star_bhns_vel_pot.C
/*
* Method of class Star_bhns to compute the velocity scalar potential $\psi$
* by solving the continuity equation.
*
* (see file star_bhns.h for documentation).
*
*/
/*
* Copyright (c) 2005-2007 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 version 2
* as published by the Free Software Foundation.
*
* 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 star_bhns_vel_pot_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star_bhns/star_bhns_vel_pot.C,v 1.3 2014/10/13 08:53:41 j_novak Exp $" ;
/*
* $Id: star_bhns_vel_pot.C,v 1.3 2014/10/13 08:53:41 j_novak Exp $
* $Log: star_bhns_vel_pot.C,v $
* Revision 1.3 2014/10/13 08:53:41 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.2 2008/05/15 19:20:29 k_taniguchi
* Change of some parameters.
*
* Revision 1.1 2007/06/22 01:33:14 k_taniguchi
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Star_bhns/star_bhns_vel_pot.C,v 1.3 2014/10/13 08:53:41 j_novak Exp $
*
*/
// C++ headers
//#include <>
// C headers
//#include <>
// Lorene headers
#include "star_bhns.h"
#include "eos.h"
#include "param.h"
#include "cmp.h"
#include "tenseur.h"
#include "utilitaires.h"
#include "unites.h"
// Local prototype
namespace Lorene {
Cmp raccord_c1(const Cmp& uu, int l1) ;
double Star_bhns::velo_pot_bhns(const double& mass_bh, const double& sepa,
bool kerrschild, int mermax, double precis,
double relax) {
// Fundamental constants and units
// -------------------------------
using namespace Unites ;
int nzm1 = mp.get_mg()->get_nzone() - 1 ;
//--------------------------------
// Specific relativistic enthalpy ---> hhh
//--------------------------------
Scalar hhh = exp(ent) ;
hhh.std_spectral_base() ;
//---------------------------------------------------
// Computation of W^i = psi4 h Gamma_n B^i/lapse_tot
// See Eq (62) from Gourgoulhon et al. (2001)
//---------------------------------------------------
Vector www = hhh * gam_euler * bsn * psi4 ;
www.change_triad( mp.get_bvect_cart() ) ; // components on the mapping
// Cartesian basis
//-------------------------------------------------
// Constant value of W^i at the center of the star
//-------------------------------------------------
Vector v_orb(mp, CON, mp.get_bvect_cart()) ;
v_orb.set_etat_qcq() ;
for (int i=1; i<=3; i++) {
v_orb.set(i) = www(i).val_grid_point(0, 0, 0, 0) ;
}
v_orb.set_triad( *(www.get_triad()) ) ;
v_orb.std_spectral_base() ;
//-------------------------------------------------
// Source and coefficients a,b for poisson_compact (independent from psi0)
//-------------------------------------------------
Scalar dndh_log = eos.der_nbar_ent(ent, nzet) ;
// In order to avoid any division by zero in the computation of zeta_h
// the value of dndh_log is set to 1 in the external domains:
for (int l=nzet; l<=nzm1; l++) {
dndh_log.set_domain(l) = 1. ;
}
Scalar zeta_h( ent / dndh_log ) ;
zeta_h.std_spectral_base() ;
double erreur ;
Scalar source(mp) ;
Vector bb(mp, CON, mp.get_bvect_spher()) ;
Metric_flat flat_spher( mp.flat_met_spher() ) ;
if (kerrschild) {
cout << "!!!!! WARNING: Not yet available !!!!!" << endl ;
abort() ;
} // End of Kerr-Schild
else { // Isotropic coordinates with the maximal slicing
Scalar lnlappsi(mp) ;
lnlappsi = log( lapconf_tot * confo_tot ) ;
lnlappsi.std_spectral_base() ;
bb = (1. - zeta_h) * ent.derive_con(flat_spher)
+ zeta_h * lnlappsi.derive_con(flat_spher) ;
Vector dentmb(mp, COV, mp.get_bvect_cart()) ;
