[Commits] [svn:einsteintoolkit] GRHydro/trunk/src/ (Rev. 200)

User: bmundim Date: 2010/12/25 12:53 AM

Added: /trunk/src/ GRHydro_Con2PrimM_polytype_pt.c

Log: Add missing file from previous commit.

File Changes:

Directory: /trunk/src/ ======================

File [added]: GRHydro_Con2PrimM_polytype_pt.c Delta lines: +916 -0 =================================================================== --- trunk/src/GRHydro_Con2PrimM_polytype_pt.c (rev 0) +++ trunk/src/GRHydro_Con2PrimM_polytype_pt.c 2010-12-25 06:53:39 UTC (rev 200) @@ -0,0 +1,916 @@ +/*********************************************************************************** + 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,rho_gm1; +static CCTK_REAL W_for_gnr2, rho_for_gnr2, W_for_gnr2_old, rho_for_gnr2_old, drho_dW; +static CCTK_REAL t2,t4,t7,t24,two_Bsq,t300,t400,s200,s100; + + +// Declarations: +static CCTK_REAL vsq_calc(CCTK_REAL W); + +static CCTK_INT oned_newton_raphson( CCTK_REAL x[], CCTK_INT n, CCTK_REAL gammaeos, + void (*funcd) (CCTK_REAL [], CCTK_REAL [], + CCTK_REAL [], CCTK_REAL [][1], + CCTK_REAL *, CCTK_REAL *, CCTK_INT, CCTK_REAL) ); + +static void func_W( CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], CCTK_REAL [][1], + CCTK_REAL *f, CCTK_REAL *df, CCTK_INT n, CCTK_REAL gammaeos); +static CCTK_REAL x1_of_x0(CCTK_REAL x0 ) ; + +static CCTK_INT gnr2( CCTK_REAL x[], CCTK_INT n, CCTK_REAL gammaeos, + void (*funcd) (CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], + CCTK_REAL [][1],CCTK_REAL *,CCTK_REAL *,CCTK_INT, CCTK_REAL) ); +static void func_rho(CCTK_REAL x[], CCTK_REAL dx[], CCTK_REAL resid[], + CCTK_REAL jac[][1], CCTK_REAL *f, CCTK_REAL *df, CCTK_INT n, CCTK_REAL gammaeos); + +static CCTK_REAL eos_info(CCTK_REAL W, CCTK_REAL vsq, CCTK_REAL *dpdw, CCTK_REAL *dpdvsq, CCTK_REAL gammaeos); +/* 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) ; +} + +/* 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_Polytype_pt) ( + CCTK_INT *handle, CCTK_REAL *gamma_eos, + CCTK_REAL *dens_in, + CCTK_REAL *sx_in, CCTK_REAL *sy_in, CCTK_REAL *sz_in, + CCTK_REAL *sc_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_Polytype_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 = as defined in GRHydro and are assumed to be densitized (i.e. with sqrt(\gamma)) + dens = D = \sqrt(\gamma) W \rho + sc_in = K D, where K is the polytropic constant + 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_Polytype_pt) ( + CCTK_INT *handle, CCTK_REAL *gamma_eos, + CCTK_REAL *dens_in, + CCTK_REAL *sx_in, CCTK_REAL *sy_in, CCTK_REAL *sz_in, + CCTK_REAL *sc_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_1d[1]; + CCTK_REAL sx, sy, sz; + CCTK_REAL usx, usy, usz; + CCTK_REAL dens, gammaeos; + CCTK_REAL QdotB,utsq,gamma_sq; + CCTK_REAL rho0,u,p,w,gammasq,gamma,gtmp,W_last,W,vsq; + CCTK_REAL g_o_WBsq, QdB_o_W; + CCTK_REAL rho_g, x_rho[1]; + CCTK_REAL detg = (*det); + CCTK_REAL sqrt_detg = sqrt(detg); + CCTK_REAL inv_sqrt_detg = 1./sqrt_detg; + CCTK_INT i,j, i_increase,ntries ; + + /* Assume ok initially: */ + *retval = 0.; + *epsnegative = 0; + + gammaeos = *gamma_eos; + +#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," *Sc = %26.16e \n", *sc_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; + 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 ; + + Qtsq = (usx * sx + usy * sy + usz * sz) ; + + D = dens; + + half_Bsq = 0.5*Bsq; + + t2 = D*D; + t4 = QdotBsq*t2; + t7 = Bsq*Bsq; + t24 = 1/t2; + two_Bsq = Bsq + Bsq; + t300 = QdotBsq*Bsq*t2; + t400 = Qtsq*t2; + + s200 = D*gammaeos*(*sc_in); + CCTK_REAL