LORENE
et_bin_equilibrium.C
1 /*
2  * Method of class Etoile_bin to compute an equilibrium configuration
3  *
4  * (see file etoile.h for documentation).
5  *
6  */
7 
8 /*
9  * Copyright (c) 2000-2001 Eric Gourgoulhon
10  * Copyright (c) 2000-2001 Keisuke Taniguchi
11  *
12  * This file is part of LORENE.
13  *
14  * LORENE is free software; you can redistribute it and/or modify
15  * it under the terms of the GNU General Public License as published by
16  * the Free Software Foundation; either version 2 of the License, or
17  * (at your option) any later version.
18  *
19  * LORENE is distributed in the hope that it will be useful,
20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22  * GNU General Public License for more details.
23  *
24  * You should have received a copy of the GNU General Public License
25  * along with LORENE; if not, write to the Free Software
26  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
27  *
28  */
29 
30 
31 char et_bin_equilibrium_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_equilibrium.C,v 1.14 2014/10/13 08:52:55 j_novak Exp $" ;
32 
33 /*
34  * $Id: et_bin_equilibrium.C,v 1.14 2014/10/13 08:52:55 j_novak Exp $
35  * $Log: et_bin_equilibrium.C,v $
36  * Revision 1.14 2014/10/13 08:52:55 j_novak
37  * Lorene classes and functions now belong to the namespace Lorene.
38  *
39  * Revision 1.13 2014/10/06 15:13:08 j_novak
40  * Modified #include directives to use c++ syntax.
41  *
42  * Revision 1.12 2009/06/15 09:25:18 k_taniguchi
43  * Improved the rescaling of the domains.
44  *
45  * Revision 1.11 2008/11/14 13:48:06 e_gourgoulhon
46  * Added parameter pent_limit to force the enthalpy values at the
47  * boundaries between the domains, in case of more than one domain inside
48  * the star.
49  *
50  * Revision 1.10 2004/09/28 15:49:23 f_limousin
51  * Improve the rescaling of the domains for nzone = 4 and nzone = 5.
52  *
53  * Revision 1.9 2004/05/13 08:47:01 f_limousin
54  * Decomment the procedure resize.
55  *
56  * Revision 1.8 2004/05/10 10:15:57 f_limousin
57  * Change to avoid a warning in the compilation of Lorene
58  *
59  * Revision 1.7 2004/05/07 12:36:34 f_limousin
60  * Add new member ssjm1_psi in order to have only one function
61  * equilibrium (the same for strange stars and neutron stars)
62  *
63  * Revision 1.6 2004/05/07 08:32:44 k_taniguchi
64  * Introduction of the version without ssjm1_psi.
65  *
66  * Revision 1.5 2004/04/19 11:06:36 f_limousin
67  * Differents call of Etoile_bin::velocity_potential depending on
68  * the equation of state.
69  *
70  * Revision 1.4 2004/03/25 10:29:04 j_novak
71  * All LORENE's units are now defined in the namespace Unites (in file unites.h).
72  *
73  * Revision 1.3 2003/01/17 13:31:13 f_limousin
74  * Add comments
75  *
76  * Revision 1.2 2002/12/10 13:28:03 k_taniguchi
77  * Change the multiplication "*" to "%"
78  * and flat_scalar_prod to flat_scalar_prod_desal.
79  *
80  * Revision 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
81  * LORENE
82  *
83  * Revision 2.23 2001/08/07 09:43:02 keisuke
84  * Change of the method to set the longest radius of a star
85  * on the first domain.
86  * Addition of a new argument in Etoile_bin::equilibrium : Tbl fact.
87  *
88  * Revision 2.22 2001/06/22 08:54:19 keisuke
89  * Set the inner values of the second domain of ent
90  * by using the outer ones of the first domain.
91  *
92  * Revision 2.21 2001/06/18 12:50:49 keisuke
93  * Addition of the filter for the source of shift vector.
94  *
95  * Revision 2.20 2001/05/17 12:18:47 keisuke
96  * Change of the method to calculate chi from setting position in map
97  * to val_point.
98  *
99  * Revision 2.19 2001/01/16 17:01:53 keisuke
100  * Change the method to set the values on the surface.
101  *
102  * Revision 2.18 2001/01/10 16:42:51 keisuke
103  * Set the inner values of the second domain of logn_auto
104  * by using the outer ones of the first domain.
105  *
106  * Revision 2.17 2000/12/22 13:08:04 eric
107  * precis_adapt = 1e-14 au lieu de 1e-15.
108  * Sorties graphiques commentees.
109  *
110  * Revision 2.16 2000/12/20 10:32:44 eric
111  * Changement important : nz_search = nzet ---> nz_search = nzet + 1
112  *
113  * Revision 2.15 2000/10/23 14:02:16 eric
114  * Modif de Map_et::adapt: on y rentre desormais avec nz_search
115  * (dans le cas present nz_search = nzet).
116  *
117  * Revision 2.14 2000/09/28 12:19:36 keisuke
118  * Construct logn_auto_regu from logn_auto.
119  * This procedure is needed for et_bin_upmetr.C.
120  *
121  * Revision 2.13 2000/05/25 13:48:12 eric
122  * Ajout de l'argument thres_adapt: l'adaptation du mapping n'est
123  * plus effectuee si dH/dr_eq passe sous un certain seuil.
