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 
32 
33 /*
34  * $Id: et_bin_equilibrium.C,v 1.15 2016/12/05 16:17:52 j_novak Exp $
35  * $Log: et_bin_equilibrium.C,v $
36  * Revision 1.15 2016/12/05 16:17:52 j_novak
37  * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
38  *
39  * Revision 1.14 2014/10/13 08:52:55 j_novak
40  * Lorene classes and functions now belong to the namespace Lorene.
41  *
42  * Revision 1.13 2014/10/06 15:13:08 j_novak
43  * Modified #include directives to use c++ syntax.
44  *
45  * Revision 1.12 2009/06/15 09:25:18 k_taniguchi
46  * Improved the rescaling of the domains.
47  *
48  * Revision 1.11 2008/11/14 13:48:06 e_gourgoulhon
49  * Added parameter pent_limit to force the enthalpy values at the
50  * boundaries between the domains, in case of more than one domain inside
51  * the star.
52  *
53  * Revision 1.10 2004/09/28 15:49:23 f_limousin
54  * Improve the rescaling of the domains for nzone = 4 and nzone = 5.
55  *
56  * Revision 1.9 2004/05/13 08:47:01 f_limousin
57  * Decomment the procedure resize.
58  *
59  * Revision 1.8 2004/05/10 10:15:57 f_limousin
60  * Change to avoid a warning in the compilation of Lorene
61  *
62  * Revision 1.7 2004/05/07 12:36:34 f_limousin
63  * Add new member ssjm1_psi in order to have only one function
64  * equilibrium (the same for strange stars and neutron stars)
65  *
66  * Revision 1.6 2004/05/07 08:32:44 k_taniguchi
67  * Introduction of the version without ssjm1_psi.
68  *
69  * Revision 1.5 2004/04/19 11:06:36 f_limousin
70  * Differents call of Etoile_bin::velocity_potential depending on
71  * the equation of state.
72  *
73  * Revision 1.4 2004/03/25 10:29:04 j_novak
74  * All LORENE's units are now defined in the namespace Unites (in file unites.h).
75  *
76  * Revision 1.3 2003/01/17 13:31:13 f_limousin
77  * Add comments
78  *
79  * Revision 1.2 2002/12/10 13:28:03 k_taniguchi
80  * Change the multiplication "*" to "%"
81  * and flat_scalar_prod to flat_scalar_prod_desal.
82  *
83  * Revision 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
84  * LORENE
85  *
86  * Revision 2.23 2001/08/07 09:43:02 keisuke
87  * Change of the method to set the longest radius of a star
88  * on the first domain.
89  * Addition of a new argument in Etoile_bin::equilibrium : Tbl fact.
90  *
91  * Revision 2.22 2001/06/22 08:54:19 keisuke
92  * Set the inner values of the second domain of ent
93  * by using the outer ones of the first domain.
94  *
95  * Revision 2.21 2001/06/18 12:50:49 keisuke
96  * Addition of the filter for the source of shift vector.
97  *
98  * Revision 2.20 2001/05/17 12:18:47 keisuke
99  * Change of the method to calculate chi from setting position in map
100  * to val_point.
101  *
102  * Revision 2.19 2001/01/16 17:01:53 keisuke
103  * Change the method to set the values on the surface.
104  *
105  * Revision 2.18 2001/01/10 16:42:51 keisuke
106  * Set the inner values of the second domain of logn_auto
107  * by using the outer ones of the first domain.
108  *
109  * Revision 2.17 2000/12/22 13:08:04 eric
110  * precis_adapt = 1e-14 au lieu de 1e-15.
111  * Sorties graphiques commentees.
112  *
113  * Revision 2.16 2000/12/20 10:32:44 eric
114  * Changement important : nz_search = nzet ---> nz_search = nzet + 1
115  *
116  * Revision 2.15 2000/10/23 14:02:16 eric
117  * Modif de Map_et::adapt: on y rentre desormais avec nz_search
118  * (dans le cas present nz_search = nzet).
119  *
120  * Revision 2.14 2000/09/28 12:19:36 keisuke
121  * Construct logn_auto_regu from logn_auto.
122  * This procedure is needed for et_bin_upmetr.C.
123  *
124  * Revision 2.13 2000/05/25 13:48:12 eric
125  * Ajout de l'argument thres_adapt: l'adaptation du mapping n'est
126  * plus effectuee si dH/dr_eq passe sous un certain seuil.