g_o_gm1 = (gammaeos/(gammaeos-1.)); + s100 = g_o_gm1*(*sc_in); + + /* 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 ; + CCTK_REAL gm1 = gammaeos-1.; + rho_gm1 = pow(rho0,gm1); + p = (*sc_in) * rho_gm1 / gamma; + u = p / gm1; + 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++; + } + + W_for_gnr2 = W_for_gnr2_old = W_last; + rho_for_gnr2 = rho_for_gnr2_old = rho0; + + // Calculate W: + x_1d[0] = W_last; + + *retval = 1.0*oned_newton_raphson( x_1d, 1, gammaeos, func_W ) ; + + W = x_1d[0]; + + /* 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; + } + } + + rho_g = x_rho[0] = rho_for_gnr2; + + ntries = 0; + while ( (*retval = gnr2( x_rho, 1, gammaeos, func_rho)) && ( ntries++ < 10 ) ) { + rho_g *= 10.; + x_rho[0] = rho_g; + } + + rho_for_gnr2 = x_rho[0]; + + if( (*retval != 0) ) { + *retval = 10; + return; + } + + // Calculate v^2 : + rho0 = rho_for_gnr2; + rho_gm1 = pow(rho0,gm1); + + utsq = (D-rho0)*(D+rho0)/(rho0*rho0); + + gamma_sq = 1.+utsq; + gamma = sqrt(gamma_sq); + + // Calculate v^2: + if( vsq >= 1. ) { + *retval = 4.; + return; + } + + // Recover the primitive variables from the scalars and conserved variables: + + w = W / gamma_sq; + + // printf("doublecheck - S, rho, gamma: %e %e %e\n",*sc_in, rho_gm1,gamma); + + p = (*sc_in) * rho_gm1 / gamma; + + u = p / gm1; + + // 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",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) +{ + 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; + +} + +/************************************************************ + + oned_newton_raphson(): + + -- performs Newton-Rapshon method on an 2d system. + + -- inspired in part by Num. Rec.'s routine newt(); + +*****************************************************************/ +static CCTK_INT oned_newton_raphson( CCTK_REAL x[], CCTK_INT n, CCTK_REAL gammaeos, + void (*funcd) (CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], + CCTK_REAL [][1], CCTK_REAL *, + CCTK_REAL *, CCTK_INT, CCTK_REAL) ) +{ + CCTK_REAL f, df, dx[1], x_old[1], resid[1], + jac[1][1]; + CCTK_REAL errx, x_orig[1]; + CCTK_INT n_iter, id, jd, i_extra, doing_extra; + CCTK_REAL dW,W,W_old; + + CCTK_INT keep_iterating, i_increase; + + + // Initialize various parameters and variables: + errx = 1. ; + df = f = 1.; + i_extra = doing_extra = 0; + //-fast for( id = 0; id < n ; id++) x_old[id] = x_orig[id] = x[id] ; + x_old[0] = x_orig[0] = x[0] ; + + 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, n, gammaeos); /* returns with new dx, f, df */ + + /* Save old values before calculating the new: */ + errx = 0.; + + //-fast for( id = 0; id < n ; id++) { x_old[id] = x[id] ; } + x_old[0] = x[0] ; + + /* don't use line search : */ + //-fast for( id = 0; id < n ; id++) { x[id] += dx[id] ; } + x[0] += dx[0] ; + +// //METHOD specific: +// i_increase = 0; +// while( (( x[0]*x[0]*x[0] * ( x[0] + 2.*Bsq ) - +// QdotBsq*(2.*x[0] + Bsq) ) <= x[0]*x[0]*(Qtsq-Bsq*Bsq)) +// && (i_increase < 10) ) { +// x[0] -= (1.*i_increase) * dx[0] / 10. ; +// i_increase++; +// } + + /****************************************/ + /* Calculate the convergence criterion */ + /****************************************/ + + /* For the new criterion, always look at error in "W" : */ + // METHOD specific: + errx = (x[0]==0.) ? fabs(dx[0]) : fabs(dx[0]/x[0]); + + + /****************************************/ + /* Make sure that the new x[] is physical : */ + /****************************************/ + x[0] = fabs(x[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)) || (!finite(x[0])) ) { +#if(DEBUG_CON2PRIMM) + fprintf(stderr,"\ngnr