124  *
125  * Revision 2.12 2000/05/25 12:58:31 eric
126  * Modifs classe Param: les int et double sont desormais passes par leurs
127  * adresses.
128  *
129  * Revision 2.11 2000/03/29 11:57:38 eric
130  * *** empty log message ***
131  *
132  * Revision 2.10 2000/03/29 11:53:41 eric
133  * Modif affichage
134  *
135  * Revision 2.9 2000/03/22 16:37:29 eric
136  * Calcul des erreurs dans la resolution des equations de Poisson
137  * et sortie de ces erreurs dans le Tbl diff.
138  *
139  * Revision 2.8 2000/03/22 12:56:18 eric
140  * Nouveau prototype d'Etoile_bin::equilibrium : diff_ent est remplace
141  * par le Tbl diff.
142  *
143  * Revision 2.7 2000/03/10 15:47:19 eric
144  * On appel desormais poisson_vect avec dzpuis = 4.
145  *
146  * Revision 2.6 2000/03/07 16:52:15 eric
147  * Modifs manipulations source pour le shift.
148  *
149  * Revision 2.5 2000/03/07 08:32:47 eric
150  * Appel de Map_radial::reevaluate_sym (pour tenir compte de la symetrie
151  * / plan y=0).
152  *
153  * Revision 2.4 2000/02/17 19:56:57 eric
154  * L'appel de Map_radial::reevaluate pour ent est fait sur nzet+1 zone
155  * et non plus nzet.
156  *
157  * Revision 2.2 2000/02/16 17:12:03 eric
158  * Premiere version avec les equations du champ gravitationnel.
159  *
160  * Revision 2.1 2000/02/15 15:59:52 eric
161  * *** empty log message ***
162  *
163  * Revision 2.0 2000/02/15 15:40:42 eric
164  * *** empty log message ***
165  *
166  *
167  * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_equilibrium.C,v 1.14 2014/10/13 08:52:55 j_novak Exp $
168  *
169  */
170 
171 // Headers C
172 #include <cmath>
173 
174 // Headers Lorene
175 #include "etoile.h"
176 #include "param.h"
177 #include "eos.h"
178 
179 #include "graphique.h"
180 #include "utilitaires.h"
181 #include "unites.h"
182 
183 namespace Lorene {
184 void Etoile_bin::equilibrium(double ent_c,
185  int mermax, int mermax_poisson,
186  double relax_poisson, int mermax_potvit,
187  double relax_potvit, double thres_adapt,
188  const Tbl& fact_resize, Tbl& diff, const Tbl* pent_limit ) {
189 
190 
191  // Fundamental constants and units
192  // -------------------------------
193 
194  using namespace Unites ;
195 
196  // Initializations
197  // ---------------
198 
199  const Mg3d* mg = mp.get_mg() ;
200  int nz = mg->get_nzone() ; // total number of domains
201 
202  // The following is required to initialize mp_prev as a Map_et:
203  Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
204 
205  // Domain and radial indices of points at the surface of the star:
206  int l_b = nzet - 1 ;
207  int i_b = mg->get_nr(l_b) - 1 ;
208  int k_b ;
209  int j_b ;
210 
211  // Value of the enthalpy defining the surface of the star
212  double ent_b = 0 ;
213 
214  // Error indicators
215  // ----------------
216 
217  double& diff_ent = diff.set(0) ;
218  double& diff_vel_pot = diff.set(1) ;
219  double& diff_logn = diff.set(2) ;
220  double& diff_beta = diff.set(3) ;
221  double& diff_shift_x = diff.set(4) ;
222  double& diff_shift_y = diff.set(5) ;
223  double& diff_shift_z = diff.set(6) ;
224 
225  // Parameters for the function Map_et::adapt
226  // -----------------------------------------
227 
228  Param par_adapt ;
229  int nitermax = 100 ;
230  int niter ;
231  int adapt_flag = 1 ; // 1 = performs the full computation,
232  // 0 = performs only the rescaling by
233  // the factor alpha_r
234  //## int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
235  int nz_search = nzet ; // Number of domains for searching the enthalpy
236  // isosurfaces
237 
238  double precis_secant = 1.e-14 ;
239  double alpha_r ;
240  double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
241 
242  par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
243  // locate zeros by the secant method
244  par_adapt.add_int(nzet, 1) ; // number of domains where the adjustment
245  // to the isosurfaces of ent is to be
246  // performed
247  par_adapt.add_int(nz_search, 2) ; // number of domains to search for
248  // the enthalpy isosurface
249  par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
250  // 0 = performs only the rescaling by
251  // the factor alpha_r
252  par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
253  // (theta_*, phi_*)
254  par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
255  // (theta_*, phi_*)
256 
257  par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
258  // the secant method
259 
260  par_adapt.add_double(precis_secant, 0) ; // required absolute precision in
261  // the determination of zeros by
262  // the secant method
263  par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
264 
265  par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
266  // distances will be multiplied
267 
268  // Enthalpy values for the adaptation
269  Tbl ent_limit(nzet) ;
270  if (pent_limit != 0x0) ent_limit = *pent_limit ;
271 
272  par_adapt.add_tbl(ent_limit, 0) ; // array of values of the field ent
273  // to define the isosurfaces.