127  *
128  * Revision 2.12 2000/05/25 12:58:31 eric
129  * Modifs classe Param: les int et double sont desormais passes par leurs
130  * adresses.
131  *
132  * Revision 2.11 2000/03/29 11:57:38 eric
133  * *** empty log message ***
134  *
135  * Revision 2.10 2000/03/29 11:53:41 eric
136  * Modif affichage
137  *
138  * Revision 2.9 2000/03/22 16:37:29 eric
139  * Calcul des erreurs dans la resolution des equations de Poisson
140  * et sortie de ces erreurs dans le Tbl diff.
141  *
142  * Revision 2.8 2000/03/22 12:56:18 eric
143  * Nouveau prototype d'Etoile_bin::equilibrium : diff_ent est remplace
144  * par le Tbl diff.
145  *
146  * Revision 2.7 2000/03/10 15:47:19 eric
147  * On appel desormais poisson_vect avec dzpuis = 4.
148  *
149  * Revision 2.6 2000/03/07 16:52:15 eric
150  * Modifs manipulations source pour le shift.
151  *
152  * Revision 2.5 2000/03/07 08:32:47 eric
153  * Appel de Map_radial::reevaluate_sym (pour tenir compte de la symetrie
154  * / plan y=0).
155  *
156  * Revision 2.4 2000/02/17 19:56:57 eric
157  * L'appel de Map_radial::reevaluate pour ent est fait sur nzet+1 zone
158  * et non plus nzet.
159  *
160  * Revision 2.2 2000/02/16 17:12:03 eric
161  * Premiere version avec les equations du champ gravitationnel.
162  *
163  * Revision 2.1 2000/02/15 15:59:52 eric
164  * *** empty log message ***
165  *
166  * Revision 2.0 2000/02/15 15:40:42 eric
167  * *** empty log message ***
168  *
169  *
170  * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_equilibrium.C,v 1.15 2016/12/05 16:17:52 j_novak Exp $
171  *
172  */
173 
174 // Headers C
175 #include <cmath>
176 
177 // Headers Lorene
178 #include "etoile.h"
179 #include "param.h"
180 #include "eos.h"
181 
182 #include "graphique.h"
183 #include "utilitaires.h"
184 #include "unites.h"
185 
186 namespace Lorene {
187 void Etoile_bin::equilibrium(double ent_c,
188  int mermax, int mermax_poisson,
189  double relax_poisson, int mermax_potvit,
190  double relax_potvit, double thres_adapt,
191  const Tbl& fact_resize, Tbl& diff, const Tbl* pent_limit ) {
192 
193 
194  // Fundamental constants and units
195  // -------------------------------
196 
197  using namespace Unites ;
198 
199  // Initializations
200  // ---------------
201 
202  const Mg3d* mg = mp.get_mg() ;
203  int nz = mg->get_nzone() ; // total number of domains
204 
205  // The following is required to initialize mp_prev as a Map_et:
206  Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
207 
208  // Domain and radial indices of points at the surface of the star:
209  int l_b = nzet - 1 ;
210  int i_b = mg->get_nr(l_b) - 1 ;
211  int k_b ;
212  int j_b ;
213 
214  // Value of the enthalpy defining the surface of the star
215  double ent_b = 0 ;
216 
217  // Error indicators
218  // ----------------
219 
220  double& diff_ent = diff.set(0) ;
221  double& diff_vel_pot = diff.set(1) ;
222  double& diff_logn = diff.set(2) ;
223  double& diff_beta = diff.set(3) ;
224  double& diff_shift_x = diff.set(4) ;
225  double& diff_shift_y = diff.set(5) ;
226  double& diff_shift_z = diff.set(6) ;
227 
228  // Parameters for the function Map_et::adapt
229  // -----------------------------------------
230 
231  Param par_adapt ;
232  int nitermax = 100 ;
233  int niter ;
234  int adapt_flag = 1 ; // 1 = performs the full computation,
235  // 0 = performs only the rescaling by
236  // the factor alpha_r
237  //## int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
238  int nz_search = nzet ; // Number of domains for searching the enthalpy
239  // isosurfaces
240 
241  double precis_secant = 1.e-14 ;
242  double alpha_r ;
243  double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
244 
245  par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
246  // locate zeros by the secant method
247  par_adapt.add_int(nzet, 1) ; // number of domains where the adjustment
248  // to the isosurfaces of ent is to be
249  // performed
250  par_adapt.add_int(nz_search, 2) ; // number of domains to search for
251  // the enthalpy isosurface
252  par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
253  // 0 = performs only the rescaling by
254  // the factor alpha_r
255  par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
256  // (theta_*, phi_*)
257  par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
258  // (theta_*, phi_*)
259 
260  par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
261  // the secant method
262 
263  par_adapt.add_double(precis_secant, 0) ; // required absolute precision in
264  // the determination of zeros by
265  // the secant method
266  par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
267 
268  par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
269  // distances will be multiplied
270 
271  // Enthalpy values for the adaptation
272  Tbl ent_limit(nzet) ;
273  if (pent_limit != 0x0) ent_limit = *pent_limit ;
274 
275  par_adapt.add_tbl(ent_limit, 0) ; // array of values of the field ent
276  // to define the isosurfaces.
