star_bhns_hydro.C

/*
 *  Method of class Star_bhns to compute hydro quantities
 *
 *    (see file star_bhns.h for documentation).
 *
 */

/*
 *   Copyright (c) 2005 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_hydro_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star_bhns/star_bhns_hydro.C,v 1.1 2007/06/22 01:31:42 k_taniguchi Exp $" ;

/*
 * $Id: star_bhns_hydro.C,v 1.1 2007/06/22 01:31:42 k_taniguchi Exp $
 * $Log: star_bhns_hydro.C,v $
 * Revision 1.1  2007/06/22 01:31:42  k_taniguchi
 * *** empty log message ***
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Star_bhns/star_bhns_hydro.C,v 1.1 2007/06/22 01:31:42 k_taniguchi Exp $
 *
 */

// C++ headers
//#include <>

// C headers
#include <math.h>

// Lorene headers
#include "star_bhns.h"
#include "utilitaires.h"
#include "unites.h"

void Star_bhns::hydro_euler_bhns(bool kerrschild, const double& mass_bh,
                 const double& sepa) {

    // Fundamental constants and units
    // -------------------------------
    using namespace Unites ;

    int nz = mp.get_mg()->get_nzone() ;
    int nzm1 = nz - 1 ;

    //--------------------------------
    // Specific relativistic enthalpy          ---> hhh
    //--------------------------------

    Scalar hhh = exp(ent) ;  // = 1 at the Newtonian limit
    hhh.std_spectral_base() ;

    if (kerrschild) {

        double mass = ggrav * mass_bh ;

    Scalar xx(mp) ;
    xx = mp.x ;
    xx.std_spectral_base() ;
    Scalar yy(mp) ;
    yy = mp.y ;
    yy.std_spectral_base() ;
    Scalar zz(mp) ;
    zz = mp.z ;
    zz.std_spectral_base() ;

    double yns = mp.get_ori_y() ;

    Scalar rbh(mp) ;
    rbh = sqrt( (xx+sepa)*(xx+sepa) + (yy+yns)*(yy+yns) + zz*zz ) ;
    rbh.std_spectral_base() ;

    Vector ll(mp, CON, mp.get_bvect_cart()) ;
    ll.set_etat_qcq() ;
    ll.set(1) = (xx+sepa) / rbh ;
    ll.set(2) = (yy+yns) / rbh ;
    ll.set(3) = zz / rbh ;
    ll.std_spectral_base() ;

    Scalar msr(mp) ;
    msr = mass / rbh ;
    msr.std_spectral_base() ;

    //--------------------------------------------
    // Lorentz factor and 3-velocity of the fluid
    //  with respect to the Eulerian observer
    //--------------------------------------------

    if (irrotational) {

        d_psi.std_spectral_base() ;

        Scalar dpsi2(mp) ;
        dpsi2 = d_psi(1)%d_psi(1) + d_psi(2)%d_psi(2)
          + d_psi(3)%d_psi(3) ;
        dpsi2.std_spectral_base() ;

        Scalar lldpsi(mp) ;
        lldpsi = ll(1)%d_psi(1) + ll(2)%d_psi(2) + ll(3)%d_psi(3) ;
        lldpsi.std_spectral_base() ;

        Scalar lap_bh2(mp) ;
        lap_bh2 = 1. / (1.+2.*msr) ;
        lap_bh2.std_spectral_base() ;

        Scalar tmp1(mp) ;
        tmp1 = 2. * msr % lap_bh2 % lldpsi % lldpsi ;
        tmp1.std_spectral_base() ;

        gam_euler = sqrt( 1.+(dpsi2-tmp1)/(hhh%hhh)/psi4 ) ;
        gam_euler.std_spectral_base() ;

        u_euler.set_etat_qcq() ;
        assert( u_euler.get_triad() == bsn.get_triad() ) ;

        for (int i=1; i<=3; i++)
          u_euler.set(i) = (d_psi(i)-2.*msr%lap_bh2%lldpsi%ll(i))
        / (hhh % gam_euler) / psi4 ;

        u_euler.std_spectral_base() ;

    }
    else {

        // Rigid rotation
        // --------------

        gam_euler = gam0 ;
        gam_euler.std_spectral_base() ;
        u_euler = bsn ;

    }

    //--------------------------------------------------------
    // Energy density E with respect to the Eulerian observer
    // See Eq (53) from Gourgoulhon et al. (2001)
    //--------------------------------------------------------

    ener_euler = gam_euler % gam_euler % (ener + press) - press ;
    ener_euler.std_spectral_base() ;

    //---------------------------------------------------
    // Trace of the stress-energy tensor with respect to
    // the Eulerian observer
    // See Eq (54) from Gourgoulhon et al. (2001)
    //---------------------------------------------------

    Scalar ueuler2(mp) ;
    ueuler2 = u_euler(1)%u_euler(1) + u_euler(2)%u_euler(2)
      + u_euler(3)%u_euler(3) ;
    ueuler2.std_spectral_base() ;

    Scalar llueuler(mp) ;
    llueuler = ll(1)%u_euler(1) + ll(2)%u_euler(2) + ll(3)%u_euler(3) ;
    llueuler.std_spectral_base() ;

    s_euler = 3. * press + (ener_euler + press) * psi4
      * (ueuler2 + 2.*msr%llueuler%llueuler) ;
    s_euler.std_spectral_base() ;