274 
275  // Parameters for the function Map_et::poisson for logn_auto
276  // ---------------------------------------------------------
277 
278  double precis_poisson = 1.e-16 ;
279 
280  Param par_poisson1 ;
281 
282  par_poisson1.add_int(mermax_poisson, 0) ; // maximum number of iterations
283  par_poisson1.add_double(relax_poisson, 0) ; // relaxation parameter
284  par_poisson1.add_double(precis_poisson, 1) ; // required precision
285  par_poisson1.add_int_mod(niter, 0) ; // number of iterations actually used
286  par_poisson1.add_cmp_mod( ssjm1_logn ) ;
287 
288  // Parameters for the function Map_et::poisson for beta_auto
289  // ---------------------------------------------------------
290 
291  Param par_poisson2 ;
292 
293  par_poisson2.add_int(mermax_poisson, 0) ; // maximum number of iterations
294  par_poisson2.add_double(relax_poisson, 0) ; // relaxation parameter
295  par_poisson2.add_double(precis_poisson, 1) ; // required precision
296  par_poisson2.add_int_mod(niter, 0) ; // number of iterations actually used
297  par_poisson2.add_cmp_mod( ssjm1_beta ) ;
298 
299 
300  // Parameters for the function Tenseur::poisson_vect
301  // -------------------------------------------------
302 
303  Param par_poisson_vect ;
304 
305  par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of iterations
306  par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
307  par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
308  par_poisson_vect.add_cmp_mod( ssjm1_khi ) ;
309  par_poisson_vect.add_tenseur_mod( ssjm1_wshift ) ;
310  par_poisson_vect.add_int_mod(niter, 0) ;
311 
312 
313  // External potential
314  // See Eq (99) from Gourgoulhon et al. (2001)
315  // -----------------------------------------
316 
317  Tenseur pot_ext = logn_comp + pot_centri + loggam ;
318 //##
319 // des_coupe_z(pot_ext(), 0., 1, "pot_ext", &(ent()) ) ;
320 //##
321 
322  Tenseur ent_jm1 = ent ; // Enthalpy at previous step
323 
324  Tenseur source(mp) ; // source term in the equation for logn_auto
325  // and beta_auto
326 
327  Tenseur source_shift(mp, 1, CON, ref_triad) ; // source term in the equation
328  // for shift_auto
329 
330  //=========================================================================
331  // Start of iteration
332  //=========================================================================
333 
334  for(int mer=0 ; mer<mermax ; mer++ ) {
335 
336  cout << "-----------------------------------------------" << endl ;
337  cout << "step: " << mer << endl ;
338  cout << "diff_ent = " << diff_ent << endl ;
339 
340  //-----------------------------------------------------
341  // Resolution of the elliptic equation for the velocity
342  // scalar potential
343  //-----------------------------------------------------
344 
345  if (irrotational) {
346  diff_vel_pot = velocity_potential(mermax_potvit,
347  precis_poisson, relax_potvit) ;
348 
349  }
350 
351  //-----------------------------------------------------
352  // Computation of the new radial scale
353  //-----------------------------------------------------
354 
355  // alpha_r (r = alpha_r r') is determined so that the enthalpy
356  // takes the requested value ent_b at the stellar surface
357 
358  // Values at the center of the star:
359  double logn_auto_c = logn_auto()(0, 0, 0, 0) ;
360  double pot_ext_c = pot_ext()(0, 0, 0, 0) ;
361 
362  // Search for the reference point (theta_*, phi_*) [notation of
363  // Bonazzola, Gourgoulhon & Marck PRD 58, 104020 (1998)]
364  // at the surface of the star
365  // ------------------------------------------------------------
366  double alpha_r2 = 0 ;
367  for (int k=0; k<mg->get_np(l_b); k++) {
368  for (int j=0; j<mg->get_nt(l_b); j++) {
369 
370  double pot_ext_b = pot_ext()(l_b, k, j, i_b) ;
371  double logn_auto_b = logn_auto()(l_b, k, j, i_b) ;
372 
373 
374  // See Eq (100) from Gourgoulhon et al. (2001)
375  double alpha_r2_jk = ( ent_c - ent_b + pot_ext_c - pot_ext_b) /
376  ( logn_auto_b - logn_auto_c ) ;
377 
378 // cout << "k, j, alpha_r2_jk : " << k << " " << j << " "
379 // << alpha_r2_jk << endl ;
380 
381  if (alpha_r2_jk > alpha_r2) {
382  alpha_r2 = alpha_r2_jk ;
383  k_b = k ;
384  j_b = j ;
385  }
386 
387  }
388  }
389 
390  alpha_r = sqrt(alpha_r2) ;
391 
392  cout << "k_b, j_b, alpha_r: " << k_b << " " << j_b << " "
393  << alpha_r << endl ;
394 
395  // New value of logn_auto
396  // ----------------------
397 
398  logn_auto = alpha_r2 * logn_auto ;
399  logn_auto_regu = alpha_r2 * logn_auto_regu ;
400  logn_auto_c = logn_auto()(0, 0, 0, 0) ;
401 
402 
403  //------------------------------------------------------------
404  // Change the values of the inner points of the second domain
405  // by those of the outer points of the first domain
406  //------------------------------------------------------------
407 
408  (logn_auto().va).smooth(nzet, (logn_auto.set()).va) ;
409 
410 
411  //------------------------------------------
412  // First integral --> enthalpy in all space
413  // See Eq (98) from Gourgoulhon et al. (2001)
414  //-------------------------------------------
415 
416  ent = (ent_c + logn_auto_c + pot_ext_c) - logn_auto - pot_ext ;
417 
418  (ent().va).smooth(nzet, (ent.set()).va) ;
419 
420  //----------------------------------------------------
421  // Adaptation of the mapping to the new enthalpy field
422  //----------------------------------------------------
423 
424  // Shall the adaptation be performed (cusp) ?
