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scvheos.c
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scvheos.c
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/*
* Copyright (c) 2020 Christian Reinhardt
*
* This file proves an interface for the SCvH equation of state (Saumon et al. 1995) for Hydrogen
* and Helium that was extended to lower temperatures by Vazan et al. (2013).
*
* Author: Christian Reinhardt
* Created: 02.04.2020
* Modified: 03.10.2022
*/
#include <stdlib.h>
#include <math.h>
#include <stdio.h>
#include <assert.h>
#include <string.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_interp2d.h>
#include <gsl/gsl_roots.h>
#include "scvheos.h"
/*
* Initalize a material.
*
* Initialize the material data, read the EOS tables and convert them to code units if desired.
*/
SCVHEOSMAT *scvheosInitMaterial(int iMat, double dKpcUnit, double dMsolUnit) {
const double KBOLTZ = 1.38e-16; /* bolzman constant in cgs */
const double MHYDR = 1.67e-24; /* mass of hydrogen atom in grams */
const double MSOLG = 1.99e33; /* solar mass in grams */
const double GCGS = 6.67e-8; /* G in cgs */
const double KPCCM = 3.085678e21; /* kiloparsec in centimeters */
const double NA = 6.022e23; /* Avogadro's number */
SCVHEOSMAT *Mat;
int nRho;
int nT;
char inFile[256];
int nSkip;
/* GSL interpolator type */
const gsl_interp2d_type *InterpType;
int bInterpBilinear = 1;
/*
* Allocate memory and initialize the data.
*
* Memory for the EOS tables is allocated in scvheosReadTable. The number of data points nRho
* and nT are set in the function if the table was read correctly.
*/
Mat = (SCVHEOSMAT *) calloc(1, sizeof(SCVHEOSMAT));
assert(Mat != NULL);
Mat->iMat = iMat;
Mat->dKpcUnit = dKpcUnit;
Mat->dMsolUnit = dMsolUnit;
Mat->nRho = 0;
Mat->nT = 0;
Mat->dLogBase = 10.0;
/* Set the reference density for ballic. */
Mat->rho0 = 1e-3;
/*
* Load the EOS table.
*/
switch(iMat)
{
case SCVHEOS_H:
/*
* Hydrogen.
*/
strcpy(inFile, "scvh_h_dt_cgs.txt");
nRho = 201;
nT = 100;
nSkip = 1;
strcpy(Mat->MatString, "Material not implemented yet.");
break;
case SCVHEOS_HE:
/*
* Helium.
*/
strcpy(inFile, "scvh_he_dt_cgs.txt");
nRho = 201;
nT = 100;
nSkip = 1;
strcpy(Mat->MatString, "Material not implemented yet.");
break;
case SCVHEOS_HHE:
/*
* Hydrogen / Helium mixture in Solar abundance.
*/
strcpy(inFile, "scvh_hhe_y0.275_dt_cgs.txt");
nRho = 201;
nT = 100;
nSkip = 1;
strcpy(Mat->MatString, "Material not implemented yet.");
break;
case SCVHEOS_HHE_LOWRHOT:
/*
* Hydrogen / Helium mixture in Solar abundance limited to low rho and T.
*/
strcpy(inFile, "scvh_hhe_y0.275_dt_cgs_lowrhot.txt");
nRho = 80;
nT = 48;
nSkip = 2;
strcpy(Mat->MatString, "SCvH EOS H-He Y=0.275 (Saumon et al. 1995, Vazan et al. 2013).");
break;
case SCVHEOS_HHE_EXT_LOWRHOT:
/*
* Hydrogen / Helium mixture (X=0.722, Y=0.278) based on the extended EOS tables
* limited to low rho and T.
*/
strcpy(inFile, "scvh_extended_dt_hydrogen_722_helium_278_lowrhot.txt");
nRho = 201;
nT = 31;
nSkip = 2;
strcpy(Mat->MatString, "SCvH EOS H-He X=0.722 Y=0.278 (Saumon et al. 1995, Vazan et al. 2013).");
break;
default:
/* Unknown material */
scvheosFinalizeMaterial(Mat);
assert(0);
}
/* Currently only SCVHEOS_HHE_EXT_LOWRHOT works. */
assert(iMat == SCVHEOS_HHE_EXT_LOWRHOT);
/*
* Allocate memory and read the EOS table.