277 
278  // Parameters for the function Map_et::poisson for logn_auto
279  // ---------------------------------------------------------
280 
281  double precis_poisson = 1.e-16 ;
282 
283  Param par_poisson1 ;
284 
285  par_poisson1.add_int(mermax_poisson, 0) ; // maximum number of iterations
286  par_poisson1.add_double(relax_poisson, 0) ; // relaxation parameter
287  par_poisson1.add_double(precis_poisson, 1) ; // required precision
288  par_poisson1.add_int_mod(niter, 0) ; // number of iterations actually used
289  par_poisson1.add_cmp_mod( ssjm1_logn ) ;
290 
291  // Parameters for the function Map_et::poisson for beta_auto
292  // ---------------------------------------------------------
293 
294  Param par_poisson2 ;
295 
296  par_poisson2.add_int(mermax_poisson, 0) ; // maximum number of iterations
297  par_poisson2.add_double(relax_poisson, 0) ; // relaxation parameter
298  par_poisson2.add_double(precis_poisson, 1) ; // required precision
299  par_poisson2.add_int_mod(niter, 0) ; // number of iterations actually used
300  par_poisson2.add_cmp_mod( ssjm1_beta ) ;
301 
302 
303  // Parameters for the function Tenseur::poisson_vect
304  // -------------------------------------------------
305 
306  Param par_poisson_vect ;
307 
308  par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of iterations
309  par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
310  par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
311  par_poisson_vect.add_cmp_mod( ssjm1_khi ) ;
312  par_poisson_vect.add_tenseur_mod( ssjm1_wshift ) ;
313  par_poisson_vect.add_int_mod(niter, 0) ;
314 
315 
316  // External potential
317  // See Eq (99) from Gourgoulhon et al. (2001)
318  // -----------------------------------------
319 
320  Tenseur pot_ext = logn_comp + pot_centri + loggam ;
321 //##
322 // des_coupe_z(pot_ext(), 0., 1, "pot_ext", &(ent()) ) ;
323 //##
324 
325  Tenseur ent_jm1 = ent ; // Enthalpy at previous step
326 
327  Tenseur source(mp) ; // source term in the equation for logn_auto
328  // and beta_auto
329 
330  Tenseur source_shift(mp, 1, CON, ref_triad) ; // source term in the equation
331  // for shift_auto
332 
333  //=========================================================================
334  // Start of iteration
335  //=========================================================================
336 
337  for(int mer=0 ; mer<mermax ; mer++ ) {
338 
339  cout << "-----------------------------------------------" << endl ;
340  cout << "step: " << mer << endl ;
341  cout << "diff_ent = " << diff_ent << endl ;
342 
343  //-----------------------------------------------------
344  // Resolution of the elliptic equation for the velocity
345  // scalar potential
346  //-----------------------------------------------------
347 
348  if (irrotational) {
349  diff_vel_pot = velocity_potential(mermax_potvit,
350  precis_poisson, relax_potvit) ;
351 
352  }
353 
354  //-----------------------------------------------------
355  // Computation of the new radial scale
356  //-----------------------------------------------------
357 
358  // alpha_r (r = alpha_r r') is determined so that the enthalpy
359  // takes the requested value ent_b at the stellar surface
360 
361  // Values at the center of the star:
362  double logn_auto_c = logn_auto()(0, 0, 0, 0) ;
363  double pot_ext_c = pot_ext()(0, 0, 0, 0) ;
364 
365  // Search for the reference point (theta_*, phi_*) [notation of
366  // Bonazzola, Gourgoulhon & Marck PRD 58, 104020 (1998)]
367  // at the surface of the star
368  // ------------------------------------------------------------
369  double alpha_r2 = 0 ;
370  for (int k=0; k<mg->get_np(l_b); k++) {
371  for (int j=0; j<mg->get_nt(l_b); j++) {
372 
373  double pot_ext_b = pot_ext()(l_b, k, j, i_b) ;
374  double logn_auto_b = logn_auto()(l_b, k, j, i_b) ;
