(stdout,"epsilon      = %26.16e \n",*epsilon  );
+  fprintf(stdout,"pressure     = %26.16e \n",*pressure );
+  fprintf(stdout,"w_lorentz    = %26.16e \n",*w_lorentz);
+  fprintf(stdout,"bsq          = %26.16e \n",*bsq      );
+  fprintf(stdout,"velx         = %26.16e \n",*velx     );
+  fprintf(stdout,"vely         = %26.16e \n",*vely     );
+  fprintf(stdout,"velz         = %26.16e \n",*velz     );
+  fprintf(stdout,"gammaeos     = %26.16e \n",gammaeos  );
+  fflush(stdout);
+#endif
+
+  /* done! */
+  return;
+
+}
+
+
+/**********************************************************************/ 
+/****************************************************************************
+   vsq_calc(): 
+    
+      -- evaluate v^2 (spatial, normalized velocity) from 
+            W = \gamma^2 w 
+
+****************************************************************************/
+static CCTK_REAL vsq_calc(CCTK_REAL W, struct LocGlob *lgp)
+{
+        CCTK_REAL Wsq,Xsq,Bsq_W;
+        
+        Wsq = W*W ;
+        Bsq_W = (lgp->Bsq + W);
+        Xsq = Bsq_W * Bsq_W;
+
+        return(  ( Wsq * lgp->Qtsq  + lgp->QdotBsq * (Bsq_W + W)) / (Wsq*Xsq) );
+}
+
+
+/********************************************************************
+
+  x1_of_x0(): 
+           
+    -- calculates v^2 from W  with some physical bounds checking;
+    -- asumes x0 is already physical
+    -- makes v^2 physical  if not;
+
+*********************************************************************/
+
+static CCTK_REAL x1_of_x0(CCTK_REAL x0, struct LocGlob *lgp ) 
+{
+  CCTK_REAL x1,vsq;
+  CCTK_REAL dv = 1.e-15;
+
+  vsq = fabs(vsq_calc(x0,lgp)) ; // guaranteed to be positive 
+
+  return( ( vsq > 1. ) ? (1.0 - dv) : vsq   ); 
+
+}
+
+/********************************************************************
+
+  validate_x(): 
+           
+    -- makes sure that x[0,1] have physical values, based upon 
+       their definitions:
+    
+*********************************************************************/
+
+static void validate_x(CCTK_REAL x[2], CCTK_REAL x0[2] ) 
+{
+  
+  const CCTK_REAL dv = 1.e-15;
+
+  /* Always take the absolute value of x[0] and check to see if it's too big:  */ 
+  x[0] = fabs(x[0]);
+  x[0] = (x[0] > W_TOO_BIG) ?  x0[0] : x[0];
+  
+  x[1] = (x[1] < 0.) ?   0.       : x[1];  /* if it's too small */
+  x[1] = (x[1] > 1.) ?  (1. - dv) : x[1];  /* if it's too big   */
+
+  return;
+
+}
+
+/************************************************************
+
+  twod_newton_raphson(): 
+
+    -- performs Newton-Rapshon method on an 2d system for polytropes.