*/
if (scvheosReadTable(Mat, inFile, nRho, nT, nSkip) != SCVHEOS_SUCCESS) {
fprintf(stderr, "SCVH EOS: Could not open EOS table %s.\n", inFile);
scvheosFinalizeMaterial(Mat);
exit(1);
}
/* Define limits of the table (or extrapolation). */
#if 0
Mat->LogRhoMin = -25.0;
Mat->LogRhoMax = 3.0;
Mat->LogTMin = -2;
Mat->LogTMax = 6;
#endif
#if 0
//Mat->LogRhoMin = -10.5;
Mat->LogRhoMin = -18.0;
Mat->LogRhoMax = -0.9;
Mat->LogTMin = -2.0;
Mat->LogTMax = 4.7;
#endif
#if 0
Mat->LogRhoMin = Mat->dLogRhoAxis[0];
Mat->LogRhoMax = Mat->dLogRhoAxis[Mat->nRho-1];
Mat->LogTMin = Mat->dLogTAxis[0];
//Mat->LogTMax = Mat->dLogTAxis[Mat->nT-1];
Mat->LogTMax = 3.6;
#endif
Mat->LogRhoMin = -25.0;
Mat->LogRhoMax = 1.0;
Mat->LogTMin = -1;
Mat->LogTMax = 4;
/*
* Convert from cgs to code units.
*/
if ((Mat->dKpcUnit > 0.0) && (Mat->dMsolUnit > 0.0)) {
Mat->dGasConst = Mat->dKpcUnit*KPCCM*KBOLTZ
/MHYDR/GCGS/Mat->dMsolUnit/MSOLG;
/* code energy per unit mass --> erg per g */
Mat->dErgPerGmUnit = GCGS*Mat->dMsolUnit*MSOLG/(Mat->dKpcUnit*KPCCM);
/* code density --> g per cc */
Mat->dGmPerCcUnit = (Mat->dMsolUnit*MSOLG)/pow(Mat->dKpcUnit*KPCCM,3.0);
/* code time --> seconds */
Mat->dSecUnit = sqrt(1/(Mat->dGmPerCcUnit*GCGS));
for (int i=0; i<Mat->nRho; i++) {
Mat->dLogRhoAxis[i] -= log10(Mat->dGmPerCcUnit);
}
for (int i=0; i<Mat->nT; i++) {
for (int j=0; j<Mat->nRho; j++) {
Mat->dLogPArray[j*Mat->nT+i] -= log10(Mat->dErgPerGmUnit*Mat->dGmPerCcUnit);
Mat->dLogUArray[j*Mat->nT+i] -= log10(Mat->dErgPerGmUnit);
Mat->dLogSArray[j*Mat->nT+i] -= log10(Mat->dErgPerGmUnit);
}
}
/* Convert table limits and reference density. */
Mat->LogRhoMin -= log10(Mat->dGmPerCcUnit);
Mat->LogRhoMax -= log10(Mat->dGmPerCcUnit);
Mat->rho0 /= Mat->dGmPerCcUnit;
} else {
/* Prevent problems if dKpcUnit or dMsolUnit are not set. */
Mat->dGasConst = 0.0;
Mat->dErgPerGmUnit = 1.0;
Mat->dGmPerCcUnit = 1.0;
Mat->dSecUnit = 1.0;
}
/*
* Initialize the GSL interpolator.
*/
if (bInterpBilinear) {
InterpType = gsl_interp2d_bilinear;
} else {
InterpType = gsl_interp2d_bicubic;
}
Mat->xAccP = gsl_interp_accel_alloc();
Mat->yAccP = gsl_interp_accel_alloc();
Mat->xAccU = gsl_interp_accel_alloc();
Mat->yAccU = gsl_interp_accel_alloc();
Mat->xAccS = gsl_interp_accel_alloc();
Mat->yAccS = gsl_interp_accel_alloc();
Mat->xAccCs = gsl_interp_accel_alloc();
Mat->yAccCs = gsl_interp_accel_alloc();
/* x corresponts to T and y corresponds to rho. */
Mat->InterpLogP = gsl_interp2d_alloc(InterpType, Mat->nT, Mat->nRho);
Mat->InterpLogU = gsl_interp2d_alloc(InterpType, Mat->nT, Mat->nRho);
Mat->InterpLogS = gsl_interp2d_alloc(InterpType, Mat->nT, Mat->nRho);
Mat->InterpLogCs = gsl_interp2d_alloc(InterpType, Mat->nT, Mat->nRho);
gsl_interp2d_init(Mat->InterpLogP, Mat->dLogTAxis, Mat->dLogRhoAxis, Mat->dLogPArray, Mat->nT, Mat->nRho);
gsl_interp2d_init(Mat->InterpLogU, Mat->dLogTAxis, Mat->dLogRhoAxis, Mat->dLogUArray, Mat->nT, Mat->nRho);
gsl_interp2d_init(Mat->InterpLogS, Mat->dLogTAxis, Mat->dLogRhoAxis, Mat->dLogSArray, Mat->nT, Mat->nRho);
/* The sound speed can only be calculated after the interpolation in P and u is initialized. */
if (scvheosGenerateSoundSpeedTable(Mat) != SCVHEOS_SUCCESS) {
fprintf(stderr, "scvheosInitMaterial: Could not generate table for sound speed.\n");
exit(1);
}
gsl_interp2d_init(Mat->InterpLogCs, Mat->dLogTAxis, Mat->dLogRhoAxis, Mat->dLogCArray, Mat->nT, Mat->nRho);
return Mat;
}
/*
* Free memory.
