binary_orbit_xcts.C
/*
* Method of class Binary_xcts to compute the orbital angular velocity
* {\tt omega} and the position of the rotation axis {\tt x_axe}.
* (See file binary_xcts.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 binary_orbit_xcts_C[] = "$Header: /cvsroot/Lorene/C++/Source/Binary_xcts/binary_orbit_xcts.C,v 1.14 2014/10/24 14:10:24 j_novak Exp $" ;
/*
* $Id: binary_orbit_xcts.C,v 1.14 2014/10/24 14:10:24 j_novak Exp $
* $Log: binary_orbit_xcts.C,v $
* Revision 1.14 2014/10/24 14:10:24 j_novak
* Minor change to prevent weird error from g++-4.8...
*
* Revision 1.13 2014/10/13 08:52:45 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.12 2014/10/06 15:12:59 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.11 2011/03/30 13:14:27 m_bejger
* Psi and chi rewritten using auto and comp parts to improve the convergence (in all the remaining fields, not only logn)
*
* Revision 1.10 2011/03/28 17:13:37 m_bejger
* logn in dnulg stated using Psi1,2 and chi1,2
*
* Revision 1.9 2011/03/27 16:41:19 e_gourgoulhon
* -- Corrected sign of ny and dny for star no. 2
* -- Added output via new function save_profile for graphics
*
* Revision 1.8 2011/03/27 14:58:48 m_bejger
* dnulg by means of dsdx(); rearrangements to use primary variables
*
* Revision 1.7 2011/03/25 16:28:36 e_gourgoulhon
* Still in progress
*
* Revision 1.6 2010/12/09 10:41:20 m_bejger
* For testing; not sure if working properly
*
* Revision 1.5 2010/10/26 19:45:45 m_bejger
* Cleanup
*
* Revision 1.4 2010/07/16 16:27:19 m_bejger
* This version is basically a copy of the one used by Binaire (binaire_orbite.C)
*
* Revision 1.3 2010/06/17 14:15:41 m_bejger
* Using method get_Psi()
*
* Revision 1.2 2010/06/15 07:57:30 m_bejger
* Minor corrections
*
* Revision 1.1 2010/05/04 07:35:54 m_bejger
* Initial version
*
* $Header: /cvsroot/Lorene/C++/Source/Binary_xcts/binary_orbit_xcts.C,v 1.14 2014/10/24 14:10:24 j_novak Exp $
*
*/
// Headers C
#include <cmath>
// Headers Lorene
#include "binary_xcts.h"
#include "eos.h"
#include "param.h"
#include "utilitaires.h"
#include "unites.h"
#include "graphique.h"
namespace Lorene {
double fonc_binary_xcts_axe(double , const Param& ) ;
double fonc_binary_xcts_orbit(double , const Param& ) ;
//******************************************************************************
void Binary_xcts::orbit(double fact_omeg_min,
double fact_omeg_max,
double& xgg1,
double& xgg2) {
using namespace Unites ;
//-------------------------------------------------------------
// Evaluation of various quantities at the center of each star
//-------------------------------------------------------------
double dnulg[2], asn2[2], dasn2[2], ny[2], dny[2], npn[2], dnpn[2], xgg[2] ;
double nyso[2], dnyso[2], npnso2[2], dnpnso2[2], ori_x[2] ;
for (int i=0; i<2; i++) {
const Map& mp = et[i]->get_mp() ;
const Metric& flat = et[i]->get_flat() ;
//------------------------------------------------------------------
// Recasting Phi and chi to manifestly equal auto and comp part
// - more fortunate from the point of view of Omega computation
//------------------------------------------------------------------
Scalar chi = et[i]->get_chi_auto() + et[i]->get_chi_comp() + 1 ;