375 
376 
377  // See Eq (100) from Gourgoulhon et al. (2001)
378  double alpha_r2_jk = ( ent_c - ent_b + pot_ext_c - pot_ext_b) /
379  ( logn_auto_b - logn_auto_c ) ;
380 
381 // cout << "k, j, alpha_r2_jk : " << k << " " << j << " "
382 // << alpha_r2_jk << endl ;
383 
384  if (alpha_r2_jk > alpha_r2) {
385  alpha_r2 = alpha_r2_jk ;
386  k_b = k ;
387  j_b = j ;
388  }
389 
390  }
391  }
392 
393  alpha_r = sqrt(alpha_r2) ;
394 
395  cout << "k_b, j_b, alpha_r: " << k_b << " " << j_b << " "
396  << alpha_r << endl ;
397 
398  // New value of logn_auto
399  // ----------------------
400 
401  logn_auto = alpha_r2 * logn_auto ;
402  logn_auto_regu = alpha_r2 * logn_auto_regu ;
403  logn_auto_c = logn_auto()(0, 0, 0, 0) ;
404 
405 
406  //------------------------------------------------------------
407  // Change the values of the inner points of the second domain
408  // by those of the outer points of the first domain
409  //------------------------------------------------------------
410 
411  (logn_auto().va).smooth(nzet, (logn_auto.set()).va) ;
412 
413 
414  //------------------------------------------
415  // First integral --> enthalpy in all space
416  // See Eq (98) from Gourgoulhon et al. (2001)
417  //-------------------------------------------
418 
419  ent = (ent_c + logn_auto_c + pot_ext_c) - logn_auto - pot_ext ;
420 
421  (ent().va).smooth(nzet, (ent.set()).va) ;
422 
423  //----------------------------------------------------
424  // Adaptation of the mapping to the new enthalpy field
425  //----------------------------------------------------
426 
427  // Shall the adaptation be performed (cusp) ?
428  // ------------------------------------------
429 
430  double dent_eq = ent().dsdr().val_point(ray_eq(),M_PI/2.,0.) ;
431  double dent_pole = ent().dsdr().val_point(ray_pole(),0.,0.) ;
432  double rap_dent = fabs( dent_eq / dent_pole ) ;
433  cout << "| dH/dr_eq / dH/dr_pole | = " << rap_dent << endl ;
434 
435  if ( rap_dent < thres_adapt ) {
436  adapt_flag = 0 ; // No adaptation of the mapping
437  cout << "******* FROZEN MAPPING *********" << endl ;
438  }
439  else{
440  adapt_flag = 1 ; // The adaptation of the mapping is to be
441  // performed
442  }
443 
444 
445  if (pent_limit == 0x0) {
446  ent_limit.set_etat_qcq() ;
447  for (int l=0; l<nzet; l++) { // loop on domains inside the star
448  ent_limit.set(l) = ent()(l, k_b, j_b, i_b) ;
449  }
450  ent_limit.set(nzet-1) = ent_b ;
451  }
452 
453  Map_et mp_prev = mp_et ;
454 
455 //## cout << "Enthalpy field at the outer boundary of domain 0 : "
456 // << endl ;
457 // for (int k=0; k<mg->get_np(0); k++) {
458 // cout << "k = " << k << " : " ;
459 // for (int j=0; j<mg->get_nt(0); j++) {
460 // cout << " " << ent()(0, k, j, mg->get_nr(0)-1) ;
461 // }
462 // cout << endl ;
463 // }
464 // cout << "Enthalpy field at the inner boundary of domain 1 : "
465 // << endl ;
466 // for (int k=0; k<mg->get_np(1); k++) {
467 // cout << "k = " << k << " : " ;
468 // for (int j=0; j<mg->get_nt(1); j++) {
469 // cout << " " << ent()(1, k, j, 0) ;
470 // }
471 // cout << endl ;
472 // }
473 // cout << "Difference enthalpy field boundary between domains 0 and 1: "
474 // << endl ;
475 // for (int k=0; k<mg->get_np(1); k++) {
476 // cout << "k = " << k << " : " ;
477 // for (int j=0; j<mg->get_nt(1); j++) {
478 // cout << " " << ent()(0, k, j, mg->get_nr(0)-1) -
479 // ent()(1, k, j, 0) ;
480 // }
481 // cout << endl ;
482 // }
483 
484 
485 //##
486 // des_coupe_z(gam_euler(), 0., 1, "gam_euler") ;
487 // des_coupe_z(loggam(), 0., 1, "loggam") ;
488 // des_coupe_y(loggam(), 0., 1, "loggam") ;
489 // des_coupe_z(d_psi(0), 0., 1, "d_psi_0") ;
490 // des_coupe_z(d_psi(1), 0., 1, "d_psi_1") ;
491 // des_coupe_z(d_psi(2), 0., 1, "d_psi_2") ;