dentmb.set_etat_qcq() ;
for (int i=1; i<=3; i++) {
dentmb.set(i) = ent.deriv(i)
- (d_lapconf_auto(i) + d_lapconf_comp(i)) / lapconf_tot
- (d_confo_auto(i) + d_confo_comp(i)) / confo_tot ;
}
dentmb.std_spectral_base() ;
source = contract(www - v_orb, 0, ent.derive_cov(flat), 0)
+zeta_h*(contract(v_orb, 0, dentmb, 0)
+ contract(www/gam_euler, 0, gam_euler.derive_cov(flat), 0)
) ;
source.annule(nzet, nzm1) ;
} // End of Isotropic coordinates
//----------------------------------------------------
// Resolution by means of Map_radial::poisson_compact
//----------------------------------------------------
Param par ;
int niter ;
par.add_int(mermax) ;
par.add_double(precis, 0) ;
par.add_double(relax, 1) ;
par.add_int_mod(niter) ;
if (psi0.get_etat() == ETATZERO) {
psi0 = 0. ;
}
Cmp source_cmp(source) ;
Cmp zeta_h_cmp(zeta_h) ;
Cmp psi0_cmp(psi0) ;
Tenseur bb_cmp(mp, 1, CON, mp.get_bvect_spher()) ;
bb_cmp.set_etat_qcq() ;
Cmp bb_cmp1(bb(1)) ;
Cmp bb_cmp2(bb(2)) ;
Cmp bb_cmp3(bb(3)) ;
bb_cmp.set(0) = bb_cmp1 ;
bb_cmp.set(1) = bb_cmp2 ;
bb_cmp.set(2) = bb_cmp3 ;
source_cmp.va.ylm() ;
mp.poisson_compact(source_cmp, zeta_h_cmp, bb_cmp, par, psi0_cmp) ;
psi0 = psi0_cmp ;
//-----------------------
// Check of the solution
//-----------------------
Scalar bb_dpsi0 = contract(bb, 0, psi0.derive_cov(flat_spher), 0) ;
Scalar oper = zeta_h * psi0.laplacian() + bb_dpsi0 ;
source.set_spectral_va().ylm_i() ;
erreur = diffrel(oper, source)(0) ;
cout << "Check of the resolution of the continuity equation : "
<< endl ;
cout << " norme(source) : " << norme(source)(0)
<< " diff oper/source : " << erreur << endl ;
//--------------------------
// Computation of grad(psi)
//--------------------------
for (int i=1; i<=3; i++)
d_psi.set(i) = (psi0.derive_cov(flat))(i) + v_orb(i) ;
// C^1 continuation of d_psi outside the star
// (to ensure a smooth enthalpy field accross the stellar surface)
// ----------------------------------------------------------------
d_psi.annule(nzet, nzm1) ;
for (int i=1; i<=3; i++) {
Cmp d_psi_i( d_psi(i) ) ;
d_psi_i = raccord_c1(d_psi_i, nzet) ;
d_psi.set(i) = d_psi_i ;
}
return erreur ;
}
}
Lorene::Cmp
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
Lorene::Cmp::va
Valeur va
The numerical value of the Cmp.
Definition cmp.h:464
Lorene::Metric_flat
Flat metric for tensor calculation.
Definition metric.h:261
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_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_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::Scalar
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:387
Lorene::Scalar::std_spectral_base
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field.
Definition scalar.C:784
Lorene::Scalar::set_domain
Tbl & set_domain(int l)
Read/write of the value in a given domain.
Definition scalar.h:615
Lorene::Scalar::annule
virtual void annule(int l_min, int l_max)
Sets the Scalar to zero in several domains.
Definition scalar.C:391
Lorene::Scalar::set_spectral_va
Valeur & set_spectral_va()
Returns va (read/write version).
Definition scalar.h:604
Lorene::Scalar::derive_con
const Vector & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of *this with respect to some metric , by raising the index of...
Definition scalar_deriv.C:402
Lorene::Star_bhns::flat
Metric_flat flat
Flat metric defined on the mapping (Spherical components with respect to the mapping of the star ).
