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tov.c
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/* file tov.c
* author Frank Loeffler, converted from fortran thorn by Ian Hawke
* date 2002/10/21
* desc TOV initial data
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <assert.h>
#include <cctk.h>
#include <cctk_Arguments.h>
#include <cctk_Parameters.h>
#include "constants.h"
#include "tov.h"
#define NUMVARS 6
#define velx (&vel[0*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define vely (&vel[1*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define velz (&vel[2*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define velx_p (&vel_p[0*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define vely_p (&vel_p[1*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define velz_p (&vel_p[2*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define velx_p_p (&vel_p_p[0*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define vely_p_p (&vel_p_p[1*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define velz_p_p (&vel_p_p[2*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sx (&scon[0*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sy (&scon[1*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sz (&scon[2*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sx_p (&scon_p[0*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sy_p (&scon_p[1*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sz_p (&scon_p[2*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sx_p_p (&scon_p_p[0*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sy_p_p (&scon_p_p[1*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
#define sz_p_p (&scon_p_p[2*cctk_lsh[0]*cctk_lsh[1]*cctk_lsh[2]])
CCTK_REAL * TOV_Surface=0;
CCTK_REAL * TOV_R_Surface=0;
CCTK_REAL * TOV_RProp_Surface=0;
CCTK_REAL * TOV_r_1d=0;
CCTK_REAL * TOV_rbar_1d=0;
CCTK_REAL * TOV_press_1d=0;
CCTK_REAL * TOV_phi_1d=0;
CCTK_REAL * TOV_m_1d=0;
CCTK_REAL * TOV_mbary_1d=0;
CCTK_REAL * TOV_rprop_1d=0;
double myrho[10000];
double myp[10000];
double mymu[10000];
char line[500];
int neos;
FILE * fin;
CCTK_REAL * getrho(double press);
CCTK_REAL * getmu(double press);
CCTK_REAL * getpress(double rho);
#include "utils.inc"
void TOV_C_ParamCheck(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
neos=0;
/* read eos for simplicityi, units are MeV/fm**3 and 1/fm**3 */
fin = fopen("myeos.dat","r");
while(!feof(fin))
{
fgets(line,300,fin);
if(sscanf(line,"%lf %lf %lf",&mymu[neos],&myp[neos],&myrho[neos])!=3) break;
/* These functions return the number of input items successfully matched
and assigned, which can be fewer than provided for, or even zero in
the event of an early matching failure.*/
// mymu[neos]/=7.514e5*.4627;
// myp[neos]/=7.514e5*.4627;
// myrho[neos]*=939.5/7.514e5/.4627;
neos++;
}
fclose(fin);
/* ->? Wozu braucht man das?*/
printf("Parameter Check!!!i");
if (TOV_Solve_for_TOVs != 3)
{
if (TOV_Solve_for_TOVs == 2)
{
CCTK_WARN(1, "TOV_Solve_for_TOVs is depreciated. "
"Use TOV_Enforce_Interpolation=\"yes\" instead.\n");
if (CCTK_ParameterSet("TOV_Enforce_Interpolation",
"TOVSolver",
"true"))
CCTK_WARN(0, "Error while steering this parameter.\n");
else
CCTK_WARN(1, "Steered this parameter for now accordingly.\n");
}
else
CCTK_WARN(1, "TOV_Solve_for_TOVs is depreciated. "
"Use TOV_Enforce_Interpolation instead.\n");
}
if (TOV_ProperPosition)
{
if (TOV_Num_TOVs != 2)
CCTK_WARN(0, "TOV_ProperPosition atm only works for TOV_Num_TOVs==2");
}
}
/* centered differencing with one-sided differencing at the boundary */
/*-->? verstehe ich nicht*/
#define DIFF_X(a) (((i==0)?(a[CCTK_GFINDEX3D(cctkGH, i+1, j, k)] - \
a[CCTK_GFINDEX3D(cctkGH, i , j, k)]): \
(i==(cctk_lsh[0]-1))? \
(a[CCTK_GFINDEX3D(cctkGH, i , j, k)] - \
a[CCTK_GFINDEX3D(cctkGH, i-1, j, k)]): \
0.5*(a[CCTK_GFINDEX3D(cctkGH, i+1, j, k)] - \
a[CCTK_GFINDEX3D(cctkGH, i-1, j, k)]))/\
CCTK_DELTA_SPACE(0))
#define DIFF_Y(a) (((j==0)?(a[CCTK_GFINDEX3D(cctkGH, i, j+1, k)] - \
a[CCTK_GFINDEX3D(cctkGH, i, j , k)]): \
(j==(cctk_lsh[1]-1))? \
(a[CCTK_GFINDEX3D(cctkGH, i, j , k)] - \
a[CCTK_GFINDEX3D(cctkGH, i, j-1, k)]): \
0.5*(a[CCTK_GFINDEX3D(cctkGH, i, j+1, k)] - \
a[CCTK_GFINDEX3D(cctkGH, i, j-1, k)]))/\
CCTK_DELTA_SPACE(1))
#define DIFF_Z(a) (((k==0)?(a[CCTK_GFINDEX3D(cctkGH, i, j, k+1)] - \
a[CCTK_GFINDEX3D(cctkGH, i, j, k )]): \
(k==(cctk_lsh[2]-1))? \
(a[CCTK_GFINDEX3D(cctkGH, i, j, k )] - \
a[CCTK_GFINDEX3D(cctkGH, i, j, k-1)]): \
0.5*(a[CCTK_GFINDEX3D(cctkGH, i, j, k+1)] - \
a[CCTK_GFINDEX3D(cctkGH, i, j, k-1)]))/\
CCTK_DELTA_SPACE(2))
/*@@
@routine TOV_Source_RHS
@date Thu Oct 24 14:30:00 2002
@author Frank Loeffler - converted fortran routine by Ian Hawke
@desc
The source terms for the ODEs. These are equations (2), (3), (4)
and (18) from the Baumgarte notes.
