et_bin_equilibrium.C
/*
* Method of class Etoile_bin to compute an equilibrium configuration
*
* (see file etoile.h for documentation).
*
*/
/*
* Copyright (c) 2000-2001 Eric Gourgoulhon
* Copyright (c) 2000-2001 Keisuke Taniguchi
*
* This file is part of LORENE.
*
* LORENE 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.
*
* LORENE 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 LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
char et_bin_equilibrium_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_equilibrium.C,v 1.14 2014/10/13 08:52:55 j_novak Exp $" ;
/*
* $Id: et_bin_equilibrium.C,v 1.14 2014/10/13 08:52:55 j_novak Exp $
* $Log: et_bin_equilibrium.C,v $
* Revision 1.14 2014/10/13 08:52:55 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.13 2014/10/06 15:13:08 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.12 2009/06/15 09:25:18 k_taniguchi
* Improved the rescaling of the domains.
*
* Revision 1.11 2008/11/14 13:48:06 e_gourgoulhon
* Added parameter pent_limit to force the enthalpy values at the
* boundaries between the domains, in case of more than one domain inside
* the star.
*
* Revision 1.10 2004/09/28 15:49:23 f_limousin
* Improve the rescaling of the domains for nzone = 4 and nzone = 5.
*
* Revision 1.9 2004/05/13 08:47:01 f_limousin
* Decomment the procedure resize.
*
* Revision 1.8 2004/05/10 10:15:57 f_limousin
* Change to avoid a warning in the compilation of Lorene
*
* Revision 1.7 2004/05/07 12:36:34 f_limousin
* Add new member ssjm1_psi in order to have only one function
* equilibrium (the same for strange stars and neutron stars)
*
* Revision 1.6 2004/05/07 08:32:44 k_taniguchi
* Introduction of the version without ssjm1_psi.
*
* Revision 1.5 2004/04/19 11:06:36 f_limousin
* Differents call of Etoile_bin::velocity_potential depending on
* the equation of state.
*
* Revision 1.4 2004/03/25 10:29:04 j_novak
* All LORENE's units are now defined in the namespace Unites (in file unites.h).
*
* Revision 1.3 2003/01/17 13:31:13 f_limousin
* Add comments
*
* Revision 1.2 2002/12/10 13:28:03 k_taniguchi
* Change the multiplication "*" to "%"
* and flat_scalar_prod to flat_scalar_prod_desal.
*
* Revision 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
* LORENE
*
* Revision 2.23 2001/08/07 09:43:02 keisuke
* Change of the method to set the longest radius of a star
* on the first domain.
* Addition of a new argument in Etoile_bin::equilibrium : Tbl fact.
*
* Revision 2.22 2001/06/22 08:54:19 keisuke
* Set the inner values of the second domain of ent
* by using the outer ones of the first domain.
*
* Revision 2.21 2001/06/18 12:50:49 keisuke
* Addition of the filter for the source of shift vector.
*
* Revision 2.20 2001/05/17 12:18:47 keisuke
* Change of the method to calculate chi from setting position in map
* to val_point.
*
* Revision 2.19 2001/01/16 17:01:53 keisuke
* Change the method to set the values on the surface.
*
* Revision 2.18 2001/01/10 16:42:51 keisuke
* Set the inner values of the second domain of logn_auto
* by using the outer ones of the first domain.
*
* Revision 2.17 2000/12/22 13:08:04 eric
* precis_adapt = 1e-14 au lieu de 1e-15.
* Sorties graphiques commentees.
*
* Revision 2.16 2000/12/20 10:32:44 eric
* Changement important : nz_search = nzet ---> nz_search = nzet + 1
*
* Revision 2.15 2000/10/23 14:02:16 eric
* Modif de Map_et::adapt: on y rentre desormais avec nz_search
* (dans le cas present nz_search = nzet).
*
* Revision 2.14 2000/09/28 12:19:36 keisuke
* Construct logn_auto_regu from logn_auto.
* This procedure is needed for et_bin_upmetr.C.
*
* Revision 2.13 2000/05/25 13:48:12 eric
* Ajout de l'argument thres_adapt: l'adaptation du mapping n'est
* plus effectuee si dH/dr_eq passe sous un certain seuil.
*
* Revision 2.12 2000/05/25 12:58:31 eric
* Modifs classe Param: les int et double sont desormais passes par leurs
* adresses.
*
* Revision 2.11 2000/03/29 11:57:38 eric
* *** empty log message ***
*
* Revision 2.10 2000/03/29 11:53:41 eric
* Modif affichage
*
* Revision 2.9 2000/03/22 16:37:29 eric
* Calcul des erreurs dans la resolution des equations de Poisson
* et sortie de ces erreurs dans le Tbl diff.
