binary_anashift.C

/*
 * 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 1.8 2005/09/13 19:38:31 f_limousin Exp $" ;

/*
 * $Id: binary_anashift.C,v 1.8 2005/09/13 19:38:31 f_limousin Exp $
 * $Log: binary_anashift.C,v $
 * 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 1.8 2005/09/13 19:38:31 f_limousin Exp $
 *
 */

// Headers C
#include "math.h"

// Headers Lorene
#include "binary.h"
#include "tenseur.h"
#include "unites.h"

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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