Scalar Psi = et[i]->get_Psi_auto() + et[i]->get_Psi_comp() + 1 ;
Scalar logn = log(chi) - log(Psi) ;
logn.std_spectral_base() ;
// Sign convention for shift (beta^i = - N^i)
Vector shift = - ( et[i]->get_beta() ) ;
shift.change_triad(et[i]->mp.get_bvect_cart()) ;
//------------------------------------------------------------------
// d/dX( log(N) + log(Gamma) )
// in the center of the star ---> dnulg[i]
//------------------------------------------------------------------
// Facteur de passage x --> X :
double factx ;
if (fabs(mp.get_rot_phi()) < 1.e-14) factx = 1. ;
else {
if (fabs(mp.get_rot_phi() - M_PI) < 1.e-14) {
factx = - 1. ;
} else {
cout << "Binary_xcts::orbit : unknown value of rot_phi !" << endl ;
abort() ;
}
}
Scalar tmp = logn + et[i]->get_loggam() ;
dnulg[i] = factx*tmp.dsdx().val_grid_point(0, 0, 0, 0) ;
// For graphical outputs:
Scalar tgraph = logn - log( (1. + et[i]->get_chi_auto()) / (1. + et[i]->get_Psi_auto()) ) ;
// tmp = log( (1. + et[i]->get_chi_comp()) / (1. + et[i]->get_Psi_comp()) ) ;
tgraph.std_spectral_base() ;
save_profile(tgraph, 0., 10., 0.5*M_PI, 0., "prof_logn.d") ;
save_profile(et[i]->get_loggam(), 0., 1.8, 0.5*M_PI, 0., "prof_loggam.d") ;
//------------------------------------------------------------------
// Psi^4/N^2 = in the center of the star ---> asn2[i]
//------------------------------------------------------------------
Scalar Psi6schi2 = pow(Psi, 6)/(chi % chi) ;
Psi6schi2.std_spectral_base() ;
asn2[i] = Psi6schi2.val_grid_point(0, 0, 0, 0) ;
//------------------------------------------------------------------
// d/dX(A^2/N^2) in the center of the star ---> dasn2[i]
//------------------------------------------------------------------
dasn2[i] = Psi6schi2.dsdx().val_grid_point(0, 0, 0, 0) ;
//------------------------------------------------------------------
// N^Y in the center of the star ---> ny[i]
//------------------------------------------------------------------
ny[i] = factx*shift(2).val_grid_point(0, 0, 0, 0) ;
nyso[i] = ny[i] / omega ;
//------------------------------------------------------------------
// dN^Y/dX in the center of the star ---> dny[i]
//------------------------------------------------------------------
dny[i] = shift(2).dsdx().val_grid_point(0, 0, 0, 0) ;
dnyso[i] = dny[i] / omega ;
//------------------------------------------------------------------
// (N^X)^2 + (N^Y)^2 + (N^Z)^2
// in the center of the star ---> npn[i]
//------------------------------------------------------------------
tmp = contract(shift, 0, shift.up_down(flat), 0) ;
npn[i] = tmp.val_grid_point(0, 0, 0, 0) ;
npnso2[i] = npn[i] / omega / omega ;
//------------------------------------------------------------------
// d/dX( (N^X)^2 + (N^Y)^2 + (N^Z)^2 )
// in the center of the star ---> dnpn[i]
//------------------------------------------------------------------
dnpn[i] = factx * tmp.dsdx().val_grid_point(0, 0, 0, 0) ;
dnpnso2[i] = dnpn[i] / omega / omega ;
cout << "Binary_xcts::orbit: central d(nu+log(Gam))/dX : "
<< dnulg[i] << endl ;
cout << "Binary_xcts::orbit: central A^2/N^2 : "
<< asn2[i] << endl ;
cout << "Binary_xcts::orbit: central d(A^2/N^2)/dX : "
<< dasn2[i] << endl ;
cout << "Binary_xcts::orbit: central N^Y : "
<< ny[i] << endl ;
