Current RIT GRMHD code contributions:

Add the magnetized counterparts for several GRHydro routines.

Adjust interface.ccl, param.ccl and schedule.ccl appropriately.



git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinEvolve/GRHydro/trunk@158 c83d129a-5a75-4d5a-9c4d-ed3a5855bf45

1 files changed, 690 insertions, 0 deletions

diff --git a/src/GRHydro_Con2PrimM_pt.c b/src/GRHydro_Con2PrimM_pt.c
new file mode 100644
index 0000000..d9ba2a6
--- /dev/null
+++ b/src/GRHydro_Con2PrimM_pt.c
@@ -0,0 +1,690 @@
+/***********************************************************************************
+    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"
+
+/* 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 */
+static CCTK_REAL Bsq,QdotBsq,Qtsq,Qdotn,D,half_Bsq ;
+
+// Declarations: 
+static CCTK_REAL vsq_calc(CCTK_REAL W);
+
+static CCTK_INT twod_newton_raphson( CCTK_REAL x[], 
+				     void (*funcd) (CCTK_REAL [], CCTK_REAL [], 
+						    CCTK_REAL [], CCTK_REAL [][2], 
+						    CCTK_REAL *, CCTK_REAL *) );
+
+static  void func_vsq( CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], CCTK_REAL [][2], 
+		       CCTK_REAL *f, CCTK_REAL *df);
+static CCTK_REAL x1_of_x0(CCTK_REAL x0 ) ;
+
+
+// EOS STUFF:
+#define gam (5./3.)
+#define GAMMA	        (gam)  
+static CCTK_REAL gam_m1_o_gam = ((GAMMA-1.)/GAMMA);
+static CCTK_REAL eos_info(CCTK_REAL W, CCTK_REAL vsq, CCTK_REAL *dpdw, CCTK_REAL *dpdvsq);
+/* pressure as a function of rho0 and u */
+static CCTK_REAL pressure_rho0_u(CCTK_REAL rho0, CCTK_REAL u)
+{
+  return((GAMMA - 1.)*u) ;
+}
+
+/* Pressure as a function of rho0 and w = rho0 + u + p */
+static CCTK_REAL pressure_rho0_w(CCTK_REAL rho0, CCTK_REAL w)
+{
+  return((GAMMA-1.)*(w - rho0)/GAMMA) ;
+}
+
+
+void CCTK_FCALL CCTK_FNAME(GRHydro_Con2PrimM_pt) (
+    CCTK_INT  *handle, 
+    CCTK_REAL *dens_in, 
+    CCTK_REAL *sx_in, CCTK_REAL *sy_in, CCTK_REAL *sz_in, 
+    CCTK_REAL *tau_in, 
+    CCTK_REAL *rho, 
+    CCTK_REAL *velx, CCTK_REAL *vely, CCTK_REAL *velz,
+    CCTK_REAL *epsilon, CCTK_REAL *pressure,
+    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_REAL *Bx, CCTK_REAL *By, CCTK_REAL *Bz, 
+    CCTK_REAL *bsq,
+    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_pt)  ( 
+    CCTK_INT  *handle, 
+    CCTK_REAL *dens_in, 
+    CCTK_REAL *sx_in, CCTK_REAL *sy_in, CCTK_REAL *sz_in, 
+    CCTK_REAL *tau_in, 
+    CCTK_REAL *rho, 
+    CCTK_REAL *velx, CCTK_REAL *vely, CCTK_REAL *velz,
+    CCTK_REAL *epsilon, CCTK_REAL *pressure,
+    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_REAL *Bx, CCTK_REAL *By, CCTK_REAL *Bz, 
+    CCTK_REAL *bsq,
+    CCTK_INT  *epsnegative,
+    CCTK_REAL *retval)
+
+{
+  CCTK_REAL x_2d[2];
+  CCTK_REAL sx, sy, sz;
+  CCTK_REAL usx, usy, usz;
+  CCTK_REAL tau, dens;
+  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 ;
+
+  /* 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," *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," *pressure    = %26.16e \n", *pressure    );
+  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," *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," *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;
+
+  // Calculate various scalars (Q.B, Q^2, etc)  from the conserved variables:
+  
+  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)) ;
+  QdotBsq = QdotB*QdotB ;
+
+  Qdotn = -(tau + dens) ;
+
+  Qtsq = (usx * sx  +  usy * sy  +  usz * sz) ;
+
+  D = dens;
+
+  half_Bsq = 0.5*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.;
+    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 = D / gamma ;
+  u = (*epsilon) * rho0;
+  p = pressure_rho0_u(rho0,u) ;  // EOS
+  w = rho0 + u + p ;
+
+  W_last = w*gammasq ;
+
+
+  // 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.*Bsq ) 