*
* Revision 2.8 2000/03/22 12:56:18 eric
* Nouveau prototype d'Etoile_bin::equilibrium : diff_ent est remplace
* par le Tbl diff.
*
* Revision 2.7 2000/03/10 15:47:19 eric
* On appel desormais poisson_vect avec dzpuis = 4.
*
* Revision 2.6 2000/03/07 16:52:15 eric
* Modifs manipulations source pour le shift.
*
* Revision 2.5 2000/03/07 08:32:47 eric
* Appel de Map_radial::reevaluate_sym (pour tenir compte de la symetrie
* / plan y=0).
*
* Revision 2.4 2000/02/17 19:56:57 eric
* L'appel de Map_radial::reevaluate pour ent est fait sur nzet+1 zone
* et non plus nzet.
*
* Revision 2.2 2000/02/16 17:12:03 eric
* Premiere version avec les equations du champ gravitationnel.
*
* Revision 2.1 2000/02/15 15:59:52 eric
* *** empty log message ***
*
* Revision 2.0 2000/02/15 15:40:42 eric
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_equilibrium.C,v 1.14 2014/10/13 08:52:55 j_novak Exp $
*
*/
// Headers C
#include <cmath>
// Headers Lorene
#include "etoile.h"
#include "param.h"
#include "eos.h"
#include "graphique.h"
#include "utilitaires.h"
#include "unites.h"
namespace Lorene {
void Etoile_bin::equilibrium(double ent_c,
int mermax, int mermax_poisson,
double relax_poisson, int mermax_potvit,
double relax_potvit, double thres_adapt,
const Tbl& fact_resize, Tbl& diff, const Tbl* pent_limit ) {
// Fundamental constants and units
// -------------------------------
using namespace Unites ;
// Initializations
// ---------------
const Mg3d* mg = mp.get_mg() ;
int nz = mg->get_nzone() ; // total number of domains
// The following is required to initialize mp_prev as a Map_et:
Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
// Domain and radial indices of points at the surface of the star:
int l_b = nzet - 1 ;
int i_b = mg->get_nr(l_b) - 1 ;
int k_b ;
int j_b ;
// Value of the enthalpy defining the surface of the star
double ent_b = 0 ;
// Error indicators
// ----------------
double& diff_ent = diff.set(0) ;
double& diff_vel_pot = diff.set(1) ;
double& diff_logn = diff.set(2) ;
double& diff_beta = diff.set(3) ;
double& diff_shift_x = diff.set(4) ;
double& diff_shift_y = diff.set(5) ;
double& diff_shift_z = diff.set(6) ;
// Parameters for the function Map_et::adapt
// -----------------------------------------
Param par_adapt ;
int nitermax = 100 ;
int niter ;
int adapt_flag = 1 ; // 1 = performs the full computation,
// 0 = performs only the rescaling by
// the factor alpha_r
//## int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
int nz_search = nzet ; // Number of domains for searching the enthalpy
// isosurfaces
double precis_secant = 1.e-14 ;
double alpha_r ;
double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
// locate zeros by the secant method
par_adapt.add_int(nzet, 1) ; // number of domains where the adjustment
// to the isosurfaces of ent is to be
// performed
par_adapt.add_int(nz_search, 2) ; // number of domains to search for
// the enthalpy isosurface
par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
// 0 = performs only the rescaling by
// the factor alpha_r
par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
// (theta_*, phi_*)
par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
// (theta_*, phi_*)
par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
// the secant method
par_adapt.add_double(precis_secant, 0) ; // required absolute precision in
// the determination of zeros by
// the secant method
par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
// distances will be multiplied
// Enthalpy values for the adaptation
Tbl ent_limit(nzet) ;
if (pent_limit != 0x0) ent_limit = *pent_limit ;
par_adapt.add_tbl(ent_limit, 0) ; // array of values of the field ent
// to define the isosurfaces.
