LORENE
star_bin_vel_pot_xcts.C
1 /*
2  * Method of class Star_bin_xcts to compute the velocity scalar
3  * potential $\psi$ by solving the continuity equation
4  * (see file star.h for documentation).
5  */
6 
7 /*
8  * Copyright (c) 2010 Michal Bejger
9  *
10  * This file is part of LORENE.
11  *
12  * LORENE is free software; you can redistribute it and/or modify
13  * it under the terms of the GNU General Public License version 2
14  * as published by the Free Software Foundation.
15  *
16  * LORENE is distributed in the hope that it will be useful,
17  * but WITHOUT ANY WARRANTY; without even the implied warranty of
18  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19  * GNU General Public License for more details.
20  *
21  * You should have received a copy of the GNU General Public License
22  * along with LORENE; if not, write to the Free Software
23  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24  *
25  */
26 
27 
28 
29 /*
30  * $Id: star_bin_vel_pot_xcts.C,v 1.8 2016/12/05 16:18:15 j_novak Exp $
31  * $Log: star_bin_vel_pot_xcts.C,v $
32  * Revision 1.8 2016/12/05 16:18:15 j_novak
33  * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
34  *
35  * Revision 1.7 2014/10/13 08:53:39 j_novak
36  * Lorene classes and functions now belong to the namespace Lorene.
37  *
38  * Revision 1.6 2010/12/09 10:47:31 m_bejger
39  * Small changes, definition of lnPsi2N
40  *
41  * Revision 1.5 2010/10/26 20:01:06 m_bejger
42  * Cleanup
43  *
44  * Revision 1.4 2010/10/18 20:56:15 m_bejger
45  * Generalization for many domains in the star: buggy
46  *
47  * Revision 1.3 2010/06/17 15:07:10 m_bejger
48  * Psi4, lnPsi2N corrected
49  *
50  * Revision 1.2 2010/06/15 08:05:55 m_bejger
51  * Various fields were lacking bases
52  *
53  * Revision 1.1 2010/05/04 07:51:05 m_bejger
54  * Initial version
55  *
56  * $Header: /cvsroot/Lorene/C++/Source/Star/star_bin_vel_pot_xcts.C,v 1.8 2016/12/05 16:18:15 j_novak Exp $
57  *
58  */
59 
60 // Headers Lorene
61 #include "star.h"
62 #include "eos.h"
63 #include "param.h"
64 #include "cmp.h"
65 #include "tenseur.h"
66 #include "graphique.h"
67 #include "utilitaires.h"
68 
69 // Local prototype
70 namespace Lorene {
71 Cmp raccord_c1(const Cmp& uu, int l1) ;
72 
74  double precis,
75  double relax) {
76 
77  int nzm1 = mp.get_mg()->get_nzone() - 1 ;
78 
79  //----------------------------------
80  // Specific relativistic enthalpy ---> hhh
81  //----------------------------------
82 
83  Scalar hhh = exp(ent) ; // = 1 at the Newtonian limit
84  hhh.std_spectral_base() ;
85 
86  //------------------------------------------------------------------
87  // Computation of W^i = Psi^4 h Gamma_n B^i/N
88  // See Eq (62) from Gourgoulhon et al. (2001)
89  //------------------------------------------------------------------
90 
91  Vector www = hhh * gam_euler * psi4 * bsn ;
92  www.change_triad( mp.get_bvect_cart() ) ; // components on the mapping
93  // Cartesian basis
94 
95  //-------------------------------------------------
96  // Constant value of W^i at the center of the star
97  //-------------------------------------------------
98 
99  Vector v_orb(mp, CON, mp.get_bvect_cart()) ;
100  v_orb.set_etat_qcq() ;
101 
102  for (int i=1; i<=3; i++)
103  v_orb.set(i) = www(i).val_grid_point(0, 0, 0, 0) ;
104 
105  v_orb.set_triad( *(www.get_triad()) ) ;
106  v_orb.std_spectral_base() ;
107 
108  //-------------------------------------------------
109  // Source and coefficients a, b for poisson_compact
110  // (independent from psi0)
111  //-------------------------------------------------
112 
113  Scalar dndh_log(mp) ;
114  dndh_log = 0 ;
115 
116  for (int l=0; l<nzet; l++) {
117 
118  Param par ; // Paramater for multi-domain equation of state
119  par.add_int(l) ;
120 
121  dndh_log = dndh_log + eos.der_nbar_ent(ent, 1, l, &par) ;