That is the vector in order is (P, m, phi, rbar).
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
/* ->? wo kommt olddata her?*/
void TOV_C_Source_RHS(CCTK_REAL r, CCTK_REAL K, CCTK_REAL Gamma,
CCTK_REAL old_data[NUMVARS], CCTK_REAL source_data[NUMVARS]);
void TOV_C_Source_RHS(CCTK_REAL r, CCTK_REAL K, CCTK_REAL Gamma,
CCTK_REAL old_data[NUMVARS], CCTK_REAL source_data[NUMVARS])
{
CCTK_REAL LOCAL_TINY, PI;
CCTK_REAL press, rho, eps, mu, m;
CCTK_REAL r_minus_two_m;
LOCAL_TINY = 1.0e-35;
PI=4.0*atan(1.0);
press = old_data[0];
if (press < LOCAL_TINY)
press = LOCAL_TINY;
m = old_data[1];
printf("HUHU\n");
rho = pow(press / K, 1.0 / Gamma);
eps = press / (Gamma - 1.0) / rho;
mu = rho * (1.0 + eps);
rho=getrho(press);
mu=getmu(press);
eps=mu/rho-1.0;
r_minus_two_m = r - 2.0 * m;
if ((r<=0.0) && (m<=0.0))
{
source_data[1] = 0.0;
source_data[2] = 0.0;
source_data[3] = 0.0;
source_data[4] = 0.0;
source_data[5] = 0.0;
}
else
{
source_data[2] = (m + 4*PI * r*r*r * press) / r_minus_two_m / r;
/* source_data[0] = -(press + mu) * source_data[2]; */
source_data[0] = -(press + mu) *
(m + 4*PI * r*r*r * press) / r_minus_two_m / r;
source_data[1] = 4*PI * r*r * mu;
source_data[3] = (sqrt(r) - sqrt(r_minus_two_m)) / r / sqrt(r_minus_two_m);
source_data[5] = 1.0/sqrt(1.0-2.0*m/r);
source_data[4] = source_data[5] * 4*PI * rho * r*r;
}
}
/*@@
@routine TOV_Integrate_RHS
@date Thu Oct 24 14:30:00 2002
@author Frank Loeffler, converted fortran routine by Ian Hawke
@desc
Integrates the ODEs using RK4.
We rescale at the end to match to a Schwarzschild exterior.
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
void TOV_C_Integrate_RHS(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS;
DECLARE_CCTK_PARAMETERS;
CCTK_REAL LOCAL_TINY;
CCTK_INT star, star_i, i, TOV_Surface_Index;
CCTK_REAL old_data[NUMVARS], source_data[NUMVARS],
in_data[NUMVARS], new_data[NUMVARS],
k1[NUMVARS], k2[NUMVARS], k3[NUMVARS], k4[NUMVARS];
CCTK_REAL Surface_Mass, factor, local_rho;
LOCAL_TINY = 1.0e-20;
printf("\nIntegrate RHS!!!\n");
assert(TOV_Surface!=0);
assert(TOV_R_Surface!=0);
assert(TOV_RProp_Surface!=0);
assert(TOV_r_1d!=0);
assert(TOV_rbar_1d!=0);
assert(TOV_press_1d!=0);
assert(TOV_phi_1d!=0);
assert(TOV_m_1d!=0);
assert(TOV_mbary_1d!=0);
assert(TOV_rprop_1d!=0);
/* do it for all stars */
for (star=0; star < TOV_Num_TOVs; star++)
{
/* remember array index */
star_i = star * TOV_Num_Radial; //CCTK_INT TOV_Num_Radial: "The number of radial points for the ODE integration;
const CCTK_REAL rho_central=TOV_Rho_Central[star]; //TOV_Rho_Central[10] "The central density"
printf("HALLO %f",rho_central);
/* Set conformal state like set in parameter file if we do not use
* the old initial data. In this case we have to use what we get */
if (!TOV_Use_Old_Initial_Data) //TOV_Use_Old_Initial_Data "Take old initial data into account (spacetime)? Default is no.