// Parameters for the function Map_et::poisson for logn_auto
// ---------------------------------------------------------
double precis_poisson = 1.e-16 ;
Param par_poisson1 ;
par_poisson1.add_int(mermax_poisson, 0) ; // maximum number of iterations
par_poisson1.add_double(relax_poisson, 0) ; // relaxation parameter
par_poisson1.add_double(precis_poisson, 1) ; // required precision
par_poisson1.add_int_mod(niter, 0) ; // number of iterations actually used
par_poisson1.add_cmp_mod( ssjm1_logn ) ;
// Parameters for the function Map_et::poisson for beta_auto
// ---------------------------------------------------------
Param par_poisson2 ;
par_poisson2.add_int(mermax_poisson, 0) ; // maximum number of iterations
par_poisson2.add_double(relax_poisson, 0) ; // relaxation parameter
par_poisson2.add_double(precis_poisson, 1) ; // required precision
par_poisson2.add_int_mod(niter, 0) ; // number of iterations actually used
par_poisson2.add_cmp_mod( ssjm1_beta ) ;
// Parameters for the function Tenseur::poisson_vect
// -------------------------------------------------
Param par_poisson_vect ;
par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of iterations
par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
par_poisson_vect.add_cmp_mod( ssjm1_khi ) ;
par_poisson_vect.add_tenseur_mod( ssjm1_wshift ) ;
par_poisson_vect.add_int_mod(niter, 0) ;
// External potential
// See Eq (99) from Gourgoulhon et al. (2001)
// -----------------------------------------
Tenseur pot_ext = logn_comp + pot_centri + loggam ;
//##
// des_coupe_z(pot_ext(), 0., 1, "pot_ext", &(ent()) ) ;
//##
Tenseur ent_jm1 = ent ; // Enthalpy at previous step
Tenseur source(mp) ; // source term in the equation for logn_auto
// and beta_auto
Tenseur source_shift(mp, 1, CON, ref_triad) ; // source term in the equation
// for shift_auto
//=========================================================================
// Start of iteration
//=========================================================================
for(int mer=0 ; mer<mermax ; mer++ ) {
cout << "-----------------------------------------------" << endl ;
cout << "step: " << mer << endl ;
cout << "diff_ent = " << diff_ent << endl ;
//-----------------------------------------------------
// Resolution of the elliptic equation for the velocity
// scalar potential
//-----------------------------------------------------
if (irrotational) {
diff_vel_pot = velocity_potential(mermax_potvit,
precis_poisson, relax_potvit) ;
}
//-----------------------------------------------------
// Computation of the new radial scale
//-----------------------------------------------------
// alpha_r (r = alpha_r r') is determined so that the enthalpy
// takes the requested value ent_b at the stellar surface
// Values at the center of the star:
double logn_auto_c = logn_auto()(0, 0, 0, 0) ;
double pot_ext_c = pot_ext()(0, 0, 0, 0) ;
// Search for the reference point (theta_*, phi_*) [notation of
// Bonazzola, Gourgoulhon & Marck PRD 58, 104020 (1998)]
// at the surface of the star
// ------------------------------------------------------------
double alpha_r2 = 0 ;
for (int k=0; k<mg->get_np(l_b); k++) {
for (int j=0; j<mg->get_nt(l_b); j++) {
double pot_ext_b = pot_ext()(l_b, k, j, i_b) ;
double logn_auto_b = logn_auto()(l_b, k, j, i_b) ;
// See Eq (100) from Gourgoulhon et al. (2001)
double alpha_r2_jk = ( ent_c - ent_b + pot_ext_c - pot_ext_b) /
( logn_auto_b - logn_auto_c ) ;
// cout << "k, j, alpha_r2_jk : " << k << " " << j << " "
// << alpha_r2_jk << endl ;
if (alpha_r2_jk > alpha_r2) {
alpha_r2 = alpha_r2_jk ;
k_b = k ;
j_b = j ;
}
}
}
alpha_r = sqrt(alpha_r2) ;
cout << "k_b, j_b, alpha_r: " << k_b << " " << j_b << " "
<< alpha_r << endl ;
// New value of logn_auto
// ----------------------
logn_auto = alpha_r2 * logn_auto ;
logn_auto_regu = alpha_r2 * logn_auto_regu ;
logn_auto_c = logn_auto()(0, 0, 0, 0) ;
//------------------------------------------------------------
// Change the values of the inner points of the second domain
// by those of the outer points of the first domain
//------------------------------------------------------------
(logn_auto().va).smooth(nzet, (logn_auto.set()).va) ;
//------------------------------------------
// First integral --> enthalpy in all space
// See Eq (98) from Gourgoulhon et al. (2001)
//-------------------------------------------
ent = (ent_c + logn_auto_c + pot_ext_c) - logn_auto - pot_ext ;
(ent().va).smooth(nzet, (ent.set()).va) ;
//----------------------------------------------------
// Adaptation of the mapping to the new enthalpy field
//----------------------------------------------------
// Shall the adaptation be performed (cusp) ?