122 
123  }
124 
125  // In order to avoid any division by zero in the computation of zeta_h
126  // the value of dndh_log is set to 1 in the external domains:
127 
128  for (int l=nzet; l <= nzm1; l++)
129  dndh_log.set_domain(l) = 1 ;
130 
131  Scalar zeta_h( ent / dndh_log ) ;
132  zeta_h.std_spectral_base() ;
133 
134  Scalar Psichi = Psi % chi ;
135  Psichi.std_spectral_base() ;
136 
137  Scalar lnPsi2N = log(Psichi) ;
138  lnPsi2N.std_spectral_base() ;
139 
140  Metric_flat flat_spher (mp.flat_met_spher()) ;
141 
142  Vector bb = (1 - zeta_h) * ent.derive_con(flat_spher)
143  + zeta_h * lnPsi2N.derive_con(flat_spher) ;
144 
145  Scalar entmb = ent - lnPsi2N ;
146 
148  v_orb.change_triad(mp.get_bvect_cart()) ;
149 
150  // Eq. 63 of Gourgoulhon et al. (2001)
151  Scalar source = contract(www - v_orb, 0, ent.derive_cov(flat), 0)
152  + zeta_h * ( contract(v_orb, 0, entmb.derive_cov(flat), 0)
153  + contract(www/gam_euler, 0, gam_euler.derive_cov(flat), 0) ) ;
154 
155  /*
156  des_meridian(zeta_h,0., 4., "zeta_h", 10) ;
157  arrete() ;
158  des_meridian(bb(1),0., 4., "bb(1)", 10) ;
159  arrete() ;
160  des_meridian(bb(2),0., 4., "bb(2)", 10) ;
161  arrete() ;
162  des_meridian(bb(3),0., 4., "bb(3)", 10) ;
163  arrete() ;
164  des_meridian(psi0,0., 4., "psi0", 10) ;
165  arrete() ;
166  des_meridian(source,0., 4., "source", 10) ;
167  arrete() ;
168  */
169 
170  source.annule(nzet, nzm1) ;
171 
172  //---------------------------------------------------
173  // Resolution by means of Map_radial::poisson_compact
174  //---------------------------------------------------
175 
176  Param par ;
177  int niter ;
178  par.add_int(mermax) ;
179  par.add_double(precis, 0) ;
180  par.add_double(relax, 1) ;
181  par.add_int_mod(niter) ;
182 
183  if (psi0.get_etat() == ETATZERO) psi0 = 0 ;
184 
185  Cmp source_cmp (source) ;
186  Cmp zeta_h_cmp (zeta_h) ;
187  Cmp psi0_cmp (psi0) ;
188 
189  Tenseur bb_cmp(mp, 1, CON, mp.get_bvect_spher()) ;
190  bb_cmp.set_etat_qcq() ;
191  Cmp bb_cmp1 (bb(1)) ;
192  Cmp bb_cmp2 (bb(2)) ;
193  Cmp bb_cmp3 (bb(3)) ;
194  bb_cmp.set(0) = bb_cmp1 ;
195  bb_cmp.set(1) = bb_cmp2 ;
196  bb_cmp.set(2) = bb_cmp3 ;
197 
198  source_cmp.va.ylm() ;
199 
200  //cout << "psiO prevu" << endl << norme(psi0) << endl ;
201 
202  mp.poisson_compact(nzet, source_cmp, zeta_h_cmp, bb_cmp, par, psi0_cmp ) ;
203 
204  psi0 = psi0_cmp ;
205 
206  cout << "psiO apres" << endl << norme(psi0) << endl ;
207 
208  //---------------------------------------------------
209  // Check of the solution
210  //---------------------------------------------------
211 
212  Scalar bb_dpsi0 = contract(bb, 0, psi0.derive_cov(flat_spher), 0) ;
213 
214  Scalar oper = zeta_h * psi0.laplacian() + bb_dpsi0 ;
215 
216  source.set_spectral_va().ylm_i() ;
217 
218  cout << "Check of the resolution of the continuity equation : " << endl ;
219  Tbl terr = diffrel(oper, source) ;
220  double erreur = 0 ;
221  for (int l=0; l<nzet; l++) {
222  double err = terr(l) ;
223  cout << " domain " << l << " : norme(source) : " << norme(source)(l)
224  << " relative error : " << err << endl ;
225  if (err > erreur) erreur = err ;
226  }
227 
228  //--------------------------------
229  // Computation of grad(psi)
230  //--------------------------------
231 
232  d_psi.set_etat_qcq() ;
233 
234  for (int i=1; i<=3; i++)
235  d_psi.set(i) = (psi0.derive_cov(flat))(i) + v_orb(i) ;
236 
238 
239  // C^1 continuation of d_psi outside the star
240  // (to ensure a smooth enthalpy field accross the stellar surface)
241  // ----------------------------------------------------------------
242 
243  d_psi.annule(nzet, nzm1) ;
244 
245  for (int i=1; i<=3; i++)
246  d_psi.set(i) = raccord_c1(d_psi(i), nzet) ;
247 
248  return erreur ;
249 }
250 }
Scalar chi
Total function .