+
+    -- inspired in part by Num. Rec.'s routine newt();
+
+*****************************************************************/
+static CCTK_INT twod_newton_raphson( CCTK_REAL x[], CCTK_REAL gammaeos, struct LocGlob *lgp, 
+                            void (*funcd) (CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], 
+                                           CCTK_REAL [][2], CCTK_REAL *, 
+                                           CCTK_REAL *, CCTK_REAL, struct LocGlob *) )
+{
+  CCTK_REAL f, df, dx[2], x_old[2];
+  CCTK_REAL resid[2], jac[2][2];
+  CCTK_REAL errx, x_orig[2];
+  CCTK_INT    n_iter, id, jd, i_extra, doing_extra;
+  CCTK_REAL dW,dvsq,vsq_old,vsq,W,W_old;
+  const CCTK_REAL dv = (1.-1.e-15);
+
+  CCTK_INT   keep_iterating;
+
+
+  // Initialize various parameters and variables:
+  errx = 1. ; 
+  df = f = 1.;
+  i_extra = doing_extra = 0;
+  x_old[0] = x_orig[0] = x[0] ;
+  x_old[1] = x_orig[1] = x[1] ;
+
+  vsq_old = vsq = W = W_old = 0.;
+  n_iter = 0;
+
+  /* Start the Newton-Raphson iterations : */
+  keep_iterating = 1;
+  while( keep_iterating ) { 
+
+    (*funcd) (x, dx, resid, jac, &f, &df, gammaeos, lgp);  /* returns with new dx, f, df */
+      
+
+    /* Save old values before calculating the new: */
+    errx = 0.;
+    x_old[0] = x[0] ; 
+    x_old[1] = x[1] ; 
+
+    /* Make the newton step: */
+    x[0] += dx[0]  ; 
+    x[1] += dx[1]  ; 
+
+    /****************************************/
+    /* Calculate the convergence criterion */
+    /****************************************/
+    errx  = (x[0]==0.) ?  fabs(dx[0]) : fabs(dx[0]/x[0]);
+
+
+    /****************************************/
+    /* Make sure that the new x[] is physical : */
+    /****************************************/
+    if( x[0] < 0. ) {  x[0] = fabs(x[0]);  } 
+    else { 
+     if(x[0] > W_TOO_BIG)  { x[0] = x_old[0] ; }
+    }
+
+    if( x[1] < 0. ) {  x[1] = 0.; } 
+    else { 
+      if( x[1] > 1. ) { x[1] = dv; }
+    }
+      
+    /*****************************************************************************/
+    /* If we've reached the tolerance level, then just do a few extra iterations */
+    /*  before stopping                                                          */
+    /*****************************************************************************/
+    
+    if( (fabs(errx) <= NEWT_TOL) && (doing_extra == 0) && (EXTRA_NEWT_ITER > 0) ) {
+      doing_extra = 1;
+    }
+
+    if( doing_extra == 1 ) i_extra++ ;
+
+    if( ((fabs(errx) <= NEWT_TOL)&&(doing_extra == 0)) 
+        || (i_extra > EXTRA_NEWT_ITER) || (n_iter >= (MAX_NEWT_ITER-1)) ) {
+      keep_iterating = 0;
+    }
+
+    n_iter++;
+
+  }   // END of while(keep_iterating)
+
+
+    /*  Check for bad untrapped divergences : */
+  if( (!finite(f)) ||  (!finite(df)) ) {
+    return(2);
+  }
+
+
+  if( fabs(errx) <= NEWT_TOL ){
+    return(0);
+  }
+  else if( (fabs(errx) <= MIN_NEWT_TOL) && (fabs(errx) > NEWT_TOL) ){
+    return(0);
+  }
+  else {
+    return(1);
+  } 
+
+  return(0);
+
+}
+
+
+/************************************************************
+
+  threed_newton_raphson_omni(): 
+
+    -- performs Newton-Rapshon method on an 2d system for polytropes.