// ------------------------------------------
double dent_eq = ent().dsdr().val_point(ray_eq(),M_PI/2.,0.) ;
double dent_pole = ent().dsdr().val_point(ray_pole(),0.,0.) ;
double rap_dent = fabs( dent_eq / dent_pole ) ;
cout << "| dH/dr_eq / dH/dr_pole | = " << rap_dent << endl ;
if ( rap_dent < thres_adapt ) {
adapt_flag = 0 ; // No adaptation of the mapping
cout << "******* FROZEN MAPPING *********" << endl ;
}
else{
adapt_flag = 1 ; // The adaptation of the mapping is to be
// performed
}
if (pent_limit == 0x0) {
ent_limit.set_etat_qcq() ;
for (int l=0; l<nzet; l++) { // loop on domains inside the star
ent_limit.set(l) = ent()(l, k_b, j_b, i_b) ;
}
ent_limit.set(nzet-1) = ent_b ;
}
Map_et mp_prev = mp_et ;
//## cout << "Enthalpy field at the outer boundary of domain 0 : "
// << endl ;
// for (int k=0; k<mg->get_np(0); k++) {
// cout << "k = " << k << " : " ;
// for (int j=0; j<mg->get_nt(0); j++) {
// cout << " " << ent()(0, k, j, mg->get_nr(0)-1) ;
// }
// cout << endl ;
// }
// cout << "Enthalpy field at the inner boundary of domain 1 : "
// << endl ;
// for (int k=0; k<mg->get_np(1); k++) {
// cout << "k = " << k << " : " ;
// for (int j=0; j<mg->get_nt(1); j++) {
// cout << " " << ent()(1, k, j, 0) ;
// }
// cout << endl ;
// }
// cout << "Difference enthalpy field boundary between domains 0 and 1: "
// << endl ;
// for (int k=0; k<mg->get_np(1); k++) {
// cout << "k = " << k << " : " ;
// for (int j=0; j<mg->get_nt(1); j++) {
// cout << " " << ent()(0, k, j, mg->get_nr(0)-1) -
// ent()(1, k, j, 0) ;
// }
// cout << endl ;
// }
//##
// des_coupe_z(gam_euler(), 0., 1, "gam_euler") ;
// des_coupe_z(loggam(), 0., 1, "loggam") ;
// des_coupe_y(loggam(), 0., 1, "loggam") ;
// des_coupe_z(d_psi(0), 0., 1, "d_psi_0") ;
// des_coupe_z(d_psi(1), 0., 1, "d_psi_1") ;
// des_coupe_z(d_psi(2), 0., 1, "d_psi_2") ;
// des_coupe_z(ent(), 0., 1, "ent before adapt", &(ent()) ) ;
//##
mp.adapt(ent(), par_adapt) ;
// Readjustment of the external boundary of domain l=nzet
// to keep a fixed ratio with respect to star's surface
double rr_in_1 = mp.val_r(nzet, -1., M_PI/2., 0.) ;
// Resizes the outer boundary of the shell including the comp. NS
double rr_out_nm2 = mp.val_r(nz-2, 1., M_PI/2., 0.) ;
mp.resize(nz-2, rr_in_1/rr_out_nm2 * fact_resize(1)) ;
// Resizes the inner boundary of the shell including the comp. NS
double rr_out_nm3 = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
mp.resize(nz-3, rr_in_1/rr_out_nm3 * fact_resize(0)) ;
if (nz > nzet+3) {
// Resize of the domain from 1(nzet) to N-4
double rr_out_nm3_new = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
for (int i=nzet-1; i<nz-4; i++) {
double rr_out_i = mp.val_r(i, 1., M_PI/2., 0.) ;
double rr_mid = rr_out_i
+ (rr_out_nm3_new - rr_out_i) / double(nz - 3 - i) ;
double rr_2timesi = 2. * rr_out_i ;
if (rr_2timesi < rr_mid) {
double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
mp.resize(i+1, rr_2timesi / rr_out_ip1) ;
}
else {
double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
mp.resize(i+1, rr_mid / rr_out_ip1) ;
} // End of else
} // End of i loop
} // End of (nz > nzet+3) loop
//----------------------------------------------------
// Computation of the enthalpy at the new grid points
//----------------------------------------------------
mp_prev.homothetie(alpha_r) ;
mp.reevaluate_symy(&mp_prev, nzet+1, ent.set()) ;
// des_coupe_z(ent(), 0., 1, "ent after reevaluate", &(ent()) ) ;
double ent_s_max = -1 ;
int k_s_max = -1 ;
int j_s_max = -1 ;
for (int k=0; k<mg->get_np(l_b); k++) {
for (int j=0; j<mg->get_nt(l_b); j++) {
double xx = fabs( ent()(l_b, k, j, i_b) ) ;
if (xx > ent_s_max) {
ent_s_max = xx ;
k_s_max = k ;
j_s_max = j ;
}
}
}
cout << "Max. abs(enthalpy) at the boundary between domains nzet-1"
<< " and nzet : " << endl ;
cout << " " << ent_s_max << " reached for k = " << k_s_max <<
" and j = " << j_s_max << endl ;