if(CCTK_EQUALS(metric_type, "static conformal")) //metric type defined in parfile;
/*->? conformal state*/
{
*conformal_state=1;
if (CCTK_EQUALS(conformal_storage,"factor+derivs"))
*conformal_state = 2;
else if (CCTK_EQUALS(conformal_storage,"factor+derivs+2nd derivs"))
*conformal_state = 3;
CCTK_VInfo(CCTK_THORNSTRING, "conformal_state set to %d",
(int)*conformal_state);
}
/* clear arrays first */
TOV_C_fill(&(TOV_press_1d[star_i]), TOV_Num_Radial, 0.0);
/* - utility routine
- fills an real-array 'tov_press' of size 'tov_num_radial' with value '0.0' */
TOV_C_fill(&(TOV_m_1d [star_i]), TOV_Num_Radial, 0.0);
TOV_C_fill(&(TOV_phi_1d [star_i]), TOV_Num_Radial, 0.0);
TOV_C_fill(&(TOV_rbar_1d [star_i]), TOV_Num_Radial, 0.0);
TOV_C_fill(&(TOV_r_1d [star_i]), TOV_Num_Radial, 0.0);
TOV_C_fill(&(TOV_mbary_1d[star_i]), TOV_Num_Radial, 0.0);
TOV_C_fill(&(TOV_rprop_1d[star_i]), TOV_Num_Radial, 0.0);
/* set start values */
TOV_press_1d[star_i] = TOV_K *
pow(rho_central, TOV_Gamma);
TOV_press_1d[star_i] = getpress(rho_central);
/* TOV_r_1d [star_i] = LOCAL_TINY;
TOV_rbar_1d [star_i] = LOCAL_TINY;*/
/* build TOV_r_1d[] */
for (i=star_i+1; i < star_i+TOV_Num_Radial; i++)
TOV_r_1d[i] = TOV_r_1d[i-1] + TOV_dr[star]; //only tiv_dr[0] occurs in par file -->?
// warum negative werte
TOV_Surface[star] = -1.0;
TOV_Surface_Index = -1.0;
#define RKLOOP for (int rk=0; rk<NUMVARS; rk++)
/* loop over all radii */
for (i=star_i; (i < star_i+TOV_Num_Radial-1) &&
(TOV_Surface[star] < 0.0); i++)
{
/* set up RK arrays */
old_data[0] = TOV_press_1d[i];
old_data[1] = TOV_m_1d[i];
old_data[2] = TOV_phi_1d[i];
if (fabs(TOV_rbar_1d[i] - TOV_r_1d[i]) < LOCAL_TINY)
old_data[3] = 0.0;
else
old_data[3] = log(TOV_rbar_1d[i] / TOV_r_1d[i]);
old_data[4] = TOV_mbary_1d[i];
old_data[5] = TOV_rprop_1d[i];
/* usual RK4
* 1. Step*/
RKLOOP in_data[rk] = old_data[rk];
TOV_C_fill(source_data, 6, 0.0);
TOV_C_Source_RHS(TOV_r_1d[i],
TOV_K, TOV_Gamma,
in_data, source_data);
/* source_data ist leer wird durch TOV_C_Source_RHS
* aber "hochgesetzt"
* TOV_dr schrittweite
* k1 also schrittweite mal ODEs
* TOV_r und in_data werden schrittweise erhöht*/
RKLOOP k1[rk] = TOV_dr[star] * source_data[rk];
/* 2.Step*/
RKLOOP in_data[rk] = old_data[rk] + 0.5 * k1[rk];
/* die eigl k1,...,k4(also ableitungen) sind hier die TOV_C_Source_RHS*/
TOV_C_Source_RHS(TOV_r_1d[i]+ 0.5 * TOV_dr[star],
TOV_K, TOV_Gamma,
in_data, source_data);
/* 3. Step*/
RKLOOP k2[rk] = TOV_dr[star] * source_data[rk];
RKLOOP in_data[rk] = old_data[rk] + 0.5 * k2[rk];
TOV_C_Source_RHS(TOV_r_1d[i]+ 0.5 * TOV_dr[star],
TOV_K, TOV_Gamma,
in_data, source_data);
/* 4. Step*/
RKLOOP k3[rk] = TOV_dr[star] * source_data[rk];
RKLOOP in_data[rk] = old_data[rk] + k3[rk];
TOV_C_Source_RHS(TOV_r_1d[i]+ TOV_dr[star],
TOV_K, TOV_Gamma,
in_data, source_data);
RKLOOP k4[rk] = TOV_dr[star] * source_data[rk];
RKLOOP new_data[rk] = old_data[rk] + (k1[rk] + k4[rk] + 2.0 * (k2[rk] + k3[rk])) /6.0;
/* code gefällt mir*/
TOV_press_1d[i+1] = new_data[0];
TOV_m_1d [i+1] = new_data[1];
TOV_phi_1d [i+1] = new_data[2];
TOV_rbar_1d [i+1] = TOV_r_1d[i+1] * exp(new_data[3]);
TOV_mbary_1d[i+1] = new_data[4];
TOV_rprop_1d[i+1] = new_data[5];
/* otherwise the code crashes later */
if (TOV_press_1d[i+1] < 0.0)
TOV_press_1d[i+1] = 0.0;