+
+    -- inspired in part by Num. Rec.'s routine newt();
+
+*****************************************************************/
+static CCTK_INT threed_newton_raphson_omni( CCTK_REAL x[], struct eosomnivars *eosvars, struct LocGlob *lgp, 
+                            void (*funcd) (CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], 
+                                           CCTK_REAL [][3], CCTK_REAL *, 
+                                           CCTK_REAL *, struct eosomnivars *, struct LocGlob *) )
+{
+  CCTK_REAL f, df, dx[3], x_old[3];
+  CCTK_REAL resid[3], jac[3][3];
+  CCTK_REAL errx, x_orig[3];
+  CCTK_INT    n_iter, id, jd, i_extra, doing_extra;
+  CCTK_REAL dW,dvsq,du,vsq_old,vsq,W,W_old,u,u_old;
+  const CCTK_REAL dv = (1.-1.e-15);
+
+  CCTK_INT   keep_iterating;
+
+
+  // Initialize various parameters and variables:
+  errx = 1. ; 
+  df = f = 1.;
+  i_extra = doing_extra = 0;
+  x_old[0] = x_orig[0] = x[0] ;
+  x_old[1] = x_orig[1] = x[1] ;
+  x_old[2] = x_orig[2] = x[2] ;
+
+  vsq_old = vsq = W = W_old = u = u_old = 0.;
+  n_iter = 0;
+
+  /* Start the Newton-Raphson iterations : */
+  keep_iterating = 1;
+  while( keep_iterating ) { 
+
+    (*funcd) (x, dx, resid, jac, &f, &df, eosvars, lgp);  /* returns with new dx, f, df */
+
+    /* Save old values before calculating the new: */
+    errx = 0.;
+    x_old[0] = x[0] ; 
+    x_old[1] = x[1] ; 
+    x_old[2] = x[2] ; 
+
+    /* Make the newton step: */
+    x[0] += dx[0]  ; 
+    x[1] += dx[1]  ; 
+    x[2] += dx[2]  ; 
+
+    //printf("Updating vars: %g %g %g %g %g %g\n",x[0],dx[0],x[1],dx[1],x[2],dx[2]);
+
+    /****************************************/
+    /* Calculate the convergence criterion */
+    /****************************************/
+    errx  = (x[0]==0.) ?  fabs(dx[0]) : fabs(dx[0]/x[0]);
+
+
+    /****************************************/
+    /* Make sure that the new x[] is physical : */
+    /****************************************/
+    if( x[0] < 0. ) {  x[0] = fabs(x[0]);  } 
+    else { 
+     if(x[0] > W_TOO_BIG)  { x[0] = x_old[0] ; }
+    }
+
+    if( x[1] < 0. ) {  x[1] = 0.; } 
+    else { 
+      if( x[1] > 1. ) { x[1] = dv; }
+    }
+
+    if( x[2] < 0. ) {  x[2] = 0.; } 
+      
+    /*****************************************************************************/
+    /* If we've reached the tolerance level, then just do a few extra iterations */
+    /*  before stopping                                                          */
+    /*****************************************************************************/
+    
+    if( (fabs(errx) <= NEWT_TOL) && (doing_extra == 0) && (EXTRA_NEWT_ITER > 0) ) {
+      doing_extra = 1;
+    }
+
+    if( doing_extra == 1 ) i_extra++ ;
+
+    if( ((fabs(errx) <= NEWT_TOL)&&(doing_extra == 0)) 
+        || (i_extra > EXTRA_NEWT_ITER) || (n_iter >= (MAX_NEWT_ITER-1)) ) {
+      keep_iterating = 0;
+    }
+
+    n_iter++;
+
+  }   // END of while(keep_iterating)
+
+
+    /*  Check for bad untrapped divergences : */