425  // ------------------------------------------
426 
427  double dent_eq = ent().dsdr().val_point(ray_eq(),M_PI/2.,0.) ;
428  double dent_pole = ent().dsdr().val_point(ray_pole(),0.,0.) ;
429  double rap_dent = fabs( dent_eq / dent_pole ) ;
430  cout << "| dH/dr_eq / dH/dr_pole | = " << rap_dent << endl ;
431 
432  if ( rap_dent < thres_adapt ) {
433  adapt_flag = 0 ; // No adaptation of the mapping
434  cout << "******* FROZEN MAPPING *********" << endl ;
435  }
436  else{
437  adapt_flag = 1 ; // The adaptation of the mapping is to be
438  // performed
439  }
440 
441 
442  if (pent_limit == 0x0) {
443  ent_limit.set_etat_qcq() ;
444  for (int l=0; l<nzet; l++) { // loop on domains inside the star
445  ent_limit.set(l) = ent()(l, k_b, j_b, i_b) ;
446  }
447  ent_limit.set(nzet-1) = ent_b ;
448  }
449 
450  Map_et mp_prev = mp_et ;
451 
452 //## cout << "Enthalpy field at the outer boundary of domain 0 : "
453 // << endl ;
454 // for (int k=0; k<mg->get_np(0); k++) {
455 // cout << "k = " << k << " : " ;
456 // for (int j=0; j<mg->get_nt(0); j++) {
457 // cout << " " << ent()(0, k, j, mg->get_nr(0)-1) ;
458 // }
459 // cout << endl ;
460 // }
461 // cout << "Enthalpy field at the inner boundary of domain 1 : "
462 // << endl ;
463 // for (int k=0; k<mg->get_np(1); k++) {
464 // cout << "k = " << k << " : " ;
465 // for (int j=0; j<mg->get_nt(1); j++) {
466 // cout << " " << ent()(1, k, j, 0) ;
467 // }
468 // cout << endl ;
469 // }
470 // cout << "Difference enthalpy field boundary between domains 0 and 1: "
471 // << endl ;
472 // for (int k=0; k<mg->get_np(1); k++) {
473 // cout << "k = " << k << " : " ;
474 // for (int j=0; j<mg->get_nt(1); j++) {
475 // cout << " " << ent()(0, k, j, mg->get_nr(0)-1) -
476 // ent()(1, k, j, 0) ;
477 // }
478 // cout << endl ;
479 // }
480 
481 
482 //##
483 // des_coupe_z(gam_euler(), 0., 1, "gam_euler") ;
484 // des_coupe_z(loggam(), 0., 1, "loggam") ;
485 // des_coupe_y(loggam(), 0., 1, "loggam") ;
486 // des_coupe_z(d_psi(0), 0., 1, "d_psi_0") ;
487 // des_coupe_z(d_psi(1), 0., 1, "d_psi_1") ;
488 // des_coupe_z(d_psi(2), 0., 1, "d_psi_2") ;
489 // des_coupe_z(ent(), 0., 1, "ent before adapt", &(ent()) ) ;
490 //##
491 
492 
493  mp.adapt(ent(), par_adapt) ;
494 
495  // Readjustment of the external boundary of domain l=nzet
496  // to keep a fixed ratio with respect to star's surface
497 
498  double rr_in_1 = mp.val_r(nzet, -1., M_PI/2., 0.) ;
499 
500  // Resizes the outer boundary of the shell including the comp. NS
501  double rr_out_nm2 = mp.val_r(nz-2, 1., M_PI/2., 0.) ;
502 
503  mp.resize(nz-2, rr_in_1/rr_out_nm2 * fact_resize(1)) ;
504 
505  // Resizes the inner boundary of the shell including the comp. NS
506  double rr_out_nm3 = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
507 
508  mp.resize(nz-3, rr_in_1/rr_out_nm3 * fact_resize(0)) ;
509 
510  if (nz > nzet+3) {
511 
512  // Resize of the domain from 1(nzet) to N-4
513  double rr_out_nm3_new = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
514 
515  for (int i=nzet-1; i<nz-4; i++) {
516 
517  double rr_out_i = mp.val_r(i, 1., M_PI/2., 0.) ;
518 
519  double rr_mid = rr_out_i
520  + (rr_out_nm3_new - rr_out_i) / double(nz - 3 - i) ;
521 
522  double rr_2timesi = 2. * rr_out_i ;
523 
524  if (rr_2timesi < rr_mid) {
525 
526  double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
527 
528  mp.resize(i+1, rr_2timesi / rr_out_ip1) ;
529 
530  }
531  else {
532 
533  double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
534 
535  mp.resize(i+1, rr_mid / rr_out_ip1) ;
536 
537  } // End of else
538 
539  } // End of i loop
540 
541  } // End of (nz > nzet+3) loop
542 
543 
544  //----------------------------------------------------
545  // Computation of the enthalpy at the new grid points
546  //----------------------------------------------------
547 
548  mp_prev.homothetie(alpha_r) ;
549 
550  mp.reevaluate_symy(&mp_prev, nzet+1, ent.set()) ;
551 
552 // des_coupe_z(ent(), 0., 1, "ent after reevaluate", &(ent()) ) ;
553 
554  double ent_s_max = -1 ;
555  int k_s_max = -1 ;
556  int j_s_max = -1 ;
557  for (int k=0; k<mg->get_np(l_b); k++) {
558  for (int j=0; j<mg->get_nt(l_b); j++) {
559  double xx = fabs( ent()(l_b, k, j, i_b) ) ;
560  if (xx > ent_s_max) {
561  ent_s_max = xx ;
562  k_s_max = k ;
563  j_s_max = j ;
564  }
565  }
566  }
567  cout << "Max. abs(enthalpy) at the boundary between domains nzet-1"