492 // des_coupe_z(ent(), 0., 1, "ent before adapt", &(ent()) ) ;
493 //##
494 
495 
496  mp.adapt(ent(), par_adapt) ;
497 
498  // Readjustment of the external boundary of domain l=nzet
499  // to keep a fixed ratio with respect to star's surface
500 
501  double rr_in_1 = mp.val_r(nzet, -1., M_PI/2., 0.) ;
502 
503  // Resizes the outer boundary of the shell including the comp. NS
504  double rr_out_nm2 = mp.val_r(nz-2, 1., M_PI/2., 0.) ;
505 
506  mp.resize(nz-2, rr_in_1/rr_out_nm2 * fact_resize(1)) ;
507 
508  // Resizes the inner boundary of the shell including the comp. NS
509  double rr_out_nm3 = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
510 
511  mp.resize(nz-3, rr_in_1/rr_out_nm3 * fact_resize(0)) ;
512 
513  if (nz > nzet+3) {
514 
515  // Resize of the domain from 1(nzet) to N-4
516  double rr_out_nm3_new = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
517 
518  for (int i=nzet-1; i<nz-4; i++) {
519 
520  double rr_out_i = mp.val_r(i, 1., M_PI/2., 0.) ;
521 
522  double rr_mid = rr_out_i
523  + (rr_out_nm3_new - rr_out_i) / double(nz - 3 - i) ;
524 
525  double rr_2timesi = 2. * rr_out_i ;
526 
527  if (rr_2timesi < rr_mid) {
528 
529  double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
530 
531  mp.resize(i+1, rr_2timesi / rr_out_ip1) ;
532 
533  }
534  else {
535 
536  double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
537 
538  mp.resize(i+1, rr_mid / rr_out_ip1) ;
539 
540  } // End of else
541 
542  } // End of i loop
543 
544  } // End of (nz > nzet+3) loop
545 
546 
547  //----------------------------------------------------
548  // Computation of the enthalpy at the new grid points
549  //----------------------------------------------------
550 
551  mp_prev.homothetie(alpha_r) ;
552 
553  mp.reevaluate_symy(&mp_prev, nzet+1, ent.set()) ;
554 
555 // des_coupe_z(ent(), 0., 1, "ent after reevaluate", &(ent()) ) ;
556 
557  double ent_s_max = -1 ;
558  int k_s_max = -1 ;
559  int j_s_max = -1 ;
560  for (int k=0; k<mg->get_np(l_b); k++) {
561  for (int j=0; j<mg->get_nt(l_b); j++) {
562  double xx = fabs( ent()(l_b, k, j, i_b) ) ;
563  if (xx > ent_s_max) {
564  ent_s_max = xx ;
565  k_s_max = k ;
566  j_s_max = j ;
567  }
568  }
569  }
570  cout << "Max. abs(enthalpy) at the boundary between domains nzet-1"
571  << " and nzet : " << endl ;
572  cout << " " << ent_s_max << " reached for k = " << k_s_max <<
573  " and j = " << j_s_max << endl ;
574 
575  //----------------------------------------------------
576  // Equation of state
577  //----------------------------------------------------
578 
579  equation_of_state() ; // computes new values for nbar (n), ener (e)
580  // and press (p) from the new ent (H)
581 
582  //---------------------------------------------------------
583  // Matter source terms in the gravitational field equations
584  //---------------------------------------------------------
585 
586  hydro_euler() ; // computes new values for ener_euler (E),
587  // s_euler (S) and u_euler (U^i)
588 
589  //--------------------------------------------------------
590  // Poisson equation for logn_auto (nu_auto)
591  //--------------------------------------------------------
592 
593  // Source
594  // See Eq (50) from Gourgoulhon et al. (2001)
595  // ------------------------------------------
596 
597  if (relativistic) {
598  source = qpig * a_car % (ener_euler + s_euler)
602 
603  }
604  else {
605  source = qpig * nbar ;
606  }
607 
608  source.set_std_base() ;
609 
610  // Resolution of the Poisson equation
611  // ----------------------------------
612 
613  source().poisson(par_poisson1, logn_auto.set()) ;
614 
615  // Construct logn_auto_regu for et_bin_upmetr.C
616  // --------------------------------------------
617 
619 
620  // Check: has the Poisson equation been correctly solved ?