not finite, f,df,x_o,x,W_o,W,rho_o,rho = %26.20e %26.20e %26.20e %26.20e %26.20e %26.20e %26.20e %26.20e \n", + f,df,x[0],x_old[0],W_for_gnr2_old,W_for_gnr2,rho_for_gnr2_old,rho_for_gnr2); fflush(stderr); +#endif + 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_W() + + -- calculates the residuals, and Newton step for general_newton_raphson(); + -- for this method, x=W 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_W(CCTK_REAL x[], CCTK_REAL dx[], CCTK_REAL resid[], + CCTK_REAL jac[][1], CCTK_REAL *f, CCTK_REAL *df, CCTK_INT n, CCTK_REAL gammaeos) +{ + CCTK_INT retval, ntries; + CCTK_REAL W, x_rho[1], rho, rho_g ; + CCTK_REAL t15, t200,t1000 ; + + W = x[0]; + W_for_gnr2_old = W_for_gnr2; + W_for_gnr2 = W; + + // get rho from NR: + rho_g = x_rho[0] = rho_for_gnr2; + + ntries = 0; + while ( (retval = gnr2( x_rho, 1, gammaeos, func_rho)) && ( ntries++ < 10 ) ) { + rho_g *= 10.; + x_rho[0] = rho_g; + } + +#if(DEBUG_CON2PRIMM) + if( x_rho[0] <= 0. ) { + fprintf(stderr,"gnr2 neg rho = %d ,rho_n,rho,rho_o,W,W_o = %26.20e %26.20e %26.20e %26.20e %26.20e \n", retval, x_rho[0], rho_for_gnr2, rho_for_gnr2_old, x[0], W_for_gnr2_old); + fflush(stderr); + } + + if( retval ) { + fprintf(stderr,"gnr2 retval = %d ,rho_n,rho,rho_o,W,W_o = %26.20e %26.20e %26.20e %26.20e %26.20e \n", retval, x_rho[0], rho_for_gnr2, rho_for_gnr2_old, x[0], W_for_gnr2_old); + fflush(stderr); + } +#endif + + rho_for_gnr2_old = rho_for_gnr2; + rho = rho_for_gnr2 = x_rho[0]; + + CCTK_REAL gm1 = gammaeos-1.; + + rho_gm1 = pow(rho,gm1); + drho_dW = -rho*rho/( -rho_gm1*s200 + W*rho); + + // t6 = rho*rho; + // t100 = (D-rho)*(D+rho); // t2 - t6; + t15 = -(D-rho)*(D+rho); // t6-t2 + t200 = W + two_Bsq; + t1000 = rho*drho_dW; + resid[0] = (t300+(t4+t4+(t400+t15*(t7+(t200)*W))*W)*W)*t24; + jac[0][0] = 2*(t4+(t400+t15*t7+(3.0*t15*Bsq+t7*t1000+(t15+t15+t1000*(t200))*W)*W)*W)*t24; + + dx[0] = -resid[0]/jac[0][0]; + + *df = - resid[0]*resid[0]; + *f = -0.5*(*df); + + +// fprintf(stdout,"QdotBsq = %28.18e ; \n",QdotBsq ); +// fprintf(stdout,"Sc = %28.18e ; \n",Sc ); +// fprintf(stdout,"Bsq = %28.18e ; \n",Bsq ); +// fprintf(stdout,"Qtsq = %28.18e ; \n",Qtsq ); +// fprintf(stdout,"Dc = %28.18e ; \n",D ); +// fprintf(stdout,"drhodW = %28.18e ; \n",drho_dW ); +// fprintf(stdout,"W = %28.18e ; \n",W ); +// fprintf(stdout,"rho = %28.18e ; \n",rho ); +// fprintf(stdout,"resid_W = %28.18e ; \n",resid[0] ); +// fprintf(stdout,"jac_W = %28.18e ; \n",jac[0][0]); +// fprintf(stdout,"deriv1 %g %g %g %g \n",W,resid[0],jac[0][0],dx[0]); + + return; + +} + + +/***********************************************************/ +/********************************************************************** + + gnr2() + + -- used to calculate rho from W + +*****************************************************************/ +static CCTK_INT gnr2( CCTK_REAL x[], CCTK_INT n, CCTK_REAL gammaeos, + void (*funcd) (CCTK_REAL [], CCTK_REAL [], CCTK_REAL [], + CCTK_REAL [][1],CCTK_REAL *,CCTK_REAL *,CCTK_INT,CCTK_REAL) ) +{ + CCTK_REAL f, df, dx[1], x_old[1], resid[1], + jac[1][1]; + CCTK_REAL errx, x_orig[1]; + CCTK_INT n_iter, id,jd, i_extra, doing_extra; + CCTK_REAL dW,W,W_old; + + CCTK_INT keep_iterating; + + + // Initialize various parameters and variables: + errx = 1. ; + df = f = 1.; + i_extra = doing_extra = 0; + //-fast for( id = 0; id < n ; id++) x_old[id] = x_orig[id] = x[id] ; + x_old[0] = x_orig[0] = x[0] ; + + n_iter = 0; + + + /* Start the Newton-Raphson iterations : */ + keep_iterating = 