*/
int scvheosFinalizeMaterial(SCVHEOSMAT *Mat) {
if (Mat != NULL) {
if (Mat->dLogRhoAxis != NULL) free(Mat->dLogRhoAxis);
if (Mat->dLogTAxis != NULL) free(Mat->dLogTAxis);
if (Mat->dLogUArray != NULL) free(Mat->dLogUArray);
if (Mat->dLogPArray != NULL) free(Mat->dLogPArray);
if (Mat->dLogSArray != NULL) free(Mat->dLogSArray);
if (Mat->dLogCArray != NULL) free(Mat->dLogCArray);
free(Mat);
}
return SCVHEOS_SUCCESS;
}
/*
* Read an EOS table from a file.
*
* The function also allocates memory of the tables and sets nRho and nT.
*
* SCVHEOS:
*
* H: nRho = 201, nT = 100, logarithmic spacing (base 10)
* He: nRho = 201, nT = 100, logarithmic spacing (base 10)
* H/He: nRho = 201, nT = 100, logarithmic spacing (base 10)
*/
int scvheosReadTable(SCVHEOSMAT *Mat, char *chInFile, int nRho, int nT, int nSkip) {
FILE *fp;
char *chLine;
size_t nCharMax = 256;
int iRet;
int i, j;
if (Mat == NULL) {
return SCVHEOS_FAIL;
}
if ((Mat->dLogRhoAxis != NULL) || (Mat->dLogTAxis != NULL) || (Mat->dLogUArray != NULL) ||
(Mat->dLogPArray != NULL) || (Mat->dLogSArray != NULL)) {
return SCVHEOS_FAIL;
}
Mat->dLogRhoAxis = (double *) calloc(nRho, sizeof(double));
Mat->dLogTAxis = (double *) calloc(nT, sizeof(double));
/* The GSL interpolation functions require the tables are 1D arrays. */
Mat->dLogUArray = (double *) calloc(nT*nRho, sizeof(double));
Mat->dLogPArray = (double *) calloc(nT*nRho, sizeof(double));
Mat->dLogSArray = (double *) calloc(nT*nRho, sizeof(double));
if ((Mat->dLogRhoAxis == NULL) || (Mat->dLogTAxis == NULL) || (Mat->dLogUArray == NULL) ||
(Mat->dLogPArray == NULL) || (Mat->dLogSArray == NULL)) {
return SCVHEOS_FAIL;
}
chLine = (char *) calloc(nCharMax, sizeof(char));
/* Open the file and skip the first few lines. */
fp = fopen(chInFile, "r");
if (fp == NULL) {
return SCVHEOS_FAIL;
}
for (i=0; i<nSkip; i++) {
if (getline(&chLine, &nCharMax, fp) == -1) {
return SCVHEOS_FAIL;
}
}
for (i=0; i<nT; i++) {
for (j=0; j<nRho; j++) {
if (getline(&chLine, &nCharMax, fp) == -1) {
return SCVHEOS_FAIL;
}
/* We store the data as A[T][rho]. */
iRet = sscanf(chLine, "%lf %lf %lf %lf %lf", &Mat->dLogTAxis[i], &Mat->dLogRhoAxis[j],
&Mat->dLogPArray[j*nT+i],
&Mat->dLogUArray[j*nT+i],
&Mat->dLogSArray[j*nT+i]);
/* Check if the number of matches is correct. */
if (iRet != 5) {
return SCVHEOS_FAIL;
}
if ((pow(Mat->dLogBase, Mat->dLogRhoAxis[j]) < 0.0) ||
(pow(Mat->dLogBase, Mat->dLogTAxis[i]) < 0.0) ||
(pow(Mat->dLogBase, Mat->dLogUArray[j*nT+i]) < 0.0) ||
(pow(Mat->dLogBase, Mat->dLogSArray[j*nT+i]) < 0.0)) {
return SCVHEOS_FAIL;
}
}
}
fclose(fp);
free(chLine);
Mat->nRho = nRho;
Mat->nT = nT;
return SCVHEOS_SUCCESS;
}
/*
* Generate an array that contains the sound speed at each EOS table data point.
*
* The sound speed is calculated from
*
* cs^2 = dP/drho + T/(rho^2*C_v)*(dP/dT)^2
*
* where
*
* c_v = du/dT
*
* is the specific heat capacity at constant volume. The derivatives are obtained
* numerically.