Definition star_bhns.h:192
Lorene::Star_bhns::velo_pot_bhns
double velo_pot_bhns(const double &mass_bh, const double &sepa, bool kerrschild, int mermax, double precis, double relax)
Computes the non-translational part of the velocity scalar potential by solving the continuity equat...
Definition star_bhns_vel_pot.C:67
Lorene::Star_bhns::bsn
Vector bsn
3-vector shift, divided by N , of the rotating coordinates, .
Definition star_bhns.h:99
Lorene::Star_bhns::d_confo_comp
Vector d_confo_comp
Derivative of the conformal factor generated by the companion black hole.
Definition star_bhns.h:173
Lorene::Star_bhns::confo_tot
Scalar confo_tot
Total conformal factor.
Definition star_bhns.h:163
Lorene::Star_bhns::psi4
Scalar psi4
Fourth power of the total conformal factor.
Definition star_bhns.h:176
Lorene::Star_bhns::d_lapconf_auto
Vector d_lapconf_auto
Derivative of the lapconf function generated by the star .
Definition star_bhns.h:130
Lorene::Star_bhns::d_psi
Vector d_psi
Gradient of (in the irrotational case) (Spherical components with respect to the mapping of the star...
Definition star_bhns.h:82
Lorene::Star_bhns::d_confo_auto
Vector d_confo_auto
Derivative of the conformal factor generated by the star .
Definition star_bhns.h:168
Lorene::Star_bhns::lapconf_tot
Scalar lapconf_tot
Total lapconf function.
Definition star_bhns.h:119
Lorene::Star_bhns::d_lapconf_comp
Vector d_lapconf_comp
Derivative of the lapconf function generated by the companion black hole.
Definition star_bhns.h:135
Lorene::Star_bhns::psi0
Scalar psi0
Scalar potential of the non-translational part of fluid 4-velocity (in the irrotational case).
Definition star_bhns.h:77
Lorene::Star::eos
const Eos & eos
Equation of state of the stellar matter.
Definition star.h:185
Lorene::Star::gam_euler
Scalar gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition star.h:204
Lorene::Star::ent
Scalar ent
Log-enthalpy.
Definition star.h:190
Lorene::Star::mp
Map & mp
Mapping associated with the star.
Definition star.h:180
Lorene::Star::nzet
int nzet
Number of domains of *mp occupied by the star.
Definition star.h:183
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::Valeur::ylm
void ylm()
Computes the coefficients of *this.
Definition valeur_ylm.C:138
Lorene::Valeur::ylm_i
void ylm_i()
Inverse of ylm().
Definition valeur_ylm_i.C:131
Lorene::Vector
Tensor field of valence 1.
Definition vector.h:188
Lorene::Vector::std_spectral_base
virtual void std_spectral_base()
Sets the standard spectal bases of decomposition for each component.
Definition vector.C:316
Lorene::Vector::change_triad
virtual void change_triad(const Base_vect &)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition vector_change_triad.C:75
Lorene::Vector::set
Scalar & set(int)
Read/write access to a component.
Definition vector.C:296
Lorene::exp
Cmp exp(const Cmp &)
Exponential.
Definition cmp_math.C:270
Lorene::diffrel
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition cmp_math.C:504
Lorene::norme
Tbl norme(const Cmp &)
Sums of the absolute values of all the values of the Cmp in each domain.
Definition cmp_math.C:481
Lorene::log
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
Lorene::Tensor::set_triad
void set_triad(const Base_vect &new_triad)
Assigns a new vectorial basis (triad) of decomposition.
Definition tensor.C:519
Lorene::Tensor::get_triad
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition tensor.h:866
Lorene::Tensor::set_etat_qcq
virtual void set_etat_qcq()
Sets the logical state of all components to ETATQCQ (ordinary state).
Definition tensor.C:481
Lorene::contract
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Definition tenseur_operateur.C:279
Lorene
Lorene prototypes.
Definition app_hor.h:64
Unites
Standard units of space, time and mass.