local_rho = pow(TOV_press_1d[i+1] / TOV_K, 1.0 / TOV_Gamma);
local_rho = getrho(TOV_press_1d[i+1]);
/* scan for the surface */
if ( (local_rho <= 0.0) ||
(TOV_press_1d[i+1] <= 0.0) )
{
TOV_Surface[star] = TOV_r_1d[i];
TOV_R_Surface[star] = TOV_rbar_1d[i];
TOV_RProp_Surface[star] = TOV_rprop_1d[i];
TOV_Surface_Index = i;
}
}
if (TOV_Surface[star] < 0.0)
CCTK_WARN(0, "Did not integrate out to surface of the star! "
"Increase TOV_dr or TOV_Num_Radial and rerun");
Surface_Mass = TOV_m_1d[TOV_Surface_Index];
factor = 0.5 * (sqrt(TOV_Surface[star] *
(TOV_Surface[star] - 2.00 * Surface_Mass)) +
TOV_Surface[star] - Surface_Mass) /
TOV_rbar_1d[TOV_Surface_Index];
TOV_R_Surface[star] *= factor;
for (i=star_i; i < star_i+TOV_Num_Radial; i++)
{
TOV_rbar_1d[i] *= factor;
TOV_phi_1d[i] -= TOV_phi_1d[TOV_Surface_Index] -
0.5 * log(1.0 - 2.0 * Surface_Mass / TOV_Surface[star]);
/* match to Schwarzschield */
if (i > TOV_Surface_Index)
{
TOV_press_1d[i] = 0.0;
TOV_rbar_1d [i] = 0.5 *
(sqrt(TOV_r_1d[i]*(TOV_r_1d[i] - 2.0*Surface_Mass)) +
TOV_r_1d[i] - Surface_Mass);
TOV_m_1d[i] = Surface_Mass;
TOV_phi_1d[i] = 0.5 * log( 1.0 - 2.0 * Surface_Mass / TOV_r_1d[i]);
TOV_mbary_1d[i] = TOV_mbary_1d[TOV_Surface_Index];
}
}
}
CCTK_INFO("Integrated TOV equation");
/* do some info */
CCTK_VInfo(CCTK_THORNSTRING, "Information about the TOVs used:");
CCTK_VInfo("", "TOV radius mass bary_mass mass(g) cent.rho rho(cgi) K K(cgi) Gamma");
for (i=0; i<TOV_Num_TOVs; i++)
if (fabs(TOV_Gamma - 2.0) < LOCAL_TINY)
CCTK_VInfo(""," %d %8g %8g %8g %8.3g %8g %8.3g %8g %8.3g %8g",
(int)i+1, TOV_R_Surface[i],
TOV_m_1d[(i+1)*TOV_Num_Radial-1],
TOV_mbary_1d[(i+1)*TOV_Num_Radial-1],
TOV_m_1d[(i+1)*TOV_Num_Radial-1]*CONSTANT_Msolar_cgi,
TOV_Rho_Central[i],
TOV_Rho_Central[i]/pow(CONSTANT_G_cgi,3.0)/
pow(CONSTANT_Msolar_cgi,2.0)*
pow(CONSTANT_c_cgi,6.0),
TOV_K,
TOV_K*pow(CONSTANT_G_cgi,3.0)*
pow(CONSTANT_Msolar_cgi,2.0)/
pow(CONSTANT_c_cgi,4.0),
TOV_Gamma);
else
CCTK_VInfo(""," %d %8g %8g %8.3g %8g %8.3g %8g %8g",
(int)i+1, TOV_R_Surface[i],
TOV_m_1d[(i+1)*TOV_Num_Radial-1],
TOV_m_1d[(i+1)*TOV_Num_Radial-1]*CONSTANT_Msolar_cgi,
TOV_Rho_Central[i],
TOV_Rho_Central[i]/pow(CONSTANT_G_cgi,3.0)/
pow(CONSTANT_Msolar_cgi,2.0)*
pow(CONSTANT_c_cgi,6.0),
TOV_K, TOV_Gamma);
}
/*----------------------------------------------------------------------------*/
/* utility routine
* recursive search-routine for arrays
* here used to look for the last index in an ordered array with its
* value < goal
*/
CCTK_INT TOV_C_find_index(CCTK_INT array_size,
CCTK_REAL *array,
CCTK_REAL goal,
CCTK_INT lower_index,
CCTK_INT upper_index);
CCTK_INT TOV_C_find_index(CCTK_INT array_size,
CCTK_REAL *array,
CCTK_REAL goal,
CCTK_INT lower_index,
CCTK_INT upper_index)
{
CCTK_INT middle_index;
if (lower_index >= (upper_index-1))
return lower_index;
middle_index = (lower_index + upper_index) /2;
if (array[middle_index] < goal)
return TOV_C_find_index(array_size, array, goal, middle_index, upper_index);
else
return TOV_C_find_index(array_size, array, goal, lower_index, middle_index);
}
/* utility rountine
* interpolates from (thorn-internal) 1D-data to Cactus 3D-grid */
/* input is all but *press_point *phi_point and *r_point */
void TOV_C_interp_tov_isotropic(
CCTK_INT star,
CCTK_REAL *TOV_press_1d_local,
CCTK_REAL *TOV_phi_1d_local,