*/
int scvheosGenerateSoundSpeedTable(SCVHEOSMAT *Mat) {
double rho;
double T;
double dPdrho;
double dPdT;
double cv;
double cs2;
if (Mat == NULL)
return SCVHEOS_FAIL;
if ((Mat->dLogRhoAxis == NULL) || (Mat->dLogTAxis == NULL))
return SCVHEOS_FAIL;
if (Mat->dLogCArray != NULL)
return SCVHEOS_FAIL;
/* The GSL interpolation functions require the tables are 1D arrays. */
Mat->dLogCArray = (double *) calloc(Mat->nT*Mat->nRho, sizeof(double));
if (Mat->dLogCArray == NULL)
return SCVHEOS_FAIL;
for (int i=0; i<Mat->nT; i++) {
for (int j=0; j<Mat->nRho; j++) {
rho = pow(Mat->dLogBase, Mat->dLogRhoAxis[j]);
T = pow(Mat->dLogBase, Mat->dLogTAxis[i]);
dPdrho = scvheosdPdRhoofRhoT(Mat, rho, T);
dPdT = scvheosdPdTofRhoT(Mat, rho, T);
cv = scvheosdUdTofRhoT(Mat, rho, T);
/* Use log(rho^2) = 2*log(rho). */
cs2 = dPdrho + T/(rho*rho*cv)*dPdT*dPdT;
assert(!isinf(cs2));
assert(cs2 > 0.0);
Mat->dLogCArray[j*Mat->nT+i] = log10(sqrt(cs2));
}
}
return SCVHEOS_SUCCESS;
}
// Functions that have to be implemented or added
// We also need derivatives to calculate the sound speed (maybe do this once and make a table)?
/*
* Calculate logP(logrho, logT).
*/
double scvheosLogPofLogRhoLogT(SCVHEOSMAT *Mat, double logrho, double logT) {
double logP;
if ((logrho < Mat->LogRhoMin) || (logrho > Mat->LogRhoMax) || (logT < Mat->LogTMin) || (logT > Mat->LogTMax)) {
fprintf(stderr, "scvheosLogPofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
if (gsl_interp2d_eval_e_extrap(Mat->InterpLogP, Mat->dLogTAxis, Mat->dLogRhoAxis, Mat->dLogPArray, logT, logrho,
Mat->xAccP, Mat->yAccP, &logP) != GSL_SUCCESS) {
fprintf(stderr, "scvheosLogPofLogRhoLogT: Interpolation failed (logrho= %15.7E logT= %15.7E).\n", logrho, logT);
exit(1);
}
return logP;
}
/*
* Calculate logU(logrho, logT).
*/
double scvheosLogUofLogRhoLogT(SCVHEOSMAT *Mat, double logrho, double logT) {
double logu;
if ((logrho < Mat->LogRhoMin) || (logrho > Mat->LogRhoMax) || (logT < Mat->LogTMin) || (logT > Mat->LogTMax)) {
fprintf(stderr, "scvheosLogUofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
if (gsl_interp2d_eval_e_extrap(Mat->InterpLogU, Mat->dLogTAxis, Mat->dLogRhoAxis, Mat->dLogUArray, logT, logrho,
Mat->xAccU, Mat->yAccU, &logu) != GSL_SUCCESS) {
fprintf(stderr, "scvheosLogUofLogRhoLogT: Interpolation failed (logrho= %15.7E logT= %15.7E).\n", logrho, logT);
exit(1);
}
return logu;
}
/*
* Calculate logs(logrho, logT).
*/
double scvheosLogSofLogRhoLogT(SCVHEOSMAT *Mat, double logrho, double logT) {
double logs;
if ((logrho < Mat->LogRhoMin) || (logrho > Mat->LogRhoMax) || (logT < Mat->LogTMin) || (logT > Mat->LogTMax)) {
fprintf(stderr, "scvheosLogSofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
if (gsl_interp2d_eval_e_extrap(Mat->InterpLogS, Mat->dLogTAxis, Mat->dLogRhoAxis, Mat->dLogSArray, logT, logrho,
Mat->xAccS, Mat->yAccS, &logs) != GSL_SUCCESS) {
fprintf(stderr, "scvheosLogSofLogRhoLogT: Interpolation failed (logrho= %15.7E logT= %15.7E).\n", logrho, logT);
exit(1);
}
return logs;
}
/*
* Calculate logcs(logrho, logT).
*/
double scvheosLogCsofLogRhoLogT(SCVHEOSMAT *Mat, double logrho, double logT) {
double logcs;
if ((logrho < Mat->LogRhoMin) || (logrho > Mat->LogRhoMax) || (logT < Mat->LogTMin) || (logT > Mat->LogTMax)) {
fprintf(stderr, "scvheosLogCsofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
if (gsl_interp2d_eval_e_extrap(Mat->InterpLogCs, Mat->dLogTAxis, Mat->dLogRhoAxis, Mat->dLogCArray, logT, logrho,
Mat->xAccCs, Mat->yAccCs, &logcs) != GSL_SUCCESS) {
fprintf(stderr, "scvheosLogCsofLogRhoLogT: Interpolation failed (logrho= %15.7E logT= %15.7E).\n", logrho, logT);
exit(1);
}
return logcs;
}
/*
* Calculate the pressure P(rho, T).
