1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
|
/*
* Method of class Binary_xcts to set some analytical form
* to the shift vector (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_anashift_xcts_C[] = "$Header: /cvsroot/Lorene/C++/Source/Binary_xcts/binary_anashift_xcts.C,v 1.3 2014/10/13 08:52:45 j_novak Exp $" ;
/*
* $Id: binary_anashift_xcts.C,v 1.3 2014/10/13 08:52:45 j_novak Exp $
* $Log: binary_anashift_xcts.C,v $
* Revision 1.3 2014/10/13 08:52:45 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.2 2010/06/15 07:58:32 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_anashift_xcts.C,v 1.3 2014/10/13 08:52:45 j_novak Exp $
*
*/
// Headers C
#include "math.h"
// Headers Lorene
#include "binary_xcts.h"
#include "tenseur.h"
#include "unites.h"
namespace Lorene {
void Binary_xcts::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 + mass_ratio)
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() ;
}
}
}
|