+	    - QdotBsq*(2.*W_last + Bsq) ) <= W_last*W_last*(Qtsq-Bsq*Bsq))
+	 && (i_increase < 10) ) {
+    W_last *= 10.;
+    i_increase++;
+  }
+  
+  // Calculate W and vsq: 
+  x_2d[0] =  fabs( W_last );
+  x_2d[1] = x1_of_x0( W_last ) ;
+  *retval = 1.0*twod_newton_raphson( x_2d, func_vsq ) ;  
+
+  W = x_2d[0];
+  vsq = x_2d[1];
+	
+  /* Problem with solver, so return denoting error before doing anything further */
+  if( ((*retval) != 0.) || (W == FAIL_VAL) ) {
+    *retval = *retval*100.+1.;
+    return;
+  }
+  else{
+    if(W <= 0. || W > W_TOO_BIG) {
+      *retval = 3.;
+      return;
+    }
+  }
+
+  // Calculate v^2:
+  if( vsq >= 1. ) {
+    *retval = 4.;
+    return;
+  }
+
+  // Recover the primitive variables from the scalars and conserved variables:
+  gtmp = sqrt(1. - vsq);
+  gamma = 1./gtmp ;
+  rho0 = D * gtmp;
+
+  w = W * (1. - vsq) ;
+  p = pressure_rho0_w(rho0,w) ;  // EOS
+  u = w - (rho0 + 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; 
+    return;
+  }
+
+  *rho = rho0;
+  *epsilon = u / rho0;
+  *w_lorentz = gamma; 
+  *pressure = p ; 
+
+  g_o_WBsq = 1./(W+Bsq);
+  QdB_o_W  = QdotB / W; 
+  *bsq = 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(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,"gam          = %26.16e \n",gam       );
+  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)
+{
+	CCTK_REAL Wsq,Xsq,Bsq_W;
+	
+	Wsq = W*W ;
+	Bsq_W = (Bsq + W);
+	Xsq = Bsq_W * Bsq_W;
+
+	return(  ( Wsq * Qtsq  + 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 ) 
+{
+  CCTK_REAL x1,vsq;
+  CCTK_REAL dv = 1.e-15;
+
+  vsq = fabs(vsq_calc(x0)) ; // 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.
+
+    -- inspired in part by Num. Rec.'s routine newt();
+
+*****************************************************************/
+static CCTK_INT twod_newton_raphson( CCTK_REAL x[], 
+			    void (*funcd) (CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], 
+					   CCTK_REAL [][2], CCTK_REAL *, 
+					   CCTK_REAL *) )
+{
+  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);  /* 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);
+
+}
+
+
+
+/**********************************************************************/
+/*********************************************************************************
+   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  W, vsq, Wsq, p_tmp, dPdvsq, dPdW;
+  CCTK_REAL t11, t16,t18,t2,t21,   t23,   t24,   t25,   t3,   t35,   t36,   t4,   t40;
+
+
+  W = x[0];
+  vsq = x[1];
+  
+  Wsq = W*W;
+  
+  p_tmp = eos_info(W, vsq, &dPdW, &dPdvsq);
+
+  // 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: 
+
+  t2 = -half_Bsq+dPdvsq;
+  t3 = Bsq+W;
+  t4 = t3*t3;
+  t23 = 1/W;
+  t16 = QdotBsq*t23*t23;
+  t11 = Qtsq-vsq*t4+t16*(Bsq+W+W);
+  t18 = -Qdotn-half_Bsq*(1.0+vsq)+0.5*t16-W+p_tmp;
+  t24 = t16*t23;
+  t25 = -1.0+dPdW-t24;
+  t35 = t25*t3+(Bsq-2.0*dPdvsq)*(t16+vsq*W)*t23;
+  //  t21 = 1/t3;
+  //  t36 = 1/t35;
+  t21 = 1/(t3*t35);
+  dx[0] = -(t2*t11+t4*t18)*t21;
+  t40 = -2*(vsq+t24)*t3;
+  dx[1] = -(-t25*t11+t40*t18)*t21;
+  //  detJ = t3*t35;
+  jac[0][0] = t40;
+  jac[0][1] = -t4;
+  jac[1][0] = t25;
+  jac[1][1] = t2;
+  resid[0] = t11;
+  resid[1] = t18;
+
+  *df = -resid[0]*resid[0] - resid[1]*resid[1];
+
+  *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)
+{
+  register double ftmp,gtmp;
+
+  ftmp = 1. - vsq;
+  gtmp = sqrt(ftmp);
+
+  *dpdw =  gam_m1_o_gam * ftmp ;
+  *dpdvsq =  gam_m1_o_gam * ( 0.5 * D/gtmp  -  W ) ;
+
+  return( gam_m1_o_gam * ( W * ftmp  -  D * gtmp )  );  // p 
+
+}
+
+
+/****************************************************************************** 
+             END   
+ ******************************************************************************/
+
+
+#undef DEBUG_CON2PRIMM