Definition: star.h:1155
Vector bsn
3-vector shift, divided by N, of the rotating coordinates, .
Definition: star.h:1126
Cmp log(const Cmp &)
Neperian logarithm.
Definition: cmp_math.C:299
virtual void set_etat_qcq()
Sets the logical state of all components to ETATQCQ (ordinary state).
Definition: tensor.C:490
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:446
Cmp exp(const Cmp &)
Exponential.
Definition: cmp_math.C:273
void add_int(const int &n, int position=0)
Adds the address of a new int to the list.
Definition: param.C:249
Map & mp
Mapping associated with the star.
Definition: star.h:180
void ylm_i()
Inverse of ylm()
Definition: valeur_ylm_i.C:134
Cmp der_nbar_ent(const Cmp &ent, int nzet, int l_min=0, Param *par=0x0) const
Computes the logarithmic derivative from the log-enthalpy and extra parameters.
Definition: eos.C:431
virtual void annule(int l_min, int l_max)
Sets the Scalar to zero in several domains.
Definition: scalar.C:397
const Base_vect_spher & get_bvect_spher() const
Returns the orthonormal vectorial basis associated with the coordinates of the mapping.
Definition: map.h:801
Lorene prototypes.
Definition: app_hor.h:67
const Eos & eos
Equation of state of the stellar matter.
Definition: star.h:185
void ylm()
Computes the coefficients of *this.
Definition: valeur_ylm.C:141
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:783
const Scalar & laplacian(int ced_mult_r=4) const
Returns the Laplacian of *this.
Definition: scalar_deriv.C:436
Flat metric for tensor calculation.
Definition: metric.h:261
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:393
virtual void poisson_compact(const Cmp &source, const Cmp &aa, const Tenseur &bb, const Param &par, Cmp &psi) const =0
Resolution of the elliptic equation in the case where the stellar interior is covered by a single do...
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field. ...
Definition: scalar.C:790
virtual void change_triad(const Base_vect &)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
int get_etat() const
Returns the logical state ETATNONDEF (undefined), ETATZERO (null) or ETATQCQ (ordinary).
Definition: scalar.h:560
Scalar ent
Log-enthalpy.
Definition: star.h:190
const Vector & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of *this with respect to some metric , by raising the index of...
Definition: scalar_deriv.C:402
Tensor field of valence 1.
Definition: vector.h:188
Tbl & set_domain(int l)
Read/write of the value in a given domain.
Definition: scalar.h:621
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition: cmp_math.C:507
int nzet
Number of domains of *mp occupied by the star.
Definition: star.h:183
Scalar gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition: star.h:204
Tbl norme(const Cmp &)
Sums of the absolute values of all the values of the Cmp in each domain.
Definition: cmp_math.C:484
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition: tensor.h:879
Vector d_psi
Gradient of (in the irrotational case) (Spherical components with respect to the mapping of the star...
Definition: star.h:1109
Parameter storage.
Definition: param.h:125
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:465
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Scalar psi4
Conformal factor .
Definition: star.h:1158
Scalar psi0
Scalar potential of the non-translational part of fluid 4-velocity (in the irrotational case) ...
Definition: star.h:1104
Metric_flat flat
Flat metric defined on the mapping (Spherical components with respect to the mapping of the star) ...
Definition: star.h:1177
Scalar Psi
Total conformal factor .
Definition: star.h:1152
Tbl & set(int l)
Read/write of the value in a given domain.
Definition: cmp.h:724
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping, i.e.
Definition: map.h:809
void add_double(const double &x, int position=0)
Adds the the address of a new double to the list.
Definition: param.C:318
void set_triad(const Base_vect &new_triad)
Assigns a new vectorial basis (triad) of decomposition.
Definition: tensor.C:528
Basic array class.
Definition: tbl.h:164
Valeur & set_spectral_va()
Returns va (read/write version)
Definition: scalar.h:610
Scalar & set(int)
Read/write access to a component.
Definition: vector.C:302
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tenseur.C:652
double velocity_potential(int mermax, double precis, double relax)
Computes the non-translational part of the velocity scalar potential by solving the continuity equat...
const Vector & derive_cov(const Metric &gam) const
Returns the gradient (1-form = covariant vector) of *this
Definition: scalar_deriv.C:390
virtual void annule(int l_min, int l_max)
Sets the Tensor to zero in several domains.
Definition: tensor.C:680
Valeur va
The numerical value of the Cmp.
Definition: cmp.h:464
const Metric_flat & flat_met_spher() const
Returns the flat metric associated with the spherical coordinates and with components expressed in th...
Definition: map.C:324
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition: tenseur.h:304
void add_int_mod(int &n, int position=0)
Adds the address of a new modifiable int to the list.
Definition: param.C:388