568  << " and nzet : " << endl ;
569  cout << " " << ent_s_max << " reached for k = " << k_s_max <<
570  " and j = " << j_s_max << endl ;
571 
572  //----------------------------------------------------
573  // Equation of state
574  //----------------------------------------------------
575 
576  equation_of_state() ; // computes new values for nbar (n), ener (e)
577  // and press (p) from the new ent (H)
578 
579  //---------------------------------------------------------
580  // Matter source terms in the gravitational field equations
581  //---------------------------------------------------------
582 
583  hydro_euler() ; // computes new values for ener_euler (E),
584  // s_euler (S) and u_euler (U^i)
585 
586  //--------------------------------------------------------
587  // Poisson equation for logn_auto (nu_auto)
588  //--------------------------------------------------------
589 
590  // Source
591  // See Eq (50) from Gourgoulhon et al. (2001)
592  // ------------------------------------------
593 
594  if (relativistic) {
595  source = qpig * a_car % (ener_euler + s_euler)
599 
600  }
601  else {
602  source = qpig * nbar ;
603  }
604 
605  source.set_std_base() ;
606 
607  // Resolution of the Poisson equation
608  // ----------------------------------
609 
610  source().poisson(par_poisson1, logn_auto.set()) ;
611 
612  // Construct logn_auto_regu for et_bin_upmetr.C
613  // --------------------------------------------
614 
616 
617  // Check: has the Poisson equation been correctly solved ?
618  // -----------------------------------------------------
619 
620  Tbl tdiff_logn = diffrel(logn_auto().laplacien(), source()) ;
621  cout <<
622  "Relative error in the resolution of the equation for logn_auto : "
623  << endl ;
624  for (int l=0; l<nz; l++) {
625  cout << tdiff_logn(l) << " " ;
626  }
627  cout << endl ;
628  diff_logn = max(abs(tdiff_logn)) ;
629 
630 
631  if (relativistic) {
632 
633  //--------------------------------------------------------
634  // Poisson equation for beta_auto
635  //--------------------------------------------------------
636 
637  // Source
638  // See Eq (51) from Gourgoulhon et al. (2001)
639  // ------------------------------------------
640 
641  source = qpig * a_car % s_euler
642  + .75 * ( akcar_auto + akcar_comp )
647 
648  source.set_std_base() ;
649 
650  // Resolution of the Poisson equation
651  // ----------------------------------
652 
653  source().poisson(par_poisson2, beta_auto.set()) ;
654 
655  // Check: has the Poisson equation been correctly solved ?
656  // -----------------------------------------------------
657 
658  Tbl tdiff_beta = diffrel(beta_auto().laplacien(), source()) ;
659  cout <<
660  "Relative error in the resolution of the equation for beta_auto : "
661  << endl ;
662  for (int l=0; l<nz; l++) {
663  cout << tdiff_beta(l) << " " ;
664  }
665  cout << endl ;
666  diff_beta = max(abs(tdiff_beta)) ;
667 
668  //--------------------------------------------------------
669  // Vector Poisson equation for shift_auto
670  //--------------------------------------------------------
671 
672  // Source
673  // See Eq (52) from Gourgoulhon et al. (2001)
674  // ------
675 
676  Tenseur vtmp = 6. * ( d_beta_auto + d_beta_comp )
677  -8. * ( d_logn_auto + d_logn_comp ) ;
678 
679  source_shift = (-4.*qpig) * nnn % a_car % (ener_euler + press)
680  % u_euler
682 
683  source_shift.set_std_base() ;
684 
685  // Resolution of the Poisson equation
686  // ----------------------------------
687 
688  // Filter for the source of shift vector
689 
690  for (int i=0; i<3; i++) {
691 
692  if (source_shift(i).get_etat() != ETATZERO)
693  source_shift.set(i).filtre(4) ;
694 
695  }
696 
697  // For Tenseur::poisson_vect, the triad must be the mapping triad,
698  // not the reference one:
699 
700  source_shift.change_triad( mp.get_bvect_cart() ) ;
701 
702  for (int i=0; i<3; i++) {
703  if(source_shift(i).dz_nonzero()) {
704  assert( source_shift(i).get_dzpuis() == 4 ) ;
705  }
706  else{
707  (source_shift.set(i)).set_dzpuis(4) ;
708  }
709  }
710 
711  //##
712  // source_shift.dec2_dzpuis() ; // dzpuis 4 -> 2
713 
714  double lambda_shift = double(1) / double(3) ;
715 
716  source_shift.poisson_vect(lambda_shift, par_poisson_vect,
718 
719 
720  // Check: has the equation for shift_auto been correctly solved ?