*/
double scvheosPofRhoT(SCVHEOSMAT *Mat, double rho, double T) {
double logrho;
double logT;
double P;
logrho = log10(rho);
logT = log10(T);
/* Interpolate in the table. */
P = pow(Mat->dLogBase, scvheosLogPofLogRhoLogT(Mat, logrho, logT));
return P;
}
/*
* Calculate the internal energy u(rho, T).
*/
double scvheosUofRhoT(SCVHEOSMAT *Mat, double rho, double T) {
double logrho;
double logT;
double u;
logrho = log10(rho);
logT = log10(T);
u = pow(Mat->dLogBase, scvheosLogUofLogRhoLogT(Mat, logrho, logT));
return u;
}
/*
* Calculate the entropy s(rho, T).
*/
double scvheosSofRhoT(SCVHEOSMAT *Mat, double rho, double T) {
double logrho;
double logT;
double s;
logrho = log10(rho);
logT = log10(T);
/* Interpolate in the table. */
s = pow(Mat->dLogBase, scvheosLogSofLogRhoLogT(Mat, logrho, logT));
return s;
}
/*
* Calculate the sound speed cs(rho, T).
*/
double scvheosCsofRhoT(SCVHEOSMAT *Mat, double rho, double T) {
double logrho;
double logT;
double Cs;
logrho = log10(rho);
logT = log10(T);
Cs = pow(Mat->dLogBase, scvheosLogCsofLogRhoLogT(Mat, logrho, logT));
return Cs;
}
/*
* Calculate the pressure P(rho, u).
*/
double scvheosPofRhoU(SCVHEOSMAT *Mat, double rho, double u) {
double logrho;
double logu;
double logT;
double P;
logrho = log10(rho);
logu = log10(u);
/* Calculate logT. */
logT = scvheosLogTofLogRhoLogU(Mat, logrho, logu);
/* Interpolate in the table. */
P = pow(Mat->dLogBase, scvheosLogPofLogRhoLogT(Mat, logrho, logT));
// CR
assert(P > 0.0);
return P;
}
/*
* Calculate the sound speed cs(rho, u).
*/
double scvheosCsofRhoU(SCVHEOSMAT *Mat, double rho, double u) {
double logrho;
double logu;
double logT;
double Cs;
logrho = log10(rho);
logu = log10(u);
/* Calculate logT. */
logT = scvheosLogTofLogRhoLogU(Mat, logrho, logu);
Cs = pow(Mat->dLogBase, scvheosLogCsofLogRhoLogT(Mat, logrho, logT));
return Cs;
}
/*
* Calculate the temperature logT(logrho, logu).
*/
double scvheosLogTofLogRhoLogU(SCVHEOSMAT *Mat, double logrho, double logu) {
/* GSL root finder */
gsl_root_fsolver *Solver;
const gsl_root_fsolver_type *SolverType;
gsl_function F;
struct LogUofLogRhoLogT_GSL_Params Params;
const double err_abs = 0.0;
const double err_rel = 1e-10;
int status;
int max_iter = 1000;
double logT_min, logT_max;
double logT = 0.0;
/* Initialize the parameters. */
Params.Mat = Mat;
Params.logrho = logrho;
Params.logu = logu;
/* Initialize the function used for root finding. */
F.function = &LogUofLogRhoLogT_GSL_rootfinder;
F.params = &Params;
/* Initialize the root finder. */
SolverType = gsl_root_fsolver_brent;
SolverType = gsl_root_fsolver_bisection;
Solver = gsl_root_fsolver_alloc(SolverType);
assert(Solver != NULL);
/* Set minimum and maximum temperature. */
logT_min = Mat->LogTMin;
logT_max = Mat->LogTMax;
/* Check if logu < logu(logrho, logT_min) or logu > logu(logrho, logT_max) and set a minimum or maximum value. */
#if 0
if (logu < scvheosLogUofLogRhoLogT(Mat, logrho, logT_min)) return logT_min;
if (logu > scvheosLogUofLogRhoLogT(Mat, logrho, logT_max)) return logT_max;
#endif
/*
/// CR: Careful, this assumes that u(T) is monotonic AND u(T_min) < u(T_max)
if (logu < scvheosLogUofLogRhoLogT(Mat, logrho, logT_min)) assert(logu >= scvheosLogUofLogRhoLogT(Mat, logrho, logT_min));
if (logu > scvheosLogUofLogRhoLogT(Mat, logrho, logT_max)) assert(logu <= scvheosLogUofLogRhoLogT(Mat, logrho, logT_max));
*/
/* Make sure the root is bracketed.*/
if (LogUofLogRhoLogT_GSL_rootfinder(logT_min, &Params)*LogUofLogRhoLogT_GSL_rootfinder(logT_max, &Params) > 0.0) {