CCTK_REAL *TOV_rbar_1d_local,
CCTK_REAL *TOV_r_1d_local,
CCTK_REAL *r,
CCTK_REAL surface,
CCTK_REAL *press_point,
CCTK_REAL *phi_point,
CCTK_REAL *r_point);
void TOV_C_interp_tov_isotropic(
CCTK_INT star,
CCTK_REAL *TOV_press_1d_local,
CCTK_REAL *TOV_phi_1d_local,
CCTK_REAL *TOV_rbar_1d_local,
CCTK_REAL *TOV_r_1d_local,
CCTK_REAL *r,
CCTK_REAL surface,
CCTK_REAL *press_point,
CCTK_REAL *phi_point,
CCTK_REAL *r_point)
{
DECLARE_CCTK_PARAMETERS
CCTK_INT left_index;
CCTK_REAL h, M;
if (*r < 0.0)
CCTK_WARN(0, "Negative radius found");
if (*r < TOV_rbar_1d_local[1])
*r=TOV_rbar_1d_local[1];
if (*r > TOV_rbar_1d_local[TOV_Num_Radial-2])
{
{
*press_point= 0.0;
M = 0.5 * TOV_r_1d_local[TOV_Num_Radial-1] *
(1.0 - exp(2.0*TOV_phi_1d_local[TOV_Num_Radial-1]));
*r_point=(2* *r+M)*(2* *r+M)*0.25/ *r;
*phi_point=0.5*log(1-2*M/ *r_point);
return;
}
}
if (TOV_Fast_Interpolation)
left_index = TOV_C_find_index(TOV_Num_Radial-1, TOV_rbar_1d_local, *r, 0,
TOV_Num_Radial-1);
else
{
left_index=0;
while( (left_index < TOV_Num_Radial-2) &&
(TOV_rbar_1d_local[left_index+1] < *r) )
left_index++;
}
h = (*r - TOV_rbar_1d_local[left_index]) /
(TOV_rbar_1d_local[left_index+1] - TOV_rbar_1d_local[left_index]);
*r_point = (1.0 - h) * TOV_r_1d_local[left_index] +
h * TOV_r_1d_local[left_index+1];
*phi_point = (1.0 - h) * TOV_phi_1d_local[left_index] +
h * TOV_phi_1d_local[left_index+1];
if (*r_point < surface)
*press_point = (1.0 - h) * TOV_press_1d_local[left_index] +
h * TOV_press_1d_local[left_index+1];
else
*press_point = 0.0;
}
/*@@
@routine TOV_Exact
@date Thu Oct 24 14:30:00 2002
@author Frank Loeffler, converted fortran routine by Ian Hawke
@desc
Schedule routine for interpolation of 1D to 3D grid
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
void TOV_C_Exact(CCTK_ARGUMENTS)
{
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
CCTK_REAL *press_point, *rho_point, *eps_point,
*mu_point, *phi_point, *r_point;
CCTK_INT LSH_MAX_I;
CCTK_INT i,j,k, i3D, star;
CCTK_REAL *r_to_star;
CCTK_REAL g_diag, max_g_diag, max_rho;
CCTK_REAL my_velx, my_vely, my_velz, my_psi4;
CCTK_REAL PI, local_tiny;
CCTK_INT tov_lapse, tov_shift;
tov_lapse = CCTK_EQUALS(initial_lapse, "tov");
tov_shift = CCTK_EQUALS(initial_shift, "tov");
PI=4.0*atan(1.0);
local_tiny=1.0e-14;
/* remember index of last member of array */
LSH_MAX_I = CCTK_GFINDEX3D(cctkGH,
cctk_lsh[0]-1, cctk_lsh[1]-1, cctk_lsh[2]-1);
assert(TOV_Surface!=0);
assert(TOV_R_Surface!=0);
assert(TOV_r_1d!=0);
assert(TOV_rbar_1d!=0);
assert(TOV_press_1d!=0);
assert(TOV_phi_1d!=0);
assert(TOV_m_1d!=0);
/* allocate local arrays */
r_to_star = (CCTK_REAL *) calloc (TOV_Num_TOVs, sizeof(CCTK_REAL));
press_point = (CCTK_REAL *) calloc (TOV_Num_TOVs, sizeof(CCTK_REAL));
rho_point = (CCTK_REAL *) calloc (TOV_Num_TOVs, sizeof(CCTK_REAL));
eps_point = (CCTK_REAL *) calloc (TOV_Num_TOVs, sizeof(CCTK_REAL));
mu_point = (CCTK_REAL *) calloc (TOV_Num_TOVs, sizeof(CCTK_REAL));
phi_point = (CCTK_REAL *) calloc (TOV_Num_TOVs, sizeof(CCTK_REAL));
r_point = (CCTK_REAL *) calloc (TOV_Num_TOVs, sizeof(CCTK_REAL));
/* clear initial data */
if (TOV_Clear_Initial_Data > 0 && !(TOV_Use_Old_Initial_Data))
{
TOV_C_fill(kxx, LSH_MAX_I+1, 0.0);
TOV_C_fill(kxy, LSH_MAX_I+1, 0.0);
TOV_C_fill(kxz, LSH_MAX_I+1, 0.0);