cout << "Binary_xcts::orbit: central dN^Y/dX : "
<< dny[i] << endl ;
cout << "Binary_xcts::orbit: central N.N : "
<< npn[i] << endl ;
cout << "Binary_xcts::orbit: central d(N.N)/dX : "
<< dnpn[i] << endl ;
ori_x[i] = (et[i]->get_mp()).get_ori_x() ;
xgg[i] = factx * (et[i]->xa_barycenter() - ori_x[i]) ;
}
xgg1 = xgg[0] ;
xgg2 = xgg[1] ;
//---------------------------------
// axis of rotation
//---------------------------------
int relat = 1 ;
double ori_x1 = ori_x[0] ;
double ori_x2 = ori_x[1] ;
if ( et[0]->get_eos() == et[1]->get_eos() &&
fabs( et[0]->get_ent().val_grid_point(0,0,0,0) -
et[1]->get_ent().val_grid_point(0,0,0,0) ) < 1.e-14 ) {
x_axe = 0. ;
} else {
Param paraxe ;
paraxe.add_int(relat) ;
paraxe.add_double( ori_x1, 0) ;
paraxe.add_double( ori_x2, 1) ;
paraxe.add_double( dnulg[0], 2) ;
paraxe.add_double( dnulg[1], 3) ;
paraxe.add_double( asn2[0], 4) ;
paraxe.add_double( asn2[1], 5) ;
paraxe.add_double( dasn2[0], 6) ;
paraxe.add_double( dasn2[1], 7) ;
paraxe.add_double( nyso[0], 8) ;
paraxe.add_double( nyso[1], 9) ;
paraxe.add_double( dnyso[0], 10) ;
paraxe.add_double( dnyso[1], 11) ;
paraxe.add_double( npnso2[0], 12) ;
paraxe.add_double( npnso2[1], 13) ;
paraxe.add_double( dnpnso2[0], 14) ;
paraxe.add_double( dnpnso2[1], 15) ;
int nitmax_axe = 200 ;
int nit_axe ;
double precis_axe = 1.e-13 ;
x_axe = zerosec(fonc_binary_xcts_axe, paraxe, 0.9*ori_x1, 0.9*ori_x2,
precis_axe, nitmax_axe, nit_axe) ;
cout << "Binary_xcts::orbit : Number of iterations in zerosec for x_axe : "
<< nit_axe << endl ;
}
cout << "Binary_xcts::orbit: x_axe [km] : " << x_axe / km << endl ;
//-------------------------------------
// Calcul de la vitesse orbitale
//-------------------------------------
Param parf ;
parf.add_int(relat) ;
parf.add_double( ori_x1, 0) ;
parf.add_double( dnulg[0], 1) ;
parf.add_double( asn2[0], 2) ;
parf.add_double( dasn2[0], 3) ;
parf.add_double( ny[0], 4) ;
parf.add_double( dny[0], 5) ;
parf.add_double( npn[0], 6) ;
parf.add_double( dnpn[0], 7) ;
parf.add_double( x_axe, 8) ;
double omega1 = fact_omeg_min * omega ;
double omega2 = fact_omeg_max * omega ;
cout << "Binary_xcts::orbit: omega1, omega2 [rad/s] : "
<< omega1 * f_unit << " " << omega2 * f_unit << endl ;
// Search for the various zeros in the interval [omega1, omega2]
// ------------------------------------------------------------
int nsub = 50 ; // total number of subdivisions of the interval
Tbl* azer = 0x0 ;
Tbl* bzer = 0x0 ;
zero_list(fonc_binary_xcts_orbit, parf, omega1, omega2, nsub,
azer, bzer) ;
// Search for the zero closest to the previous value of omega
// ----------------------------------------------------------
double omeg_min, omeg_max ;
int nzer = azer->get_taille() ; // number of zeros found by zero_list
cout << "Binary_xcts:orbit : " << nzer <<
" zero(s) found in the interval [omega1, omega2]." << endl ;
cout << "omega, omega1, omega2 : " << omega << " " << omega1
<< " " << omega2 << endl ;
cout << "azer : " << *azer << endl ;
cout << "bzer : " << *bzer << endl ;
if (nzer == 0) {
cout <<
"Binary_xcts::orbit: WARNING : no zero detected in the interval"
<< endl << " [" << omega1 * f_unit << ", "
<< omega2 * f_unit << "] rad/s !" << endl ;
omeg_min = omega1 ;
omeg_max = omega2 ;
}
else {