721  // --------------------------------------------------------------
722 
723  // Divergence of shift_auto :
724  Tenseur divn = contract(shift_auto.gradient(), 0, 1) ;
725  divn.dec2_dzpuis() ; // dzpuis 2 -> 0
726 
727  // Grad(div) :
728  Tenseur graddivn = divn.gradient() ;
729  graddivn.inc2_dzpuis() ; // dzpuis 2 -> 4
730 
731  // Full operator :
732  Tenseur lap_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
733  lap_shift.set_etat_qcq() ;
734  for (int i=0; i<3; i++) {
735  lap_shift.set(i) = shift_auto(i).laplacien()
736  + lambda_shift * graddivn(i) ;
737  }
738 
739  Tbl tdiff_shift_x = diffrel(lap_shift(0), source_shift(0)) ;
740  Tbl tdiff_shift_y = diffrel(lap_shift(1), source_shift(1)) ;
741  Tbl tdiff_shift_z = diffrel(lap_shift(2), source_shift(2)) ;
742 
743  cout <<
744  "Relative error in the resolution of the equation for shift_auto : "
745  << endl ;
746  cout << "x component : " ;
747  for (int l=0; l<nz; l++) {
748  cout << tdiff_shift_x(l) << " " ;
749  }
750  cout << endl ;
751  cout << "y component : " ;
752  for (int l=0; l<nz; l++) {
753  cout << tdiff_shift_y(l) << " " ;
754  }
755  cout << endl ;
756  cout << "z component : " ;
757  for (int l=0; l<nz; l++) {
758  cout << tdiff_shift_z(l) << " " ;
759  }
760  cout << endl ;
761 
762  diff_shift_x = max(abs(tdiff_shift_x)) ;
763  diff_shift_y = max(abs(tdiff_shift_y)) ;
764  diff_shift_z = max(abs(tdiff_shift_z)) ;
765 
766  // Final result
767  // ------------
768  // The output of Tenseur::poisson_vect is on the mapping triad,
769  // it should therefore be transformed to components on the
770  // reference triad :
771 
773 
774 
775  } // End of relativistic equations
776 
777 
778  if (nzet > 1) {
779  cout.precision(10) ;
780 
781  for (int ltrans = 0; ltrans < nzet-1; ltrans++) {
782  cout << endl << "Values at boundary between domains no. " << ltrans << " and " << ltrans+1 << " for theta = pi/2 and phi = 0 :" << endl ;
783 
784  double rt1 = mp.val_r(ltrans, 1., M_PI/2, 0.) ;
785  double rt2 = mp.val_r(ltrans+1, -1., M_PI/2, 0.) ;
786  cout << " Coord. r [km] (left, right, rel. diff) : "
787  << rt1 / km << " " << rt2 / km << " " << (rt2 - rt1)/rt1 << endl ;
788 
789  int ntm1 = mg->get_nt(ltrans) - 1;
790  int nrm1 = mg->get_nr(ltrans) - 1 ;
791  double ent1 = ent()(ltrans, 0, ntm1, nrm1) ;
792  double ent2 = ent()(ltrans+1, 0, ntm1, 0) ;
793  cout << " Enthalpy (left, right, rel. diff) : "
794  << ent1 << " " << ent2 << " " << (ent2-ent1)/ent1 << endl ;
795 
796  double press1 = press()(ltrans, 0, ntm1, nrm1) ;
797  double press2 = press()(ltrans+1, 0, ntm1, 0) ;
798  cout << " Pressure (left, right, rel. diff) : "
799  << press1 << " " << press2 << " " << (press2-press1)/press1 << endl ;
800 
801  double nb1 = nbar()(ltrans, 0, ntm1, nrm1) ;
802  double nb2 = nbar()(ltrans+1, 0, ntm1, 0) ;
803  cout << " Baryon density (left, right, rel. diff) : "
804  << nb1 << " " << nb2 << " " << (nb2-nb1)/nb1 << endl ;
805  }
806  }
807 /* if (mer % 10 == 0) {
808  cout << "mer = " << mer << endl ;
809  double r_max = 1.2 * ray_eq() ;
810  des_profile(nbar(), 0., r_max, M_PI/2, 0., "n", "Baryon density") ;
811  des_profile(ener(), 0., r_max, M_PI/2, 0., "e", "Energy density") ;
812  des_profile(press(), 0., r_max, M_PI/2, 0., "p", "Pressure") ;
813  des_profile(ent(), 0., r_max, M_PI/2, 0., "H", "Enthalpy") ;
814  }*/
815 
816  //-------------------------------------------------
817  // Relative change in enthalpy
818  //-------------------------------------------------
819 
820  Tbl diff_ent_tbl = diffrel( ent(), ent_jm1() ) ;
821  diff_ent = diff_ent_tbl(0) ;
822  for (int l=1; l<nzet; l++) {
823  diff_ent += diff_ent_tbl(l) ;
824  }
825  diff_ent /= nzet ;
826 
827 
828  ent_jm1 = ent ;
829 
830 
831  } // End of main loop
832 
833  //=========================================================================
834  // End of iteration
835  //=========================================================================
836 
837 
838 }
839 }
Lorene::Etoile::press
Tenseur press
Fluid pressure.