621  // -----------------------------------------------------
622 
623  Tbl tdiff_logn = diffrel(logn_auto().laplacien(), source()) ;
624  cout <<
625  "Relative error in the resolution of the equation for logn_auto : "
626  << endl ;
627  for (int l=0; l<nz; l++) {
628  cout << tdiff_logn(l) << " " ;
629  }
630  cout << endl ;
631  diff_logn = max(abs(tdiff_logn)) ;
632 
633 
634  if (relativistic) {
635 
636  //--------------------------------------------------------
637  // Poisson equation for beta_auto
638  //--------------------------------------------------------
639 
640  // Source
641  // See Eq (51) from Gourgoulhon et al. (2001)
642  // ------------------------------------------
643 
644  source = qpig * a_car % s_euler
645  + .75 * ( akcar_auto + akcar_comp )
650 
651  source.set_std_base() ;
652 
653  // Resolution of the Poisson equation
654  // ----------------------------------
655 
656  source().poisson(par_poisson2, beta_auto.set()) ;
657 
658  // Check: has the Poisson equation been correctly solved ?
659  // -----------------------------------------------------
660 
661  Tbl tdiff_beta = diffrel(beta_auto().laplacien(), source()) ;
662  cout <<
663  "Relative error in the resolution of the equation for beta_auto : "
664  << endl ;
665  for (int l=0; l<nz; l++) {
666  cout << tdiff_beta(l) << " " ;
667  }
668  cout << endl ;
669  diff_beta = max(abs(tdiff_beta)) ;
670 
671  //--------------------------------------------------------
672  // Vector Poisson equation for shift_auto
673  //--------------------------------------------------------
674 
675  // Source
676  // See Eq (52) from Gourgoulhon et al. (2001)
677  // ------
678 
679  Tenseur vtmp = 6. * ( d_beta_auto + d_beta_comp )
680  -8. * ( d_logn_auto + d_logn_comp ) ;
681 
682  source_shift = (-4.*qpig) * nnn % a_car % (ener_euler + press)
683  % u_euler
685 
686  source_shift.set_std_base() ;
687 
688  // Resolution of the Poisson equation
689  // ----------------------------------
690 
691  // Filter for the source of shift vector
692 
693  for (int i=0; i<3; i++) {
694 
695  if (source_shift(i).get_etat() != ETATZERO)
696  source_shift.set(i).filtre(4) ;
697 
698  }
699 
700  // For Tenseur::poisson_vect, the triad must be the mapping triad,
701  // not the reference one:
702 
703  source_shift.change_triad( mp.get_bvect_cart() ) ;
704 
705  for (int i=0; i<3; i++) {
706  if(source_shift(i).dz_nonzero()) {
707  assert( source_shift(i).get_dzpuis() == 4 ) ;
708  }
709  else{
710  (source_shift.set(i)).set_dzpuis(4) ;
711  }
712  }
713 
714  //##
715  // source_shift.dec2_dzpuis() ; // dzpuis 4 -> 2
716 
717  double lambda_shift = double(1) / double(3) ;
718 
719  source_shift.poisson_vect(lambda_shift, par_poisson_vect,
721 
722 
723  // Check: has the equation for shift_auto been correctly solved ?