TOV_C_fill(kyy, LSH_MAX_I+1, 0.0);
TOV_C_fill(kyz, LSH_MAX_I+1, 0.0);
TOV_C_fill(kzz, LSH_MAX_I+1, 0.0);
TOV_C_fill(gxx, LSH_MAX_I+1, 0.0);
TOV_C_fill(gyy, LSH_MAX_I+1, 0.0);
TOV_C_fill(gzz, LSH_MAX_I+1, 0.0);
TOV_C_fill(gxy, LSH_MAX_I+1, 0.0);
TOV_C_fill(gxz, LSH_MAX_I+1, 0.0);
TOV_C_fill(gyz, LSH_MAX_I+1, 0.0);
TOV_C_fill(alp, LSH_MAX_I+1, 1.0);
if (*shift_state != 0)
{
TOV_C_fill(betax, LSH_MAX_I+1, 0.0);
TOV_C_fill(betay, LSH_MAX_I+1, 0.0);
TOV_C_fill(betaz, LSH_MAX_I+1, 0.0);
}
if (*conformal_state != 0)
{
TOV_C_fill(psi, LSH_MAX_I+1, 1.0);
if (*conformal_state > 1)
{
TOV_C_fill(psix, LSH_MAX_I+1, 0.0);
TOV_C_fill(psiy, LSH_MAX_I+1, 0.0);
TOV_C_fill(psiz, LSH_MAX_I+1, 0.0);
if (*conformal_state > 2)
{
TOV_C_fill(psixx, LSH_MAX_I+1, 0.0);
TOV_C_fill(psixy, LSH_MAX_I+1, 0.0);
TOV_C_fill(psixz, LSH_MAX_I+1, 0.0);
TOV_C_fill(psiyy, LSH_MAX_I+1, 0.0);
TOV_C_fill(psiyz, LSH_MAX_I+1, 0.0);
TOV_C_fill(psizz, LSH_MAX_I+1, 0.0);
}
}
}
}
if (!TOV_Use_Old_Matter_Initial_Data)
{
CCTK_INFO("Not using old matter initial data");
TOV_C_fill(rho, LSH_MAX_I+1, 0.0);
TOV_C_fill(eps, LSH_MAX_I+1, 0.0);
TOV_C_fill(press, LSH_MAX_I+1, 0.0);
TOV_C_fill(w_lorentz, LSH_MAX_I+1, 0.0);
TOV_C_fill(velx, LSH_MAX_I+1, 0.0);
TOV_C_fill(vely, LSH_MAX_I+1, 0.0);
TOV_C_fill(velz, LSH_MAX_I+1, 0.0);
}
/* use the fast interpolation? only useful for testing this */
if (TOV_Fast_Interpolation == 0)
CCTK_INFO("Interpolating the slow way.");
/* go over all 3D-grid points */
for(i=0; i<cctk_lsh[0]; i++)
for(j=0; j<cctk_lsh[1]; j++)
for(k=0; k<cctk_lsh[2]; k++)
{
i3D=CCTK_GFINDEX3D(cctkGH, i, j, k);
/* remember the old conformal factor to the power of 4 */
if (*conformal_state != 0)
my_psi4=pow(psi[i3D], 4.0);
else
my_psi4=1.0;
for (star=0; star<TOV_Num_TOVs; star++)
{
r_to_star[star] =
sqrt( (x[i3D]-TOV_Position_x[star]) *
(x[i3D]-TOV_Position_x[star]) +
(y[i3D]-TOV_Position_y[star]) *
(y[i3D]-TOV_Position_y[star]) +
(z[i3D]-TOV_Position_z[star]) *
(z[i3D]-TOV_Position_z[star]) );
int star_i = star * TOV_Num_Radial;
/* do the actual interpolation */
TOV_C_interp_tov_isotropic(star,
&(TOV_press_1d[star_i]), &(TOV_phi_1d[star_i]),
&(TOV_rbar_1d[star_i]), &(TOV_r_1d[star_i]),
&(r_to_star[star]), TOV_Surface[star],
&(press_point[star]),
&(phi_point[star]), &(r_point[star]));
/* is some perturbation wanted? */
if (Perturb[star] == 0)
{
rho_point[star] = pow(press_point[star]/TOV_K,
1.0/TOV_Gamma);
rho_point[star] = getrho(press_point[star]);
}
else
{
rho_point[star] = pow(press_point[star]/TOV_K,
1.0/TOV_Gamma) *
(1.0 +
Pert_Amplitude[star] *
cos(PI/2.0 * r[i3D] / TOV_R_Surface[star]));
rho_point[star] = getrho(press_point[star])*
(1.0 +
Pert_Amplitude[star] *
cos(PI/2.0 * r[i3D] / TOV_R_Surface[star]));
}
if (rho_point[star] > local_tiny)
{
eps_point[star] = press_point[star] / (TOV_Gamma - 1.0)
/ rho_point[star];
eps_point[star] = getmu(press_point[star])/rho_point[star]-1.0;
}
else
eps_point[star] = 0.0;
mu_point[star] = rho_point[star] * (1.0 + eps_point[star]);
}
/* find out from which star we want to have the data */
if (CCTK_EQUALS(TOV_Combine_Method, "maximum"))
{
/* to do this, we use here simply the max of the gxx-value */
star=0;
max_g_diag = 0.0;
max_rho = rho_point[0];
for (int star_i=0; star_i<TOV_Num_TOVs; star_i++)
{
g_diag = (r_point[star_i] / (r_to_star[star_i] + 1.0e-30)) *