// CR: 04.10.2022
fprintf(stderr, "scvheosLogTofLogRhoLogU:\n");
fprintf(stderr, "logrho= %g ", logrho);
fprintf(stderr, "logu= %g\n", logu);
fprintf(stderr, "LogTMin= %g ", Mat->LogTMin);
fprintf(stderr, "LogTMax= %g\n", Mat->LogTMax);
fprintf(stderr, "loguMin= %g\n", scvheosLogUofLogRhoLogT(Mat, logrho, Mat->LogTMin));
fprintf(stderr, "loguMax= %g\n", scvheosLogUofLogRhoLogT(Mat, logrho, Mat->LogTMax));
fprintf(stderr, "loguMax= %g\n", LogUofLogRhoLogT_GSL_rootfinder(logT_min, &Params)*LogUofLogRhoLogT_GSL_rootfinder(logT_max, &Params));
fprintf(stderr, "Could not bracket root.\n");
assert(0);
}
gsl_root_fsolver_set(Solver, &F, logT_min, logT_max);
for (int i=0; i<max_iter; i++) {
/* Do one iteration of the root solver. */
status = gsl_root_fsolver_iterate(Solver);
/* Estimate of the root. */
logT = gsl_root_fsolver_root(Solver);
/* Current interval that brackets the root. */
logT_min = gsl_root_fsolver_x_lower(Solver);
logT_max = gsl_root_fsolver_x_upper(Solver);
/* Test for convergence. */
status = gsl_root_test_interval(logT_min, logT_max, err_abs, err_rel);
#if 0
if (status == GSL_SUCCESS)
fprintf(stderr, "Converged: x= %g\n", x);
#endif
if (status != GSL_CONTINUE) break;
}
if (status != GSL_SUCCESS) logT = -1.0;
gsl_root_fsolver_free(Solver);
return logT;
}
/*
* Calculate the temperature logT(logrho, logs).
*/
double scvheosLogTofLogRhoLogS(SCVHEOSMAT *Mat, double logrho, double logs) {
/* GSL root finder */
gsl_root_fsolver *Solver;
const gsl_root_fsolver_type *SolverType;
gsl_function F;
struct LogSofLogRhoLogT_GSL_Params Params;
const double err_abs = 0.0;
const double err_rel = 1e-10;
int status;
int max_iter = 1000;
double logT_min, logT_max;
double logT = 0.0;
/* Initialize the parameters. */
Params.Mat = Mat;
Params.logrho = logrho;
Params.logs = logs;
/* Initialize the function used for root finding. */
F.function = &LogSofLogRhoLogT_GSL_rootfinder;
F.params = &Params;
/* Initialize the root finder. */
SolverType = gsl_root_fsolver_brent;
SolverType = gsl_root_fsolver_bisection;
Solver = gsl_root_fsolver_alloc(SolverType);
assert(Solver != NULL);
/* Set minimum and maximum temperature. */
logT_min = Mat->LogTMin;
logT_max = Mat->LogTMax;
/* Check if logs < logs(logrho, logT_min) or logs > logs(logrho, logT_max) and set a minimum or maximum value. */
if (logs < scvheosLogSofLogRhoLogT(Mat, logrho, logT_min)) return logT_min;
if (logs > scvheosLogSofLogRhoLogT(Mat, logrho, logT_max)) return logT_max;
/* Make sure the root is bracketed.*/
if (LogSofLogRhoLogT_GSL_rootfinder(logT_min, &Params)*LogSofLogRhoLogT_GSL_rootfinder(logT_max, &Params) > 0.0) {
fprintf(stderr, "Could not bracket root.\n");
assert(0);
}
gsl_root_fsolver_set(Solver, &F, logT_min, logT_max);
for (int i=0; i<max_iter; i++) {
/* Do one iteration of the root solver. */
status = gsl_root_fsolver_iterate(Solver);
/* Estimate of the root. */
logT = gsl_root_fsolver_root(Solver);
/* Current interval that brackets the root. */
logT_min = gsl_root_fsolver_x_lower(Solver);
logT_max = gsl_root_fsolver_x_upper(Solver);
/* Test for convergence. */
status = gsl_root_test_interval(logT_min, logT_max, err_abs, err_rel);
#if 0
if (status == GSL_SUCCESS)
fprintf(stderr, "Converged: x= %g\n", x);
#endif
if (status != GSL_CONTINUE) break;
}
if (status != GSL_SUCCESS) logT = -1.0;
gsl_root_fsolver_free(Solver);
return logT;
}
/*
* Calculate the density logrho(logP, logT).