    //--------------------------------------------
    // Lorentz factor between the fluid and        ---> gam
    //  co-orbiting observers
    // See Eq (58) from Gourgoulhon et al. (2001)
    //--------------------------------------------

    if (irrotational) {

        Scalar bsnueuler(mp) ;
        bsnueuler = bsn(1)%u_euler(1) + bsn(2)%u_euler(2)
          + bsn(3)%u_euler(3) ;
        bsnueuler.std_spectral_base() ;

        Scalar llbsn(mp) ;
        llbsn = ll(1)%bsn(1) + ll(2)%bsn(2) + ll(3)%bsn(3) ;
        llbsn.std_spectral_base() ;

        Scalar tmp2(mp) ;
        tmp2 = 1. - psi4 * (bsnueuler + 2.*msr%llueuler%llbsn) ;
        tmp2.std_spectral_base() ;

        gam = gam0 % gam_euler % tmp2 ;
        gam.std_spectral_base() ;

        //--------------------------------------------
        // Spetial projection of the fluid 3-velocity
        // with respect to the co-orbiting observer
        //--------------------------------------------

        wit_w = gam_euler / gam * u_euler - gam0 * bsn ;
        wit_w.std_spectral_base() ;
        wit_w.annule_domain(nzm1) ;

        //-----------------------------------------
        // Logarithm of the Lorentz factor between
        // the fluid and co-orbiting observer
        //-----------------------------------------

        loggam = log( gam ) ;
        loggam.std_spectral_base() ;

        //-------------------------------------------------
        // Velocity fields set to zero in external domains
        //-------------------------------------------------

        loggam.annule_domain(nzm1) ;
        wit_w.annule_domain(nzm1) ;
        u_euler.annule_domain(nzm1) ;

        loggam.set_dzpuis(0) ;

    }
    else {  // Rigid rotation

        gam = 1. ;
        gam.std_spectral_base() ;
        loggam = 0. ;
        wit_w.set_etat_zero() ;

    }

    }  // End of Kerr-Schild
    else {  // Isotropic coordinates with the maximal slicing

    //--------------------------------------------
    // Lorentz factor and 3-velocity of the fluid
    //  with respect to the Eulerian observer
    //--------------------------------------------

    if (irrotational) {

        d_psi.std_spectral_base() ;

        Scalar dpsi2(mp) ;
        dpsi2 = d_psi(1)%d_psi(1) + d_psi(2)%d_psi(2)
          + d_psi(3)%d_psi(3) ;
        dpsi2.std_spectral_base() ;

        gam_euler = sqrt( 1. + dpsi2/(hhh%hhh)/psi4 ) ;
        gam_euler.std_spectral_base() ;

        u_euler.set_etat_qcq() ;
        for (int i=1; i<=3; i++)
          u_euler.set(i) = d_psi(i)/(hhh%gam_euler)/psi4 ;

        u_euler.std_spectral_base() ;

    }
    else {

        // Rigid rotation
        // --------------

        gam_euler = gam0 ;
        gam_euler.std_spectral_base() ;
        u_euler = bsn ;

    }

    //--------------------------------------------------------
    // Energy density E with respect to the Eulerian observer
    // See Eq (53) from Gourgoulhon et al. (2001)
    //--------------------------------------------------------

    ener_euler = gam_euler % gam_euler % (ener + press) - press ;
    ener_euler.std_spectral_base() ;

    //---------------------------------------------------
    // Trace of the stress-energy tensor with respect to
    // the Eulerian observer
    // See Eq (54) from Gourgoulhon et al. (2001)
    //---------------------------------------------------

    Scalar ueuler2(mp) ;
    ueuler2 = u_euler(1)%u_euler(1) + u_euler(2)%u_euler(2)
      + u_euler(3)%u_euler(3) ;
    ueuler2.std_spectral_base() ;

    s_euler = 3.*press + (ener_euler+press)*psi4*ueuler2 ;
    s_euler.std_spectral_base() ;


    //--------------------------------------------
    // Lorentz factor between the fluid and        ---> gam
    //  co-orbiting observers
    // See Eq (58) from Gourgoulhon et al. (2001)
    //--------------------------------------------

    if (irrotational) {

        Scalar bsnueuler(mp) ;
        bsnueuler = bsn(1)%u_euler(1) + bsn(2)%u_euler(2)
          + bsn(3)%u_euler(3) ;
        bsnueuler.std_spectral_base() ;

        Scalar tmp3(mp) ;
        tmp3 = 1. - psi4 % bsnueuler ;
        tmp3.std_spectral_base() ;

        gam = gam0 % gam_euler % tmp3 ;
        gam.std_spectral_base() ;

        //--------------------------------------------
        // Spetial projection of the fluid 3-velocity
        // with respect to the co-orbiting observer
        //--------------------------------------------

        wit_w = gam_euler / gam * u_euler - gam0 * bsn ;
        wit_w.std_spectral_base() ;
        wit_w.annule_domain(nzm1) ;

        //-----------------------------------------
        // Logarithm of the Lorentz factor between
        // the fluid and co-orbiting observer
        //-----------------------------------------

        loggam = log( gam ) ;
        loggam.std_spectral_base() ;

        //-------------------------------------------------
        // Velocity fields set to zero in external domains
        //-------------------------------------------------

        loggam.annule_domain(nzm1) ;
        wit_w.annule_domain(nzm1) ;
        u_euler.annule_domain(nzm1) ;

        loggam.set_dzpuis(0) ;

    }
    else {  // Rigid rotation

        gam = 1. ;
        gam.std_spectral_base() ;
        loggam = 0. ;
        wit_w.set_etat_zero() ;

    }

    }   // End of Isotropic coordinates

    // The derived quantities are obsolete
    // -----------------------------------

    del_deriv() ;

}

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