//----------------------------------------------------
// Equation of state
//----------------------------------------------------
equation_of_state() ; // computes new values for nbar (n), ener (e)
// and press (p) from the new ent (H)
//---------------------------------------------------------
// Matter source terms in the gravitational field equations
//---------------------------------------------------------
hydro_euler() ; // computes new values for ener_euler (E),
// s_euler (S) and u_euler (U^i)
//--------------------------------------------------------
// Poisson equation for logn_auto (nu_auto)
//--------------------------------------------------------
// Source
// See Eq (50) from Gourgoulhon et al. (2001)
// ------------------------------------------
if (relativistic) {
source = qpig * a_car % (ener_euler + s_euler)
+ akcar_auto + akcar_comp
- flat_scalar_prod_desal(d_logn_auto,
d_beta_auto + d_beta_comp) ;
}
else {
source = qpig * nbar ;
}
source.set_std_base() ;
// Resolution of the Poisson equation
// ----------------------------------
source().poisson(par_poisson1, logn_auto.set()) ;
// Construct logn_auto_regu for et_bin_upmetr.C
// --------------------------------------------
logn_auto_regu = logn_auto ;
// Check: has the Poisson equation been correctly solved ?
// -----------------------------------------------------
Tbl tdiff_logn = diffrel(logn_auto().laplacien(), source()) ;
cout <<
"Relative error in the resolution of the equation for logn_auto : "
<< endl ;
for (int l=0; l<nz; l++) {
cout << tdiff_logn(l) << " " ;
}
cout << endl ;
diff_logn = max(abs(tdiff_logn)) ;
if (relativistic) {
//--------------------------------------------------------
// Poisson equation for beta_auto
//--------------------------------------------------------
// Source
// See Eq (51) from Gourgoulhon et al. (2001)
// ------------------------------------------
source = qpig * a_car % s_euler
+ .75 * ( akcar_auto + akcar_comp )
- .5 * flat_scalar_prod_desal(d_logn_auto,
d_logn_auto + d_logn_comp)
- .5 * flat_scalar_prod_desal(d_beta_auto,
d_beta_auto + d_beta_comp) ;
source.set_std_base() ;
// Resolution of the Poisson equation
// ----------------------------------
source().poisson(par_poisson2, beta_auto.set()) ;
// Check: has the Poisson equation been correctly solved ?
// -----------------------------------------------------
Tbl tdiff_beta = diffrel(beta_auto().laplacien(), source()) ;
cout <<
"Relative error in the resolution of the equation for beta_auto : "
<< endl ;
for (int l=0; l<nz; l++) {
cout << tdiff_beta(l) << " " ;
}
cout << endl ;
diff_beta = max(abs(tdiff_beta)) ;
//--------------------------------------------------------
// Vector Poisson equation for shift_auto
//--------------------------------------------------------
// Source
// See Eq (52) from Gourgoulhon et al. (2001)
// ------
Tenseur vtmp = 6. * ( d_beta_auto + d_beta_comp )
-8. * ( d_logn_auto + d_logn_comp ) ;
source_shift = (-4.*qpig) * nnn % a_car % (ener_euler + press)
% u_euler
+ nnn % flat_scalar_prod_desal(tkij_auto, vtmp) ;
source_shift.set_std_base() ;
// Resolution of the Poisson equation
// ----------------------------------
// Filter for the source of shift vector
for (int i=0; i<3; i++) {
if (source_shift(i).get_etat() != ETATZERO)
source_shift.set(i).filtre(4) ;
}
// For Tenseur::poisson_vect, the triad must be the mapping triad,
// not the reference one:
source_shift.change_triad( mp.get_bvect_cart() ) ;
for (int i=0; i<3; i++) {
if(source_shift(i).dz_nonzero()) {
assert( source_shift(i).get_dzpuis() == 4 ) ;
}
else{
(source_shift.set(i)).set_dzpuis(4) ;
}
}
//##
// source_shift.dec2_dzpuis() ; // dzpuis 4 -> 2
double lambda_shift = double(1) / double(3) ;
source_shift.poisson_vect(lambda_shift, par_poisson_vect,
shift_auto, w_shift, khi_shift) ;
// Check: has the equation for shift_auto been correctly solved ?