*/
double scvheosLogRhoofLogPLogT(SCVHEOSMAT *Mat, double logP, double logT) {
/* GSL root finder */
gsl_root_fsolver *Solver;
const gsl_root_fsolver_type *SolverType;
gsl_function F;
struct LogPofLogRhoLogT_GSL_Params Params;
const double err_abs = 0.0;
const double err_rel = 1e-10;
int status;
int max_iter = 1000;
double logrho_min, logrho_max;
double logrho = 0.0;
/* Initialize the parameters. */
Params.Mat = Mat;
Params.logT = logT;
Params.logP = logP;
/* Initialize the function used for root finding. */
F.function = &LogPofLogRhoLogT_GSL_rootfinder;
F.params = &Params;
/* Initialize the root finder. */
SolverType = gsl_root_fsolver_brent;
SolverType = gsl_root_fsolver_bisection;
Solver = gsl_root_fsolver_alloc(SolverType);
assert(Solver != NULL);
/* Set minimum and maximum density. */
logrho_min = Mat->LogRhoMin;
logrho_max = Mat->LogRhoMax;
/* Make sure the root is bracketed.*/
if (LogPofLogRhoLogT_GSL_rootfinder(logrho_min, &Params)*LogPofLogRhoLogT_GSL_rootfinder(logrho_max, &Params) > 0.0) {
fprintf(stderr, "Could not bracket root.\n");
assert(0);
}
gsl_root_fsolver_set(Solver, &F, logrho_min, logrho_max);
for (int i=0; i<max_iter; i++) {
/* Do one iteration of the root solver. */
status = gsl_root_fsolver_iterate(Solver);
/* Estimate of the root. */
logrho = gsl_root_fsolver_root(Solver);
/* Current interval that brackets the root. */
logrho_min = gsl_root_fsolver_x_lower(Solver);
logrho_max = gsl_root_fsolver_x_upper(Solver);
/* Test for convergence. */
status = gsl_root_test_interval(logrho_min, logrho_max, err_abs, err_rel);
#if 0
if (status == GSL_SUCCESS)
fprintf(stderr, "Converged: x= %g\n", x);
#endif
if (status != GSL_CONTINUE) break;
}
if (status != GSL_SUCCESS) logrho = -1.0;
gsl_root_fsolver_free(Solver);
return logrho;
}
/*
* Calculate the temperature T(rho, u).
*/
double scvheosTofRhoU(SCVHEOSMAT *Mat, double rho, double u) {
double logrho;
double logu;
double T;
logrho = log10(rho);
logu = log10(u);
T = pow(Mat->dLogBase, scvheosLogTofLogRhoLogU(Mat, logrho, logu));
return T;
}
/*
* Calculate the temperature T(rho, s).
*/
double scvheosTofRhoS(SCVHEOSMAT *Mat, double rho, double s) {
double logrho;
double logs;
double T;
logrho = log10(rho);
logs = log10(s);
T = pow(Mat->dLogBase, scvheosLogTofLogRhoLogS(Mat, logrho, logs));
return T;
}
/*
* Calculate the density rho(P, T).
*/
double scvheosRhoofPT(SCVHEOSMAT *Mat, double P, double T) {
double logP;
double logT;
double rho;
logP = log10(P);
logT = log10(T);
rho = pow(Mat->dLogBase, scvheosLogRhoofLogPLogT(Mat, logP, logT));
return rho;
}
/*
* Calculate the derivative dlogP/dlogrho(logrho, logT).
*/
double scvheosdLogPdLogRhoofLogRhoLogT(SCVHEOSMAT *Mat, double logrho, double logT) {
/* Finite difference. */
double h = 1e-5*logrho;
double dLogPdLogRho;
if (!scvheosCheckBoundsLogRhoLogT(Mat, logrho, logT)) {
fprintf(stderr, "scvheosdLogPdLogRhoofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
/* If (rho, T) is inside of the EOS table use GSL. */
if (scvheosCheckTableBoundsLogRhoLogT(Mat, logrho, logT)) {
if (gsl_interp2d_eval_deriv_y_e(Mat->InterpLogP, Mat->dLogTAxis, Mat->dLogRhoAxis,
Mat->dLogPArray, logT, logrho, Mat->xAccP, Mat->yAccP, &dLogPdLogRho) == GSL_EDOM) {
fprintf(stderr, "scvheosdLogPdLogRhoofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
return dLogPdLogRho;
}
if ((logrho-h > Mat->LogRhoMin) && (logrho+h < Mat->LogRhoMax)) {
/* Central difference. */
dLogPdLogRho = (scvheosLogPofLogRhoLogT(Mat, logrho+h, logT)-scvheosLogPofLogRhoLogT(Mat, logrho-h, logT))/(2.0*h);
} else if (logrho-h > Mat->LogRhoMin) {
/* Backward finite difference. */
dLogPdLogRho = (scvheosLogPofLogRhoLogT(Mat, logrho, logT) - scvheosLogPofLogRhoLogT(Mat, logrho-h, logT))/h;
} else if (logrho+h < Mat->LogRhoMax) {
/* Forward finite difference. */
dLogPdLogRho = (scvheosLogPofLogRhoLogT(Mat, logrho+h, logT) - scvheosLogPofLogRhoLogT(Mat, logrho, logT))/h;
} else {
/* Both points are problematic so h is reduced. */
h *= 1e-4;
dLogPdLogRho = (scvheosLogPofLogRhoLogT(Mat, logrho+h, logT) - scvheosLogPofLogRhoLogT(Mat, logrho-h, logT))/(2.0*h);
}
return dLogPdLogRho;
}
/*
* Calculate the derivative dlogP/dlogT(logrho, logT).