+  if( (!finite(f)) ||  (!finite(df)) ) {
+    return(2);
+  }
+
+
+  if( fabs(errx) <= eosvars->prec ){
+    return(0);
+  }
+  else if( (fabs(errx) <= eosvars->prec) && (fabs(errx) > eosvars->prec) ){
+    return(0);
+  }
+  //if( fabs(errx) <= NEWT_TOL ){
+  //  return(0);
+  //}
+  //else if( (fabs(errx) <= MIN_NEWT_TOL) && (fabs(errx) > NEWT_TOL) ){
+  //  return(0);
+  //}
+  else {
+    return(1);
+  } 
+
+  return(0);
+
+}
+
+/**********************************************************************/
+/*********************************************************************************
+   func_vsq(): 
+
+        -- calculates the residuals, and Newton step for general_newton_raphson();
+        -- for this method, x=W,vsq here;
+
+     Arguments:
+          x   = current value of independent var's (on input & output);
+         dx   = Newton-Raphson step (on output);
+        resid = residuals based on x (on output);
+         jac  = Jacobian matrix based on x (on output);
+         f    =  resid.resid/2  (on output)
+        df    = -2*f;  (on output)
+         n    = dimension of x[];
+ *********************************************************************************/
+
+static void func_vsq(CCTK_REAL x[], CCTK_REAL dx[], CCTK_REAL resid[], 
+                     CCTK_REAL jac[][2], CCTK_REAL *f, CCTK_REAL *df, CCTK_REAL gammaeos, struct LocGlob *lgp)
+{
+
+  
+  CCTK_REAL  W, vsq, Wsq, p_tmp, dPdvsq, dPdW;
+  CCTK_REAL res0, QB2Winv2,res1,j11,detJinv,   Winv,   QB2Winv3,   j10,   B2plusW,   detJ,   t36,   mj01,   j00;
+
+
+  W = x[0];
+  vsq = x[1];
+  
+  Wsq = W*W;
+  
+  p_tmp = eos_info(W, vsq, &dPdW, &dPdvsq, gammaeos, lgp);
+
+  // These expressions were calculated using Mathematica, but made into efficient 
+  // code using Maple.  Since we know the analytic form of the equations, we can 
+  // explicitly calculate the Newton-Raphson step: 
+
+  //j11 = dP/dv^2-B^2/2
+  j11 = -lgp->half_Bsq+dPdvsq;
+
+  B2plusW = lgp->Bsq+W;
+
+  //mj01 is B2plusW squared = - (partial Eq. 4 / partial v^2)
+  mj01 = B2plusW*B2plusW;
+
+  Winv = 1/W;
+
+  QB2Winv2 = lgp->QdotBsq*Winv*Winv;
+
+  //Eq. 4 - Residual 0: Qtsq - v^2(B^2+W)^2 -QdotBsq(B^2+2W)/W^2
+  res0 = lgp->Qtsq-vsq*mj01+QB2Winv2*(lgp->Bsq+W+W);
+
+  //Eq. 5 - Residual 1: -Qdotn - B^2/2(1+v^2)+1/2 QdotBsq/W^2 - W+p
+  res1 = -lgp->Qdotn-lgp->half_Bsq*(1.0+vsq)+0.5*QB2Winv2-W+p_tmp;
+
+  QB2Winv3 = QB2Winv2*Winv;
+
+  //j10 is -QB2Winv3 - 1 + dp/dW - (partial Eq. 5 / partial W)
+  j10 = -1.0+dPdW-QB2Winv3;
+
+  //This is detJ: j10*mj01/B2W +  -2 j11            *   -j00/2
+  detJ = B2plusW*(j10*B2plusW+(lgp->Bsq-2.0*dPdvsq)*(QB2Winv2+vsq*W)*Winv);
+
+  detJinv = 1/detJ;
+
+  // - (Jinv00 * res0 + Jinv01 * res 1)/detJ
+  dx[0] = -(j11*res0+mj01*res1)*detJinv;
+
+  //j00 is -2v^2(B^2+W)-2QB2 (B2+W)/W^3 - (partial Eq. 4 / partial W)
+  j00 = -2*(vsq+QB2Winv3)*B2plusW;
+
+  // (-Jinv10 * res0 -Jinv11 * res1) / DetJ
+  dx[1] = (j10*res0-j00*res1)*detJinv;
+  //  detJ = B2plusW*detJ_gcf;