// --------------------------------------------------------------
// Divergence of shift_auto :
Tenseur divn = contract(shift_auto.gradient(), 0, 1) ;
divn.dec2_dzpuis() ; // dzpuis 2 -> 0
// Grad(div) :
Tenseur graddivn = divn.gradient() ;
graddivn.inc2_dzpuis() ; // dzpuis 2 -> 4
// Full operator :
Tenseur lap_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
lap_shift.set_etat_qcq() ;
for (int i=0; i<3; i++) {
lap_shift.set(i) = shift_auto(i).laplacien()
+ lambda_shift * graddivn(i) ;
}
Tbl tdiff_shift_x = diffrel(lap_shift(0), source_shift(0)) ;
Tbl tdiff_shift_y = diffrel(lap_shift(1), source_shift(1)) ;
Tbl tdiff_shift_z = diffrel(lap_shift(2), source_shift(2)) ;
cout <<
"Relative error in the resolution of the equation for shift_auto : "
<< endl ;
cout << "x component : " ;
for (int l=0; l<nz; l++) {
cout << tdiff_shift_x(l) << " " ;
}
cout << endl ;
cout << "y component : " ;
for (int l=0; l<nz; l++) {
cout << tdiff_shift_y(l) << " " ;
}
cout << endl ;
cout << "z component : " ;
for (int l=0; l<nz; l++) {
cout << tdiff_shift_z(l) << " " ;
}
cout << endl ;
diff_shift_x = max(abs(tdiff_shift_x)) ;
diff_shift_y = max(abs(tdiff_shift_y)) ;
diff_shift_z = max(abs(tdiff_shift_z)) ;
// Final result
// ------------
// The output of Tenseur::poisson_vect is on the mapping triad,
// it should therefore be transformed to components on the
// reference triad :
shift_auto.change_triad( ref_triad ) ;
} // End of relativistic equations
if (nzet > 1) {
cout.precision(10) ;
for (int ltrans = 0; ltrans < nzet-1; ltrans++) {
cout << endl << "Values at boundary between domains no. " << ltrans << " and " << ltrans+1 << " for theta = pi/2 and phi = 0 :" << endl ;
double rt1 = mp.val_r(ltrans, 1., M_PI/2, 0.) ;
double rt2 = mp.val_r(ltrans+1, -1., M_PI/2, 0.) ;
cout << " Coord. r [km] (left, right, rel. diff) : "
<< rt1 / km << " " << rt2 / km << " " << (rt2 - rt1)/rt1 << endl ;
int ntm1 = mg->get_nt(ltrans) - 1;
int nrm1 = mg->get_nr(ltrans) - 1 ;
double ent1 = ent()(ltrans, 0, ntm1, nrm1) ;
double ent2 = ent()(ltrans+1, 0, ntm1, 0) ;
cout << " Enthalpy (left, right, rel. diff) : "
<< ent1 << " " << ent2 << " " << (ent2-ent1)/ent1 << endl ;
double press1 = press()(ltrans, 0, ntm1, nrm1) ;
double press2 = press()(ltrans+1, 0, ntm1, 0) ;
cout << " Pressure (left, right, rel. diff) : "
<< press1 << " " << press2 << " " << (press2-press1)/press1 << endl ;
double nb1 = nbar()(ltrans, 0, ntm1, nrm1) ;
double nb2 = nbar()(ltrans+1, 0, ntm1, 0) ;
cout << " Baryon density (left, right, rel. diff) : "
<< nb1 << " " << nb2 << " " << (nb2-nb1)/nb1 << endl ;
}
}
/* if (mer % 10 == 0) {
cout << "mer = " << mer << endl ;
double r_max = 1.2 * ray_eq() ;
des_profile(nbar(), 0., r_max, M_PI/2, 0., "n", "Baryon density") ;
des_profile(ener(), 0., r_max, M_PI/2, 0., "e", "Energy density") ;
des_profile(press(), 0., r_max, M_PI/2, 0., "p", "Pressure") ;
des_profile(ent(), 0., r_max, M_PI/2, 0., "H", "Enthalpy") ;
}*/
//-------------------------------------------------
// Relative change in enthalpy
//-------------------------------------------------
Tbl diff_ent_tbl = diffrel( ent(), ent_jm1() ) ;
diff_ent = diff_ent_tbl(0) ;
for (int l=1; l<nzet; l++) {
diff_ent += diff_ent_tbl(l) ;
}
diff_ent /= nzet ;
ent_jm1 = ent ;
} // End of main loop
//=========================================================================
// End of iteration
//=========================================================================
}
}
Lorene::Cmp::filtre
void filtre(int n)
Sets the n lasts coefficients in r to 0 in the external domain.