1; + while( keep_iterating ) { + + (*funcd) (x, dx, resid, jac, &f, &df, n,gammaeos); /* returns with new dx, f, df */ + + /* Save old values before calculating the new: */ + //-fast errx = 0.; + //-fast for( id = 0; id < n ; id++) { x_old[id] = x[id] ; } + x_old[0] = x[0] ; + + /* Make the newton step: */ + //-fast for( id = 0; id < n ; id++) { x[id] += dx[id] ; } + x[0] += dx[0] ; + + /* Calculate the convergence criterion */ + //-fast for( id = 0; id < n ; id++) { errx += (x[id]==0.) ? fabs(dx[id]) : fabs(dx[id]/x[id]); } + //-fast errx /= 1.*n; + errx = (x[0]==0.) ? fabs(dx[0]) : fabs(dx[0]/x[0]); + + /* Make sure that the new x[] is physical : */ + // METHOD specific: + x[0] = fabs(x[0]); + + + /* If we've reached the tolerance level, then just do a few extra iterations */ + /* before stopping */ + if( (fabs(errx) <= NEWT_TOL2) && (doing_extra == 0) && (EXTRA_NEWT_ITER > 0) ) { + doing_extra = 0; + } + + if( doing_extra == 1 ) i_extra++ ; + + // See if we've done the extra iterations, or have done too many iterations: + if( ((fabs(errx) <= NEWT_TOL2)&&(doing_extra == 0)) || + (i_extra > EXTRA_NEWT_ITER) || (n_iter >= (MAX_NEWT_ITER-1)) ) { + keep_iterating = 0; + } + + n_iter++; + + } + + + /* Check for bad untrapped divergences : */ + if( (!finite(f)) || (!finite(df)) || (!finite(x[0])) ) { +#if(DEBUG_CON2PRIMM) + fprintf(stderr,"\ngnr2 not finite, f,df,x_o,x,W_o,W,rho_o,rho = %26.20e %26.20e %26.20e %26.20e %26.20e %26.20e %26.20e %26.20e \n", + f,df,x[0],x_old[0],W_for_gnr2_old,W_for_gnr2,rho_for_gnr2_old,rho_for_gnr2); fflush(stderr); +#endif + return(2); + } + + // Return in different ways depending on whether a solution was found: + 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_rho(): + + -- residual/jacobian routine to calculate rho from W via the polytrope: + + W = ( 1 + GAMMA * K_atm * rho^(GAMMA-1)/(GAMMA-1) ) D^2 / rho + + 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[]; + *********************************************************************************/ +// for the isentropic version: eq. (27) +static void func_rho(CCTK_REAL x[], CCTK_REAL dx[], CCTK_REAL resid[], + CCTK_REAL jac[][1], CCTK_REAL *f, CCTK_REAL *df, CCTK_INT n, CCTK_REAL gammaeos) +{ + + CCTK_REAL A, B, C, rho, W, B0; + CCTK_REAL t40,t14; + + CCTK_REAL gm1 = gammaeos-1.; + + rho = x[0]; + W = W_for_gnr2; + + rho_gm1 = t40 = pow(rho,gm1); + + resid[0] = (rho*W+(-t40*s100-D)*D); + t14 = t40/rho; // rho^(g-2) + jac[0][0] = -t14*s200 + W; + // drho_dW = -rho/jac[0][0]; + + dx[0] = -resid[0]/jac[0][0]; + *df = - resid[0]*resid[0]; + *f = -0.5*(*df); + + // fprintf(stdout,"deriv3 %g %g %g %g %g \n",rho,W,resid[0],jac[0][0],dx[0]); +// fprintf(stdout,"Dc := %28.18e ; \n",D); +// fprintf(stdout,"Sc := %28.18e ; \n",Sc); +// fprintf(stdout,"rho := %28.18e ; \n",rho); +// fprintf(stdout,"W := %28.18e ; \n",W); +// fprintf(stdout,"resid_rho := %28.18e ; \n",resid[0] ); +// fprintf(stdout,"jac_rho := %28.18e ; \n",jac[0][0] ); + + return; + +} + + +/********************************************************************** + ********************************************************************** + + 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) +{ + register double 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 * D/gtmp - W ) ; + + return( gam_m1_o_gam * ( W * ftmp - D * gtmp ) ); // p + +} + + +/****************************************************************************** + END + ******************************************************************************/ + + +#undef DEBUG_CON2PRIMM