(r_point[star_i] / (r_to_star[star_i] + 1.0e-30));
if ((g_diag - max_g_diag) > local_tiny)
{
max_g_diag=g_diag;
star=star_i;
}
if ((rho_point[star_i] - max_rho) > local_tiny)
{
max_rho=rho_point[star_i];
star=star_i;
}
}
/* handle initial data */
if (TOV_Use_Old_Initial_Data)
{
/* check metric */
if ((my_psi4 * gxx[i3D] < max_g_diag) &&
(my_psi4 * gyy[i3D] < max_g_diag) &&
(my_psi4 * gzz[i3D] < max_g_diag))
{
if (TOV_Conformal_Flat_Three_Metric)
{
psi[i3D] = pow(max_g_diag, 0.25);
my_psi4 = max_g_diag;
}
else
{
gxx[i3D] = max_g_diag/my_psi4;
gyy[i3D] = max_g_diag/my_psi4;
gzz[i3D] = max_g_diag/my_psi4;
gxy[i3D] = gxz[i3D] = gyz[i3D] = 0.0;
}
}
/* check matter */
if (TOV_Use_Old_Matter_Initial_Data)
{
if (rho[i3D] > max_rho)
{
/* we do not need this array element anymore, since we use
* the initial data, so lets use it */
star=0;
max_rho =rho[i3D];
eps_point[star] =eps[i3D];
press_point[star]=press[i3D];
my_velx=velx[i3D];
my_vely=vely[i3D];
my_velz=velz[i3D];
}
else
{
if (tov_lapse)
alp[i3D] = exp(phi_point[star]);
if (tov_shift)
{
betax[i3D] = 0.0;
betay[i3D] = 0.0;
betaz[i3D] = 0.0;
}
my_velx=TOV_Velocity_x[star];
my_vely=TOV_Velocity_y[star];
my_velz=TOV_Velocity_z[star];
}
}
else
{
if (tov_lapse)
alp[i3D] = exp(phi_point[star]);
if (tov_shift)
{
betax[i3D] = 0.0;
betay[i3D] = 0.0;
betaz[i3D] = 0.0;
}
my_velx=TOV_Velocity_x[star];
my_vely=TOV_Velocity_y[star];
my_velz=TOV_Velocity_z[star];
}
}
else /* do not use old initial data */
{
/* no psi, since it is 1.0 here */
/* but maybe we want to have it != 1.0 */
if (TOV_Conformal_Flat_Three_Metric)
{
psi[i3D] = pow(max_g_diag, 0.25);
my_psi4 = max_g_diag;
gxx[i3D] = gyy[i3D] = gzz[i3D] = 1.0;
gxy[i3D] = gxz[i3D] = gyz[i3D] = 0.0;
}
else
{
gxx[i3D] = max_g_diag;
gyy[i3D] = max_g_diag;
gzz[i3D] = max_g_diag;
gxy[i3D] = gxz[i3D] = gyz[i3D] = 0.0;
}
if (tov_lapse)
alp[i3D] = exp(phi_point[star]);
if (tov_shift)
{
betax[i3D] = 0.0;
betay[i3D] = 0.0;
betaz[i3D] = 0.0;
}
my_velx=TOV_Velocity_x[star];
my_vely=TOV_Velocity_y[star];
my_velz=TOV_Velocity_z[star];
}
/* set to defined velocity. default is 0.0 because other velocities
* violate Einsteins equations */
velx[i3D] = my_velx;
vely[i3D] = my_vely;
velz[i3D] = my_velz;
w_lorentz[i3D] = 1/sqrt(1.0-(
gxx[i3D] * velx[i3D] * velx[i3D]+
gyy[i3D] * vely[i3D] * vely[i3D]+
gzz[i3D] * velz[i3D] * velz[i3D]+
2*gxy[i3D] * velx[i3D] * vely[i3D]+
2*gxz[i3D] * velx[i3D] * velz[i3D]+
2*gyz[i3D] * vely[i3D] * velz[i3D])*
my_psi4);
rho[i3D] = max_rho;
eps[i3D] = eps_point[star];
press[i3D] = press_point[star];
}
else if (CCTK_EQUALS(TOV_Combine_Method, "average"))
{
/* here we 'average' all values in a more intelligent way */
if (TOV_Use_Old_Matter_Initial_Data)
max_rho=rho[i3D];
else
{
max_rho=0.0;
rho[i3D] = 0.0;
}
star=-1;
for (int star_i=0; star_i<TOV_Num_TOVs; star_i++)
{
if (tov_lapse)
alp[i3D] *= exp(phi_point[star_i]);
if (tov_shift)
{
betax[i3D] = 0.0;
betay[i3D] = 0.0;
betaz[i3D] = 0.0;
}
if (TOV_Conformal_Flat_Three_Metric)
{
/* This is a hack, since it does not check if the input data is
* really conformally flat. It simply assumes this by only using
* gxx */
my_psi4 = (r_point[star_i] * r_point[star_i] /
(r_to_star[star_i] * r_to_star[star_i] + 1.0e-30)) /
my_psi4 + pow(psi[i3D], 4.0) * gxx[i3D];
