star_bin_vel_pot_xcts.C
/*
* Method of class Star_bin_xcts to compute the velocity scalar
* potential $\psi$ by solving the continuity equation
* (see file star.h for documentation).
*/
/*
* Copyright (c) 2010 Michal Bejger
*
* 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_bin_vel_pot_xcts_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star/star_bin_vel_pot_xcts.C,v 1.7 2014/10/13 08:53:39 j_novak Exp $" ;
/*
* $Id: star_bin_vel_pot_xcts.C,v 1.7 2014/10/13 08:53:39 j_novak Exp $
* $Log: star_bin_vel_pot_xcts.C,v $
* Revision 1.7 2014/10/13 08:53:39 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.6 2010/12/09 10:47:31 m_bejger
* Small changes, definition of lnPsi2N
*
* Revision 1.5 2010/10/26 20:01:06 m_bejger
* Cleanup
*
* Revision 1.4 2010/10/18 20:56:15 m_bejger
* Generalization for many domains in the star: buggy
*
* Revision 1.3 2010/06/17 15:07:10 m_bejger
* Psi4, lnPsi2N corrected
*
* Revision 1.2 2010/06/15 08:05:55 m_bejger
* Various fields were lacking bases
*
* Revision 1.1 2010/05/04 07:51:05 m_bejger
* Initial version
*
* $Header: /cvsroot/Lorene/C++/Source/Star/star_bin_vel_pot_xcts.C,v 1.7 2014/10/13 08:53:39 j_novak Exp $
*
*/
// Headers Lorene
#include "star.h"
#include "eos.h"
#include "param.h"
#include "cmp.h"
#include "tenseur.h"
#include "graphique.h"
#include "utilitaires.h"
// Local prototype
namespace Lorene {
Cmp raccord_c1(const Cmp& uu, int l1) ;
double Star_bin_xcts::velocity_potential(int mermax,
double precis,
double relax) {
int nzm1 = mp.get_mg()->get_nzone() - 1 ;
//----------------------------------
// Specific relativistic enthalpy ---> hhh
//----------------------------------
Scalar hhh = exp(ent) ; // = 1 at the Newtonian limit
hhh.std_spectral_base() ;
//------------------------------------------------------------------
// Computation of W^i = Psi^4 h Gamma_n B^i/N
// See Eq (62) from Gourgoulhon et al. (2001)
//------------------------------------------------------------------
Vector www = hhh * gam_euler * psi4 * bsn ;
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(mp) ;
dndh_log = 0 ;
for (int l=0; l<nzet; l++) {
Param par ; // Paramater for multi-domain equation of state
par.add_int(l) ;
dndh_log = dndh_log + eos.der_nbar_ent(ent, 1, l, &par) ;
}
// 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() ;
Scalar Psichi = Psi % chi ;
Psichi.std_spectral_base() ;
Scalar lnPsi2N = log(Psichi) ;
lnPsi2N.std_spectral_base() ;
Metric_flat flat_spher (mp.flat_met_spher()) ;
Vector bb = (1 - zeta_h) * ent.derive_con(flat_spher)
+ zeta_h * lnPsi2N.derive_con(flat_spher) ;
Scalar entmb = ent - lnPsi2N ;
www.change_triad(mp.get_bvect_cart()) ;
v_orb.change_triad(mp.get_bvect_cart()) ;
// Eq. 63 of Gourgoulhon et al. (2001)
Scalar source = contract(www - v_orb, 0, ent.derive_cov(flat), 0)
+ zeta_h * ( contract(v_orb, 0, entmb.derive_cov(flat), 0)
+ contract(www/gam_euler, 0, gam_euler.derive_cov(flat), 0) ) ;
/*
des_meridian(zeta_h,0., 4., "zeta_h", 10) ;
arrete() ;
des_meridian(bb(1),0., 4., "bb(1)", 10) ;
arrete() ;
des_meridian(bb(2),0., 4., "bb(2)", 10) ;
arrete() ;
des_meridian(bb(3),0., 4., "bb(3)", 10) ;
arrete() ;
des_meridian(psi0,0., 4., "psi0", 10) ;
arrete() ;
des_meridian(source,0., 4., "source", 10) ;
arrete() ;
*/
source.annule(nzet, nzm1) ;
//---------------------------------------------------
// 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() ;
//cout << "psiO prevu" << endl << norme(psi0) << endl ;
mp.poisson_compact(nzet, source_cmp, zeta_h_cmp, bb_cmp, par, psi0_cmp ) ;
psi0 = psi0_cmp ;
cout << "psiO apres" << endl << norme(psi0) << endl ;
//---------------------------------------------------
// 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() ;
cout << "Check of the resolution of the continuity equation : " << endl ;
Tbl terr = diffrel(oper, source) ;
double erreur = 0 ;
for (int l=0; l<nzet; l++) {
double err = terr(l) ;
cout << " domain " << l << " : norme(source) : " << norme(source)(l)
<< " relative error : " << err << endl ;
if (err > erreur) erreur = err ;
}
//--------------------------------
// Computation of grad(psi)
//--------------------------------
d_psi.set_etat_qcq() ;
for (int i=1; i<=3; i++)
d_psi.set(i) = (psi0.derive_cov(flat))(i) + v_orb(i) ;
d_psi.change_triad(mp.get_bvect_cart()) ;
// 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++)
d_psi.set(i) = raccord_c1(d_psi(i), nzet) ;
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::derive_cov
const Vector & derive_cov(const Metric &gam) const
Returns the gradient (1-form = covariant vector) of *this.
Definition scalar_deriv.C:390
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_bin_xcts::Psi
Scalar Psi
Total conformal factor .
Definition star.h:1152
Lorene::Star_bin_xcts::psi0
Scalar psi0
Scalar potential of the non-translational part of fluid 4-velocity (in the irrotational case).
Definition star.h:1104
Lorene::Star_bin_xcts::psi4
Scalar psi4
Conformal factor .
Definition star.h:1158
Lorene::Star_bin_xcts::flat
Metric_flat flat
Flat metric defined on the mapping (Spherical components with respect to the mapping of the star) .
Definition star.h:1177
Lorene::Star_bin_xcts::chi
Scalar chi
Total function .
Definition star.h:1155
Lorene::Star_bin_xcts::bsn
Vector bsn
3-vector shift, divided by N, of the rotating coordinates, .
Definition star.h:1126
Lorene::Star_bin_xcts::d_psi
Vector d_psi
Gradient of (in the irrotational case) (Spherical components with respect to the mapping of the star...
Definition star.h:1109
Lorene::Star_bin_xcts::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 star_bin_vel_pot_xcts.C:70
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::Tbl
Basic array class.
Definition tbl.h:161
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