Definition: etoile.h:461
Lorene::Map_et
Radial mapping of rather general form.
Definition: map.h:2752
Lorene::Etoile_bin::akcar_comp
Tenseur akcar_comp
Part of the scalar generated by shift_auto and shift_comp , i.e.
Definition: etoile.h:944
Lorene::Etoile::a_car
Tenseur a_car
Total conformal factor .
Definition: etoile.h:515
Lorene::Etoile::nzet
int nzet
Number of domains of *mp occupied by the star.
Definition: etoile.h:432
Lorene::Etoile::relativistic
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition: etoile.h:437
Lorene::Etoile::u_euler
Tenseur u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Definition: etoile.h:474
Lorene::Tbl::set
double & set(int i)
Read/write of a particular element (index i) (1D case)
Definition: tbl.h:281
Lorene::Mg3d::get_np
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition: grilles.h:462
Lorene::Etoile_bin::ssjm1_wshift
Tenseur ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for by means...
Definition: etoile.h:983
Lorene::Tenseur
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition: tenseur.h:301
Lorene::Etoile_bin::shift_auto
Tenseur shift_auto
Part of the shift vector generated principaly by the star.
Definition: etoile.h:889
Lorene::Etoile_bin::w_shift
Tenseur w_shift
Vector used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Definition: etoile.h:908
Lorene::Etoile::ent
Tenseur ent
Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case)
Definition: etoile.h:457
Lorene::Etoile::logn_auto
Tenseur logn_auto
Total of the logarithm of the part of the lapse N generated principaly by the star.
Definition: etoile.h:484
Lorene::Mg3d
Multi-domain grid.
Definition: grilles.h:273
Lorene::Tenseur::set
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition: tenseur.C:824
Lorene::Etoile_bin::akcar_auto
Tenseur akcar_auto
Part of the scalar generated by shift_auto , i.e.
Definition: etoile.h:938
Lorene::Tenseur::inc2_dzpuis
void inc2_dzpuis()
dzpuis += 2 ;
Definition: tenseur.C:1143
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::diffrel
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition: cmp_math.C:504
Lorene::Mg3d::get_nt
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition: grilles.h:457
Lorene
Lorene prototypes.
Definition: app_hor.h:64
Lorene::Etoile::nbar
Tenseur nbar
Baryon density in the fluid frame.
Definition: etoile.h:459
Lorene::Tenseur::gradient
const Tenseur & gradient() const
Returns the gradient of *this (Cartesian coordinates)
Definition: tenseur.C:1542
Lorene::Map::get_mg
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:765
Lorene::Tenseur::poisson_vect
void poisson_vect(double lambda, Param &par, Tenseur &shift, Tenseur &vect, Tenseur &scal) const
Solves the vectorial Poisson equation : .
Definition: tenseur_pde.C:118
Lorene::Etoile::mp
Map & mp
Mapping associated with the star.
Definition: etoile.h:429
Lorene::Map::adapt
virtual void adapt(const Cmp &ent, const Param &par, int nbr=0)=0
Adaptation of the mapping to a given scalar field.
Lorene::Map::val_r
virtual double val_r(int l, double xi, double theta, double pphi) const =0
Returns the value of the radial coordinate r for a given in a given domain.
Lorene::max
Tbl max(const Cmp &)
Maximum values of a Cmp in each domain.
Definition: cmp_math.C:435
Lorene::abs
Cmp abs(const Cmp &)
Absolute value.
Definition: cmp_math.C:410
Lorene::Map::resize
virtual void resize(int l, double lambda)=0
Rescales the outer boundary of one domain.
Lorene::Etoile::ray_pole
double ray_pole() const
Coordinate radius at [r_unit].
Definition: etoile_global.C:415
Lorene::Etoile_bin::ref_triad
const Base_vect & ref_triad
Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's...
Definition: etoile.h:828
Lorene::Etoile_bin::pot_centri
Tenseur pot_centri
Centrifugal potential.
Definition: etoile.h:953
Lorene::Etoile::logn_auto_regu
Tenseur logn_auto_regu
Regular part of the logarithm of the part of the lapse N generated principaly by the star.
Definition: etoile.h:491
Lorene::Etoile_bin::ssjm1_logn
Cmp ssjm1_logn
Effective source at the previous step for the resolution of the Poisson equation for logn_auto by mea...
Definition: etoile.h:959
Lorene::Etoile::nnn
Tenseur nnn
Total lapse function.
Definition: etoile.h:509
Lorene::Etoile_bin::ssjm1_beta
Cmp ssjm1_beta
Effective source at the previous step for the resolution of the Poisson equation for beta_auto by mea...