Definition cmp_manip.C:74
Lorene::Etoile_bin::d_beta_auto
Tenseur d_beta_auto
Gradient of beta_auto (Cartesian components with respect to ref_triad ).
Definition etoile.h:879
Lorene::Etoile_bin::d_logn_auto
Tenseur d_logn_auto
Gradient of logn_auto (Cartesian components with respect to ref_triad ).
Definition etoile.h:859
Lorene::Etoile_bin::akcar_comp
Tenseur akcar_comp
Part of the scalar generated by shift_auto and shift_comp , i.e.
Definition etoile.h:944
Lorene::Etoile_bin::ssjm1_khi
Cmp ssjm1_khi
Effective source at the previous step for the resolution of the Poisson equation for the scalar by m...
Definition etoile.h:973
Lorene::Etoile_bin::velocity_potential
double velocity_potential(int mermax, double precis, double relax)
Computes the non-translational part of the velocity scalar potential by solving the continuity equat...
Definition et_bin_vel_pot.C:142
Lorene::Etoile_bin::equilibrium
void equilibrium(double ent_c, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, double thres_adapt, const Tbl &fact, Tbl &diff, const Tbl *ent_limit=0x0)
Computes an equilibrium configuration.
Definition et_bin_equilibrium.C:184
Lorene::Etoile_bin::ref_triad
const Base_vect & ref_triad
Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's...
Definition etoile.h:828
Lorene::Etoile_bin::irrotational
bool irrotational
true for an irrotational star, false for a corotating one
Definition etoile.h:822
Lorene::Etoile_bin::w_shift
Tenseur w_shift
Vector used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Definition etoile.h:908
Lorene::Etoile_bin::logn_comp
Tenseur logn_comp
Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by ...
Definition etoile.h:854
Lorene::Etoile_bin::d_logn_comp
Tenseur d_logn_comp
Gradient of logn_comp (Cartesian components with respect to ref_triad ).
Definition etoile.h:869
Lorene::Etoile_bin::hydro_euler
virtual void hydro_euler()
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid fram...
Definition et_bin_hydro.C:106
Lorene::Etoile_bin::ssjm1_wshift
Tenseur ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for by means...
Definition etoile.h:983
Lorene::Etoile_bin::ssjm1_logn
Cmp ssjm1_logn
Effective source at the previous step for the resolution of the Poisson equation for logn_auto by mea...
Definition etoile.h:959
Lorene::Etoile_bin::pot_centri
Tenseur pot_centri
Centrifugal potential.
Definition etoile.h:953
Lorene::Etoile_bin::loggam
Tenseur loggam
Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Definition etoile.h:849
Lorene::Etoile_bin::shift_auto
Tenseur shift_auto
Part of the shift vector generated principaly by the star.
Definition etoile.h:889
Lorene::Etoile_bin::tkij_auto
Tenseur_sym tkij_auto
Part of the extrinsic curvature tensor generated by shift_auto .
Definition etoile.h:925
Lorene::Etoile_bin::akcar_auto
Tenseur akcar_auto
Part of the scalar generated by shift_auto , i.e.
Definition etoile.h:938
Lorene::Etoile_bin::ssjm1_beta
Cmp ssjm1_beta
Effective source at the previous step for the resolution of the Poisson equation for beta_auto by mea...
Definition etoile.h:965
Lorene::Etoile_bin::d_beta_comp
Tenseur d_beta_comp
Gradient of beta_comp (Cartesian components with respect to ref_triad ).
Definition etoile.h:884
Lorene::Etoile_bin::khi_shift
Tenseur khi_shift
Scalar used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Definition etoile.h:918
Lorene::Etoile::nzet
int nzet
Number of domains of *mp occupied by the star.
Definition etoile.h:432
Lorene::Etoile::logn_auto_regu
Tenseur logn_auto_regu
Regular part of the logarithm of the part of the lapse N generated principaly by the star.
Definition etoile.h:491
Lorene::Etoile::ray_eq
double ray_eq() const
Coordinate radius at , [r_unit].
Definition etoile_global.C:120
Lorene::Etoile::nnn
Tenseur nnn
Total lapse function.
Definition etoile.h:509
Lorene::Etoile::logn_auto
Tenseur logn_auto
Total of the logarithm of the part of the lapse N generated principaly by the star.
Definition etoile.h:484
Lorene::Etoile::nbar
Tenseur nbar
Baryon density in the fluid frame.
Definition etoile.h:459
Lorene::Etoile::equation_of_state
virtual void equation_of_state()
Computes the proper baryon and energy density, as well as pressure from the enthalpy.
