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/*
* Method of class Binary to set some analytical form to the shift vector.
*
* (see file binary.h for documentation).
*/
/*
* Copyright (c) 2004 Francois Limousin
*
* 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 binary_anashift_C[] = "$Header: /cvsroot/Lorene/C++/Source/Binary/binary_anashift.C,v 1.9 2014/10/13 08:52:44 j_novak Exp $" ;
/*
* $Id: binary_anashift.C,v 1.9 2014/10/13 08:52:44 j_novak Exp $
* $Log: binary_anashift.C,v $
* Revision 1.9 2014/10/13 08:52:44 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.8 2005/09/13 19:38:31 f_limousin
* Reintroduction of the resolution of the equations in cartesian coordinates.
*
* Revision 1.7 2005/02/17 17:34:50 f_limousin
* Change the name of some quantities to be consistent with other classes
* (for instance nnn is changed to nn, shift to beta, beta to lnq...)
*
* Revision 1.6 2004/03/25 10:29:01 j_novak
* All LORENE's units are now defined in the namespace Unites (in file unites.h).
*
* Revision 1.5 2004/02/27 10:01:32 f_limousin
* Correct sign of shift_auto to agree with the new convention
* for shift.
*
* Revision 1.4 2004/01/22 10:09:41 f_limousin
* First executable version
*
* Revision 1.3 2004/01/20 15:21:23 f_limousin
* First version
*
*
* $Header: /cvsroot/Lorene/C++/Source/Binary/binary_anashift.C,v 1.9 2014/10/13 08:52:44 j_novak Exp $
*
*/
// Headers C
#include "math.h"
// Headers Lorene
#include "binary.h"
#include "tenseur.h"
#include "unites.h"
namespace Lorene {
void Binary::analytical_shift(){
using namespace Unites ;
for (int i=0; i<2; i++) {
// Radius of the star:
double a0 = et[i]->ray_eq() ;
// Mass ratio
double p_mass = et[i]->mass_g() / et[1-i]->mass_g() ;
// G M Omega R / (1+p)
double www = ggrav * et[i]->mass_g() * omega
* separation() / (1. + p_mass) ;
const Map& mp = et[i]->get_mp() ;
Scalar tmp(mp) ;
Scalar tmp_ext(mp) ;
int nzet = et[i]->get_nzet() ;
int nzm1 = mp.get_mg()->get_nzone() - 1 ;
Vector w_beta (mp, CON, mp.get_bvect_cart()) ;
Scalar khi_beta (mp) ;
// Computation of w_beta
// ----------------------
// X component
// -----------
w_beta.set(1) = 0 ;
// Y component
// -----------
// For the incompressible case :
tmp = - 6 * www / a0 * ( 1 - (mp.r)*(mp.r) / (3*a0*a0) ) ;
tmp.annule(nzet, nzm1) ;
tmp_ext = - 4 * www / mp.r ;
tmp_ext.annule(0, nzet-1) ;
w_beta.set(2) = tmp + tmp_ext ;
// Z component
// -----------
w_beta.set(3) = 0 ;
w_beta.std_spectral_base() ;
// Computation of khi_beta
// ------------------------
tmp = 2 * www / a0 * (mp.y) * ( 1 - 3 * (mp.r)*(mp.r) / (5*a0*a0) ) ;
tmp.annule(nzet, nzm1) ;
tmp_ext = 0.8 * www * a0*a0 * (mp.sint) * (mp.sinp)
/ (mp.r * mp.r) ;
tmp_ext.annule(0, nzet-1) ;
khi_beta = tmp + tmp_ext ;
// Sets the standard spectral bases for a scalar field
khi_beta.std_spectral_base() ;
// Computation of beta auto.
// --------------------------
Tensor xdw_temp (w_beta.derive_con(et[i]->get_flat())) ;
Tenseur x_d_w_temp (et[i]->get_mp(),2,CON,et[i]->get_mp().get_bvect_cart()) ;
x_d_w_temp.set_etat_qcq() ;
for (int j=0; j<3; j++)
for (int k=0; k<3; k++)
x_d_w_temp.set(j,k) = xdw_temp(k+1, j+1) ;
Tenseur x_d_w = skxk (x_d_w_temp) ;
x_d_w.dec_dzpuis() ;
Vector xdw (et[i]->get_mp(), CON, et[i]->get_mp().get_bvect_cart()) ;
for (int j=0; j<3; j++)
xdw.set(j+1) = x_d_w(j) ;
// See Eq (92) from Gourgoulhon et al.(2001) and with the new
// convention for shift = - N^i
Vector d_khi = khi_beta.derive_con(et[i]->get_flat()) ;
d_khi.dec_dzpuis(2) ;
et[i]->set_beta_auto() = - 7./8. * w_beta + 1./8. *
(d_khi + xdw) ;
et[i]->set_beta_auto().std_spectral_base() ;
}
}
}
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