Definition: etoile.h:965
Unites
Standard units of space, time and mass.
Lorene::Map::reevaluate_symy
virtual void reevaluate_symy(const Map *mp_prev, int nzet, Cmp &uu) const =0
Recomputes the values of a Cmp at the collocation points after a change in the mapping.
Lorene::Tbl::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tbl.C:361
Lorene::flat_scalar_prod_desal
Tenseur flat_scalar_prod_desal(const Tenseur &t1, const Tenseur &t2)
Same as flat_scalar_prod but with desaliasing.
Definition: tenseur_operateur.C:735
Lorene::Etoile_bin::loggam
Tenseur loggam
Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Definition: etoile.h:849
Lorene::Etoile_bin::hydro_euler
virtual void hydro_euler()
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid fram...
Definition: et_bin_hydro.C:106
Lorene::Etoile_bin::equilibrium
void equilibrium(double ent_c, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, double thres_adapt, const Tbl &fact, Tbl &diff, const Tbl *ent_limit=0x0)
Computes an equilibrium configuration.
Definition: et_bin_equilibrium.C:184
Lorene::Etoile_bin::logn_comp
Tenseur logn_comp
Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by ...
Definition: etoile.h:854
Lorene::Etoile_bin::d_logn_auto
Tenseur d_logn_auto
Gradient of logn_auto (Cartesian components with respect to ref_triad )
Definition: etoile.h:859
Lorene::Etoile_bin::velocity_potential
double velocity_potential(int mermax, double precis, double relax)
Computes the non-translational part of the velocity scalar potential by solving the continuity equat...
Definition: et_bin_vel_pot.C:142
Lorene::Tenseur::change_triad
void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition: tenseur.C:668
Lorene::Tbl
Basic array class.
Definition: tbl.h:161
Lorene::Cmp::filtre
void filtre(int n)
Sets the n lasts coefficients in r to 0 in the external domain.
Definition: cmp_manip.C:74
Lorene::Mg3d::get_nzone
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:448
Lorene::Etoile_bin::d_logn_comp
Tenseur d_logn_comp
Gradient of logn_comp (Cartesian components with respect to ref_triad )
Definition: etoile.h:869
Lorene::Etoile::beta_auto
Tenseur beta_auto
Logarithm of the part of the product AN generated principaly by by the star.
Definition: etoile.h:506
Lorene::Mg3d::get_nr
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition: grilles.h:452
Lorene::Param::add_int_mod
void add_int_mod(int &n, int position=0)
Adds the address of a new modifiable int to the list.
Definition: param.C:385
Lorene::Etoile::ener_euler
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition: etoile.h:465
Lorene::Map::get_bvect_cart
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping,...
Definition: map.h:791
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
Lorene::Etoile_bin::tkij_auto
Tenseur_sym tkij_auto
Part of the extrinsic curvature tensor generated by shift_auto .
Definition: etoile.h:925
Lorene::Tenseur::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tenseur.C:636
Lorene::Param::add_tbl
void add_tbl(const Tbl &ti, int position=0)
Adds the address of a new Tbl to the list.
Definition: param.C:522
Lorene::Param
Parameter storage.
Definition: param.h:125
Lorene::Map_et::homothetie
virtual void homothetie(double lambda)
Sets a new radial scale.
Definition: map_et.C:905
Lorene::Etoile::ray_eq
double ray_eq() const
Coordinate radius at , [r_unit].
Definition: etoile_global.C:120
Lorene::Etoile_bin::irrotational
bool irrotational
true for an irrotational star, false for a corotating one
Definition: etoile.h:822
Lorene::Param::add_cmp_mod
void add_cmp_mod(Cmp &ti, int position=0)
Adds the address of a new modifiable Cmp to the list.
Definition: param.C:1004
Lorene::Etoile_bin::khi_shift
Tenseur khi_shift
Scalar used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Definition: etoile.h:918
Lorene::Etoile_bin::ssjm1_khi
Cmp ssjm1_khi
Effective source at the previous step for the resolution of the Poisson equation for the scalar by m...
Definition: etoile.h:973
Lorene::Etoile_bin::d_beta_comp
Tenseur d_beta_comp
Gradient of beta_comp (Cartesian components with respect to ref_triad )
Definition: etoile.h:884
Lorene::Etoile::equation_of_state
virtual void equation_of_state()
Computes the proper baryon and energy density, as well as pressure from the enthalpy.
Definition: etoile.C:566
Lorene::Tenseur::dec2_dzpuis
void dec2_dzpuis()
dzpuis -= 2 ;
Definition: tenseur.C:1130
Lorene::Etoile::s_euler
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition: etoile.h:468
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::Tenseur::set_std_base
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition: tenseur.C:1170
Lorene::Etoile_bin::d_beta_auto
Tenseur d_beta_auto
Gradient of beta_auto (Cartesian components with respect to ref_triad )
Definition: etoile.h:879
Lorene::contract
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Definition: tenseur_operateur.C:279
Lorene::Param::add_tenseur_mod
void add_tenseur_mod(Tenseur &ti, int position=0)
Adds the address of a new modifiable Tenseur to the list.
Definition: param.C:1142