psi[i3D] = pow(my_psi4, 0.25);
if (!TOV_Use_Old_Initial_Data)
{
gxx[i3D] = gyy[i3D] = gzz[i3D] = 1.0;
gxy[i3D] = gxz[i3D] = gyz[i3D] = 0.0;
}
}
else
gxx[i3D] += (r_point[star_i] * r_point[star_i] /
(r_to_star[star_i] * r_to_star[star_i] + 1.0e-30)) /
my_psi4;
rho[i3D] += rho_point[star_i];
eps[i3D] += eps_point[star_i];
press[i3D] += press_point[star_i];
/* we still have to know if we are inside one star - and which */
if (rho_point[star_i] > max_rho)
{
max_rho=rho_point[star_i];
star=star_i;
}
}
if (TOV_Conformal_Flat_Three_Metric)
{
my_psi4 -= ((TOV_Num_TOVs+TOV_Use_Old_Initial_Data-1)/my_psi4);
psi[i3D] = pow(my_psi4, 0.25);
}
else
{
gxx[i3D] -= ((TOV_Num_TOVs+TOV_Use_Old_Initial_Data-1)/my_psi4);
gyy[i3D] = gxx[i3D];
gzz[i3D] = gxx[i3D];
}
/* set to defined velocity. default is 0.0 because other velocities
* violate the constraints */
if (star > -1)
{
velx[i3D] = TOV_Velocity_x[star];
vely[i3D] = TOV_Velocity_y[star];
velz[i3D] = TOV_Velocity_z[star];
}
w_lorentz[i3D] = 1/sqrt(1.0-(
gxx[i3D] * velx[i3D] * velx[i3D]+
gyy[i3D] * vely[i3D] * vely[i3D]+
gzz[i3D] * velz[i3D] * velz[i3D]+
2*gxy[i3D] * velx[i3D] * vely[i3D]+
2*gxz[i3D] * velx[i3D] * velz[i3D]+
2*gyz[i3D] * vely[i3D] * velz[i3D]) * my_psi4);
}
}
/* if used, recalculate the derivatives of the conformal factor */
if (*conformal_state > 1)
/* go again over all 3D-grid points */
for(i=0; i<cctk_lsh[0]; i++)
for(j=0; j<cctk_lsh[1]; j++)
for(k=0; k<cctk_lsh[2]; k++)
{
i3D=CCTK_GFINDEX3D(cctkGH, i, j, k);
psix[i3D]=(((i==0)?
(psi[CCTK_GFINDEX3D(cctkGH, i+1, j, k)] -
psi[CCTK_GFINDEX3D(cctkGH, i , j, k)]):
(i==(cctk_lsh[0]-1))?
(psi[CCTK_GFINDEX3D(cctkGH, i , j, k)] -
psi[CCTK_GFINDEX3D(cctkGH, i-1, j, k)]):
0.5*(psi[CCTK_GFINDEX3D(cctkGH, i+1, j, k)] -
psi[CCTK_GFINDEX3D(cctkGH, i-1, j, k)])));
psix[i3D] = DIFF_X(psi);
psiy[i3D] = DIFF_Y(psi);
psiz[i3D] = DIFF_Z(psi);
}
if (*conformal_state > 2)
/* go again over all 3D-grid points */
for(i=0; i<cctk_lsh[0]; i++)
for(j=0; j<cctk_lsh[1]; j++)
for(k=0; k<cctk_lsh[2]; k++)
{
i3D=CCTK_GFINDEX3D(cctkGH, i, j, k);
psixx[i3D] = DIFF_X(psix)/psi[i3D];
psiyy[i3D] = DIFF_Y(psiy)/psi[i3D];
psizz[i3D] = DIFF_Z(psiz)/psi[i3D];
psixy[i3D] = DIFF_X(psiy)/psi[i3D];
psiyz[i3D] = DIFF_Y(psiz)/psi[i3D];
psixz[i3D] = DIFF_Z(psix)/psi[i3D];
}
if (*conformal_state > 1)
/* go again over all 3D-grid points */
for(i=0; i<cctk_lsh[0]; i++)
for(j=0; j<cctk_lsh[1]; j++)
for(k=0; k<cctk_lsh[2]; k++)
{
i3D=CCTK_GFINDEX3D(cctkGH, i, j, k);
psix[i3D] /= psi[i3D];
psiy[i3D] /= psi[i3D];
psiz[i3D] /= psi[i3D];
}
i3D = cctk_lsh[2]*cctk_lsh[1]*cctk_lsh[0];
switch(TOV_Populate_Timelevels)
{
case 3:
TOV_Copy(i3D, gxx_p_p, gxx);
TOV_Copy(i3D, gyy_p_p, gyy);
TOV_Copy(i3D, gzz_p_p, gzz);
TOV_Copy(i3D, gxy_p_p, gxy);
TOV_Copy(i3D, gxz_p_p, gxz);
TOV_Copy(i3D, gyz_p_p, gyz);
TOV_Copy(i3D, rho_p_p, rho);
TOV_Copy(i3D, eps_p_p, eps);
TOV_Copy(i3D, velx_p_p, velx);
TOV_Copy(i3D, vely_p_p, vely);
TOV_Copy(i3D, velz_p_p, velz);
TOV_Copy(i3D, w_lorentz_p_p, w_lorentz);
// fall through
case 2:
TOV_Copy(i3D, gxx_p, gxx);
TOV_Copy(i3D, gyy_p, gyy);
TOV_Copy(i3D, gzz_p, gzz);
TOV_Copy(i3D, gxy_p, gxy);
TOV_Copy(i3D, gxz_p, gxz);
TOV_Copy(i3D, gyz_p, gyz);
TOV_Copy(i3D, rho_p, rho);
TOV_Copy(i3D, eps_p, eps);
TOV_Copy(i3D, velx_p, velx);
TOV_Copy(i3D, vely_p, vely);