*/
double scvheosdLogPdLogTofLogRhoLogT(SCVHEOSMAT *Mat, double logrho, double logT) {
/* Finite difference. */
double h = 1e-5*logT;
double dLogPdLogT;
if (!scvheosCheckBoundsLogRhoLogT(Mat, logrho, logT)) {
fprintf(stderr, "scvheosdLogPdLogTofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
/* If (rho, T) is inside of the EOS table use GSL. */
if (scvheosCheckTableBoundsLogRhoLogT(Mat, logrho, logT)) {
if (gsl_interp2d_eval_deriv_x_e(Mat->InterpLogP, Mat->dLogTAxis, Mat->dLogRhoAxis,
Mat->dLogPArray, logT, logrho, Mat->xAccP, Mat->yAccP, &dLogPdLogT) == GSL_EDOM) {
fprintf(stderr, "scvheosdLogPdLogTofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
return dLogPdLogT;
}
if ((logT-h > Mat->LogTMin) && (logT+h < Mat->LogTMax)) {
/* Central difference. */
dLogPdLogT = (scvheosLogPofLogRhoLogT(Mat, logrho, logT+h)-scvheosLogPofLogRhoLogT(Mat, logrho, logT-h))/(2.0*h);
} else if (logT-h > Mat->LogTMin) {
/* Backward finite difference. */
dLogPdLogT = (scvheosLogPofLogRhoLogT(Mat, logrho, logT)-scvheosLogPofLogRhoLogT(Mat, logrho, logT-h))/h;
} else if (logT+h < Mat->LogTMax) {
/* Forward finite difference. */
dLogPdLogT = (scvheosLogPofLogRhoLogT(Mat, logrho, logT+h)-scvheosLogPofLogRhoLogT(Mat, logrho, logT))/h;
} else {
/* Both points are problematic so h is reduced. */
h *= 1e-4;
dLogPdLogT = (scvheosLogPofLogRhoLogT(Mat, logrho, logT+h)-scvheosLogPofLogRhoLogT(Mat, logrho, logT-h))/(2.0*h);
}
return dLogPdLogT;
}
/*
* Calculate the derivative dlogu/dlogrho(logrho, logT).
*/
double scvheosdLogUdLogRhoofLogRhoLogT(SCVHEOSMAT *Mat, double logrho, double logT) {
/* Finite difference. */
double h = 1e-5*logrho;
double dLogUdLogRho;
if (!scvheosCheckBoundsLogRhoLogT(Mat, logrho, logT)) {
fprintf(stderr, "scvheosdLogUdLogRhoofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
/* If (rho, T) is inside of the EOS table use GSL. */
if (scvheosCheckTableBoundsLogRhoLogT(Mat, logrho, logT)) {
if (gsl_interp2d_eval_deriv_y_e(Mat->InterpLogU, Mat->dLogTAxis, Mat->dLogRhoAxis,
Mat->dLogUArray, logT, logrho, Mat->xAccU, Mat->yAccU, &dLogUdLogRho) == GSL_EDOM) {
fprintf(stderr, "scvheosdLogUdLogRhoofLogRhoLogT: logrho= %15.7E logT= %15.7E outside of the EOS table.\n", logrho, logT);
exit(1);
}
return dLogUdLogRho;
}
if ((logrho-h > Mat->LogRhoMin) && (logrho+h < Mat->LogRhoMax)) {
/* Central difference. */
dLogUdLogRho = (scvheosLogUofLogRhoLogT(Mat, logrho+h, logT)-scvheosLogUofLogRhoLogT(Mat, logrho-h, logT))/(2.0*h);
} else if (logrho-h > Mat->LogRhoMin) {
/* Backward finite difference. */
dLogUdLogRho = (scvheosLogUofLogRhoLogT(Mat, logrho, logT)-scvheosLogUofLogRhoLogT(Mat, logrho-h, logT))/h;
} else if (logrho+h < Mat->LogRhoMax) {
/* Forward finite difference. */
dLogUdLogRho = (scvheosLogUofLogRhoLogT(Mat, logrho+h, logT)-scvheosLogUofLogRhoLogT(Mat, logrho, logT))/h;
} else {