Definition etoile.C:566
Lorene::Etoile::u_euler
Tenseur u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Definition etoile.h:474
Lorene::Etoile::mp
Map & mp
Mapping associated with the star.
Definition etoile.h:429
Lorene::Etoile::press
Tenseur press
Fluid pressure.
Definition etoile.h:461
Lorene::Etoile::relativistic
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition etoile.h:437
Lorene::Etoile::ener_euler
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition etoile.h:465
Lorene::Etoile::s_euler
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition etoile.h:468
Lorene::Etoile::ent
Tenseur ent
Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case).
Definition etoile.h:457
Lorene::Etoile::beta_auto
Tenseur beta_auto
Logarithm of the part of the product AN generated principaly by by the star.
Definition etoile.h:506
Lorene::Etoile::a_car
Tenseur a_car
Total conformal factor .
Definition etoile.h:515
Lorene::Etoile::ray_pole
double ray_pole() const
Coordinate radius at [r_unit].
Definition etoile_global.C:415
Lorene::Map_et
Radial mapping of rather general form.
Definition map.h:2752
Lorene::Map_et::homothetie
virtual void homothetie(double lambda)
Sets a new radial scale.
Definition map_et.C:905
Lorene::Mg3d
Multi-domain grid.
Definition grilles.h:273
Lorene::Mg3d::get_np
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition grilles.h:462
Lorene::Mg3d::get_nt
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition grilles.h:457
Lorene::Mg3d::get_nzone
int get_nzone() const
Returns the number of domains.
Definition grilles.h:448
Lorene::Mg3d::get_nr
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition grilles.h:452
Lorene::Param
Parameter storage.
Definition param.h:125
Lorene::Param::add_double
void add_double(const double &x, int position=0)
Adds the the address of a new double to the list.
Definition param.C:315
Lorene::Param::add_cmp_mod
void add_cmp_mod(Cmp &ti, int position=0)
Adds the address of a new modifiable Cmp to the list.
Definition param.C:1004
Lorene::Param::add_int_mod
void add_int_mod(int &n, int position=0)
Adds the address of a new modifiable int to the list.
Definition param.C:385
Lorene::Param::add_tenseur_mod
void add_tenseur_mod(Tenseur &ti, int position=0)
Adds the address of a new modifiable Tenseur to the list.
Definition param.C:1142
Lorene::Param::add_int
void add_int(const int &n, int position=0)
Adds the address of a new int to the list.
Definition param.C:246
Lorene::Param::add_tbl
void add_tbl(const Tbl &ti, int position=0)
Adds the address of a new Tbl to the list.
Definition param.C:522
Lorene::Tbl
Basic array class.
Definition tbl.h:161
Lorene::Tbl::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tbl.C:361
Lorene::Tbl::set
double & set(int i)
Read/write of a particular element (index i) (1D case).
Definition tbl.h:281
Lorene::Tenseur
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:301
Lorene::Tenseur::set
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:824
Lorene::Tenseur::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tenseur.C:636
Lorene::Tenseur::dec2_dzpuis
void dec2_dzpuis()
dzpuis -= 2 ;
Definition tenseur.C:1130
Lorene::Tenseur::gradient
const Tenseur & gradient() const
Returns the gradient of *this (Cartesian coordinates).
Definition tenseur.C:1542
Lorene::Tenseur::set_std_base
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition tenseur.C:1170
Lorene::Tenseur::inc2_dzpuis
void inc2_dzpuis()
dzpuis += 2 ;
Definition tenseur.C:1143
Lorene::Tenseur::change_triad
void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition tenseur.C:668
Lorene::Tenseur::poisson_vect
void poisson_vect(double lambda, Param &par, Tenseur &shift, Tenseur &vect, Tenseur &scal) const
Solves the vectorial Poisson equation : .
Definition tenseur_pde.C:118
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Lorene::diffrel
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition cmp_math.C:504
Lorene::max
Tbl max(const Cmp &)
Maximum values of a Cmp in each domain.
Definition cmp_math.C:435
Lorene::abs
Cmp abs(const Cmp &)
Absolute value.
Definition cmp_math.C:410
Lorene::contract
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Definition tenseur_operateur.C:279
Lorene::flat_scalar_prod_desal
Tenseur flat_scalar_prod_desal(const Tenseur &t1, const Tenseur &t2)
Same as flat_scalar_prod but with desaliasing.
Definition tenseur_operateur.C:735
Lorene
Lorene prototypes.
Definition app_hor.h:64
Lorene::laplacien
virtual void laplacien(const Scalar &uu, int zec_mult_r, Scalar &lap) const =0
Computes the Laplacian of a scalar field.
Unites
Standard units of space, time and mass.