+  jac[0][0] = j00;
+  jac[0][1] = -mj01;
+  jac[1][0] = j10;
+  jac[1][1] = j11;
+  resid[0] = res0;
+  resid[1] = res1;
+
+  *df = -resid[0]*resid[0] - resid[1]*resid[1];
+
+  *f = -0.5 * ( *df );
+
+}
+
+/**********************************************************************/
+/*********************************************************************************
+   func_vsq_eosomni(): 
+
+        -- calculates the residuals, and Newton step for general_newton_raphson();
+        -- for this method, x=W,vsq,u here;
+
+     Arguments:
+          x   = current value of independent var's (on input & output);
+         dx   = Newton-Raphson step (on output);
+        resid = residuals based on x (on output);
+         jac  = Jacobian matrix based on x (on output);
+         f    =  resid.resid/2  (on output)
+        df    = -2*f;  (on output)
+         n    = dimension of x[];
+ *********************************************************************************/
+
+static void func_vsq_eosomni(CCTK_REAL x[], CCTK_REAL dx[], CCTK_REAL resid[], 
+                             CCTK_REAL jac[][3], CCTK_REAL *f, CCTK_REAL *df, 
+                             struct eosomnivars *eosvars, struct LocGlob *lgp)
+{
+
+  CCTK_REAL  W, vsq, u, p_tmp,epsilon,Wsq, dPdvsq, dPdW;
+  CCTK_REAL res0, LorInv, rho0, Winv, QB2Winv2, drho0_dv, res1, j11, detJ,detJinv;
+  CCTK_REAL QB2Winv3, j10,B2plusW,detJ_gcf,t36,B2plusW_sq, j00,j01,j12,j20,j21,j22;
+  CCTK_REAL dpress_dv,dpress_du,dpdrho,dpdeps,c00,c01,c02,c10,c11,c12,c20,c21,c22;
+
+
+  W = x[0];
+  vsq = x[1];
+  u = x[2];
+  
+  Wsq = W*W;
+  
+  LorInv = sqrt(1.0-vsq);
+  rho0 = lgp->D * LorInv;
+  epsilon = u/rho0;
+  p_tmp = pressure_rho0_eps_eosomni(rho0,epsilon,&dpdrho,&dpdeps,eosvars);
+
+  B2plusW = lgp->Bsq+W;
+  B2plusW_sq = B2plusW*B2plusW;
+  Winv = 1/W;
+  QB2Winv2 = lgp->QdotBsq*Winv*Winv;
+  QB2Winv3=QB2Winv2*Winv;
+
+  //Eq. 4: Qtsq-v^2(B^2+W)^2-QdotBsq(B^2+2W)/W^2=0 <-No u or p dependence
+
+  resid[0] = lgp->Qtsq - vsq*B2plusW_sq+QB2Winv2*(lgp->Bsq+W+W);
+
+  j00 = -2*(vsq+QB2Winv3)*B2plusW;
+  j01 = -1.0*B2plusW_sq;
+
+
+  //Eq. 5: -Qdotn - B^2(1+vsq)/2 + QdotBsq/2/W^2 - vsq W - rho_0(vsq) - u = 0
+  //rho0 = D * sqrt(1-vsq)
+
+  resid[1] = -lgp->Qdotn - lgp->half_Bsq*(1.0+vsq) + 0.5*QB2Winv2 - vsq*W - rho0 - u;
+
+  drho0_dv = -0.5*lgp->D / LorInv;
+
+  j10 = -vsq-QB2Winv3;
+  j11 = -lgp->half_Bsq - W - drho0_dv;
+
+  //Eq. 6: u+ p - W(1-vsq) + rho0 = 0  =>  p-W = -W vsq - rho0 - u
+
+  resid[2] = u + p_tmp - W*(1.0-vsq) + rho0;
+
+  //dp/dv = (dp/drho)u *  drho/dv
+  //dp/drho_u = dp/drho_eps - eps/rho0 dpdeps 
+  dpress_dv = drho0_dv*dpdrho+
+    u/2.0/lgp->D*pow(1.0-vsq,-1.5)*dpdeps;
+
+  //dp/du = 1/rho dp deps, since rho0 is function of v only
+  dpress_du=dpdeps/rho0;
+
+  jac[0][0] = j00;
+  jac[0][1] = j01;
+  jac[0][2] = 0.0;
+  jac[1][0] = j10;
+  jac[1][1] = j11;
+  jac[1][2] = -1.0;
+  jac[2][0] = vsq-1.0; 
+  jac[2][1] = dpress_dv + W + drho0_dv;
+  jac[2][2] = dpress_du + 1.0;
+
+  c00 = j11*jac[2][2]+jac[2][1];