double dist_min = fabs(omega2 - omega1) ;
int i_dist_min = -1 ;
for (int i=0; i<nzer; i++) {
// Distance of previous value of omega from the center of the
// interval [azer(i), bzer(i)]
double dist = fabs( omega - 0.5 * ( (*azer)(i) + (*bzer)(i) ) ) ;
if (dist < dist_min) {
dist_min = dist ;
i_dist_min = i ;
}
}
omeg_min = (*azer)(i_dist_min) ;
omeg_max = (*bzer)(i_dist_min) ;
}
delete azer ; // Tbl allocated by zero_list
delete bzer ; //
cout << "Binary_xcts::orbit : interval selected for the search of the zero : "
<< endl << " [" << omeg_min << ", " << omeg_max << "] = ["
<< omeg_min * f_unit << ", " << omeg_max * f_unit << "] rad/s " << endl ;
// Computation of the zero in the selected interval by the secant method
// ---------------------------------------------------------------------
int nitermax = 200 ;
int niter ;
double precis = 1.e-13 ;
omega = zerosec_b(fonc_binary_xcts_orbit, parf, omeg_min, omeg_max,
precis, nitermax, niter) ;
cout << "Binary_xcts::orbit : Number of iterations in zerosec for omega : "
<< niter << endl ;
cout << "Binary_xcts::orbit : omega [rad/s] : "
<< omega * f_unit << endl ;
}
//*************************************************
// Function used for search of the rotation axis
//*************************************************
double fonc_binary_xcts_axe(double x_rot, const Param& paraxe) {
int relat = paraxe.get_int() ;
double ori_x1 = paraxe.get_double(0) ;
double ori_x2 = paraxe.get_double(1) ;
double dnulg_1 = paraxe.get_double(2) ;
double dnulg_2 = paraxe.get_double(3) ;
double asn2_1 = paraxe.get_double(4) ;
double asn2_2 = paraxe.get_double(5) ;
double dasn2_1 = paraxe.get_double(6) ;
double dasn2_2 = paraxe.get_double(7) ;
double nyso_1 = paraxe.get_double(8) ;
double nyso_2 = paraxe.get_double(9) ;
double dnyso_1 = paraxe.get_double(10) ;
double dnyso_2 = paraxe.get_double(11) ;
double npnso2_1 = paraxe.get_double(12) ;
double npnso2_2 = paraxe.get_double(13) ;
double dnpnso2_1 = paraxe.get_double(14) ;
double dnpnso2_2 = paraxe.get_double(15) ;
double om2_star1 ;
double om2_star2 ;
double x1 = ori_x1 - x_rot ;
double x2 = ori_x2 - x_rot ;
if (relat == 1) {
double andan_1 = 0.5 * dasn2_1 + asn2_1 * dnulg_1 ;
double andan_2 = 0.5 * dasn2_2 + asn2_2 * dnulg_2 ;
double bpb_1 = x1 * x1 - 2. * nyso_1 * x1 + npnso2_1 ;
double bpb_2 = x2 * x2 - 2. * nyso_2 * x2 + npnso2_2 ;
double cpc_1 = 0.5 * dnpnso2_1 + x1 * (1. - dnyso_1) - nyso_1 ;
double cpc_2 = 0.5 * dnpnso2_2 + x2 * (1. - dnyso_2) - nyso_2 ;
om2_star1 = dnulg_1 / (andan_1 * bpb_1 + asn2_1 * cpc_1) ;
om2_star2 = dnulg_2 / (andan_2 * bpb_2 + asn2_2 * cpc_2) ;
}
else {
om2_star1 = dnulg_1 / x1 ;
om2_star2 = dnulg_2 / x2 ;
}
return om2_star1 - om2_star2 ;
}
//*****************************************************************************
// Fonction utilisee pour la recherche de omega par la methode de la secante
//*****************************************************************************
double fonc_binary_xcts_orbit(double om, const Param& parf) {
int relat = parf.get_int() ;
double xc = parf.get_double(0) ;
double dnulg = parf.get_double(1) ;
double asn2 = parf.get_double(2) ;
double dasn2 = parf.get_double(3) ;
double ny = parf.get_double(4) ;
double dny = parf.get_double(5) ;