+  c01 = -1*j01*jac[2][2];
+  c02 = j01*jac[1][2];
+
+  c10 = -jac[2][0]-j10*jac[2][2];
+  c11 = j00*jac[2][2];
+  c12 = j00;
+
+  c20 = j10*jac[2][1]-j11*jac[2][0];
+  c21 = j01*jac[2][0]-j00*jac[2][1];
+  c22 = j00*j11-j01*j10;
+
+  detJ=j00*c00+j01*c10;
+  detJinv = 1/detJ;
+  
+  dx[0] = -(c00*resid[0]+c01*resid[1]+c02*resid[2])*detJinv;
+  dx[1] = -(c10*resid[0]+c11*resid[1]+c12*resid[2])*detJinv;
+  dx[2] = -(c20*resid[0]+c21*resid[1]+c22*resid[2])*detJinv;
+
+  *df = -resid[0]*resid[0] - resid[1]*resid[1] - resid[2]*resid[2];
+
+  *f = -0.5 * ( *df );
+
+}
+
+
+/********************************************************************** 
+ ********************************************************************** 
+   
+ The following routines specify the equation of state.  All routines 
+  above here should be indpendent of EOS.  If the user wishes 
+  to use another equation of state, the below functions must be replaced 
+  by equivalent routines based upon the new EOS. 
+
+ **********************************************************************
+**********************************************************************/
+
+/**********************************************************************/
+/********************************************************************** 
+  eos_info():
+ 
+      -- returns with all the EOS-related values needed;
+ **********************************************************************/
+static CCTK_REAL eos_info(CCTK_REAL W, CCTK_REAL vsq, CCTK_REAL *dpdw, CCTK_REAL *dpdvsq, CCTK_REAL gammaeos, struct LocGlob *lgp)
+{
+  register CCTK_REAL ftmp,gtmp;
+
+  ftmp = 1. - vsq;
+  gtmp = sqrt(ftmp);
+
+  CCTK_REAL gam_m1_o_gam = ((gammaeos-1.)/gammaeos);
+
+  *dpdw =  gam_m1_o_gam * ftmp ;
+  *dpdvsq =  gam_m1_o_gam * ( 0.5 * lgp->D/gtmp  -  W ) ;
+
+  return( gam_m1_o_gam * ( W * ftmp  -  lgp->D * gtmp )  );  // p 
+
+}
+
+static CCTK_REAL pressure_rho0_eps_eosomni(CCTK_REAL rho,CCTK_REAL epsilon, CCTK_REAL* dpdrho, CCTK_REAL* dpdeps, struct eosomnivars *eosvars)
+{
+
+  CCTK_REAL rhopt[1],epspt[1],press[1];
+  rhopt[0]=rho;
+  epspt[0]=epsilon;
+
+  EOS_Omni_press(eosvars->eoshandle,eosvars->eoskeytemp,eosvars->eosprec,1,
+                 &rho,&epsilon,eosvars->eos_temp,
+                 eosvars->eos_y_e,press,eosvars->eoskeyerr,eosvars->eosanyerr);
+
+  EOS_Omni_DPressByDRho(eosvars->eoshandle,eosvars->eoskeytemp,eosvars->eosprec,1,
+                 &rho,&epsilon,eosvars->eos_temp,
+                 eosvars->eos_y_e,dpdrho,eosvars->eoskeyerr,eosvars->eosanyerr);
+
+  EOS_Omni_DPressByDEps(eosvars->eoshandle,eosvars->eoskeytemp,eosvars->eosprec,1,
+                 &rho,&epsilon,eosvars->eos_temp,
+                 eosvars->eos_y_e,dpdeps,eosvars->eoskeyerr,eosvars->eosanyerr);
+
+  return press[0];
+
+}
+
+
+/****************************************************************************** 
+             END   
+ ******************************************************************************/
+
+
+#undef DEBUG_CON2PRIMM