double npn = parf.get_double(6) ;
double dnpn = parf.get_double(7) ;
double x_axe = parf.get_double(8) ;
double xx = xc - x_axe ;
double om2 = om*om ;
double dphi_cent ;
if (relat == 1) {
double bpb = om2 * xx*xx - 2*om * ny * xx + npn ;
dphi_cent = ( asn2* ( om* (ny + xx*dny) - om2*xx - 0.5*dnpn )
- 0.5*bpb* dasn2 )
/ ( 1 - asn2 * bpb ) ;
}
else {
dphi_cent = - om2*xx ;
}
return dnulg + dphi_cent ;
}
}
Lorene::Binary_xcts::x_axe
double x_axe
Absolute X coordinate of the rotation axis.
Definition binary_xcts.h:84
Lorene::Binary_xcts::orbit
void orbit(double fact_omeg_min, double fact_omeg_max, double &xgg1, double &xgg2)
Computes the orbital angular velocity omega and the position of the rotation axis x_axe.
Definition binary_orbit_xcts.C:97
Lorene::Binary_xcts::et
Star_bin_xcts * et[2]
Array of the two stars (to perform loops on the stars): et[0] contains the address of star1 and et[1]...
Definition binary_xcts.h:75
Lorene::Binary_xcts::omega
double omega
Angular velocity with respect to an asymptotically inertial observer.
Definition binary_xcts.h:80
Lorene::Metric
Metric for tensor calculation.
Definition metric.h:90
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::get_int
const int & get_int(int position=0) const
Returns the reference of a int stored in the list.
Definition param.C:292
Lorene::Param::get_double
const double & get_double(int position=0) const
Returns the reference of a double stored in the list.
Definition param.C:361
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::val_grid_point
double val_grid_point(int l, int k, int j, int i) const
Returns the value of the field at a specified grid point.
Definition scalar.h:637
Lorene::Scalar::dsdx
const Scalar & dsdx() const
Returns of *this , where .
Definition scalar_deriv.C:266
Lorene::Tbl
Basic array class.
Definition tbl.h:161
Lorene::Tbl::get_taille
int get_taille() const
Gives the total size (ie dim.taille).
Definition tbl.h:397
Lorene::Vector
Tensor field of valence 1.
Definition vector.h:188
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::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Lorene::log
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
Lorene::zero_list
void zero_list(double(*f)(double, const Param &), const Param &par, double xmin, double xmax, int nsub, Tbl *&az, Tbl *&bz)
Locates approximatively all the zeros of a function in a given interval.
Definition zero_list.C:57
Lorene::zerosec_b
double zerosec_b(double(*f)(double, const Param &), const Param &par, double a, double b, double precis, int nitermax, int &niter)
Finding the zero a function on a bounded domain.
Definition zerosec_borne.C:68
Lorene::zerosec
double zerosec(double(*f)(double, const Param &), const Param &par, double a, double b, double precis, int nitermax, int &niter, bool abort=true)
Finding the zero a function.
Definition zerosec.C:89
Lorene::Tensor::up_down
Tensor up_down(const Metric &gam) const
Computes a new tensor by raising or lowering all the indices of *this .
Definition tensor_calculus.C:305
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
Lorene::Map
Map(const Mg3d &)
Constructor from a multi-domain 3D grid.
Definition map.C:139
Unites
Standard units of space, time and mass.