724  // --------------------------------------------------------------
725 
726  // Divergence of shift_auto :
727  Tenseur divn = contract(shift_auto.gradient(), 0, 1) ;
728  divn.dec2_dzpuis() ; // dzpuis 2 -> 0
729 
730  // Grad(div) :
731  Tenseur graddivn = divn.gradient() ;
732  graddivn.inc2_dzpuis() ; // dzpuis 2 -> 4
733 
734  // Full operator :
735  Tenseur lap_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
736  lap_shift.set_etat_qcq() ;
737  for (int i=0; i<3; i++) {
738  lap_shift.set(i) = shift_auto(i).laplacien()
739  + lambda_shift * graddivn(i) ;
740  }
741 
742  Tbl tdiff_shift_x = diffrel(lap_shift(0), source_shift(0)) ;
743  Tbl tdiff_shift_y = diffrel(lap_shift(1), source_shift(1)) ;
744  Tbl tdiff_shift_z = diffrel(lap_shift(2), source_shift(2)) ;
745 
746  cout <<
747  "Relative error in the resolution of the equation for shift_auto : "
748  << endl ;
749  cout << "x component : " ;
750  for (int l=0; l<nz; l++) {
751  cout << tdiff_shift_x(l) << " " ;
752  }
753  cout << endl ;
754  cout << "y component : " ;
755  for (int l=0; l<nz; l++) {
756  cout << tdiff_shift_y(l) << " " ;
757  }
758  cout << endl ;
759  cout << "z component : " ;
760  for (int l=0; l<nz; l++) {
761  cout << tdiff_shift_z(l) << " " ;
762  }
763  cout << endl ;
764 
765  diff_shift_x = max(abs(tdiff_shift_x)) ;
766  diff_shift_y = max(abs(tdiff_shift_y)) ;
767  diff_shift_z = max(abs(tdiff_shift_z)) ;
768 
769  // Final result
770  // ------------
771  // The output of Tenseur::poisson_vect is on the mapping triad,
772  // it should therefore be transformed to components on the
773  // reference triad :
774 
776 
777 
778  } // End of relativistic equations
779 
780 
781  if (nzet > 1) {
782  cout.precision(10) ;
783 
784  for (int ltrans = 0; ltrans < nzet-1; ltrans++) {
785  cout << endl << "Values at boundary between domains no. " << ltrans << " and " << ltrans+1 << " for theta = pi/2 and phi = 0 :" << endl ;
786 
787  double rt1 = mp.val_r(ltrans, 1., M_PI/2, 0.) ;
788  double rt2 = mp.val_r(ltrans+1, -1., M_PI/2, 0.) ;
789  cout << " Coord. r [km] (left, right, rel. diff) : "
790  << rt1 / km << " " << rt2 / km << " " << (rt2 - rt1)/rt1 << endl ;
791 
792  int ntm1 = mg->get_nt(ltrans) - 1;
793  int nrm1 = mg->get_nr(ltrans) - 1 ;
794  double ent1 = ent()(ltrans, 0, ntm1, nrm1) ;
795  double ent2 = ent()(ltrans+1, 0, ntm1, 0) ;
796  cout << " Enthalpy (left, right, rel. diff) : "
797  << ent1 << " " << ent2 << " " << (ent2-ent1)/ent1 << endl ;
798 
799  double press1 = press()(ltrans, 0, ntm1, nrm1) ;
800  double press2 = press()(ltrans+1, 0, ntm1, 0) ;
801  cout << " Pressure (left, right, rel. diff) : "
802  << press1 << " " << press2 << " " << (press2-press1)/press1 << endl ;
803 
804  double nb1 = nbar()(ltrans, 0, ntm1, nrm1) ;
805  double nb2 = nbar()(ltrans+1, 0, ntm1, 0) ;
806  cout << " Baryon density (left, right, rel. diff) : "
807  << nb1 << " " << nb2 << " " << (nb2-nb1)/nb1 << endl ;
808  }
809  }
810 /* if (mer % 10 == 0) {
811  cout << "mer = " << mer << endl ;
812  double r_max = 1.2 * ray_eq() ;
813  des_profile(nbar(), 0., r_max, M_PI/2, 0., "n", "Baryon density") ;
814  des_profile(ener(), 0., r_max, M_PI/2, 0., "e", "Energy density") ;
815  des_profile(press(), 0., r_max, M_PI/2, 0., "p", "Pressure") ;
816  des_profile(ent(), 0., r_max, M_PI/2, 0., "H", "Enthalpy") ;
817  }*/
818 
819  //-------------------------------------------------
820  // Relative change in enthalpy
821  //-------------------------------------------------
822 
823  Tbl diff_ent_tbl = diffrel( ent(), ent_jm1() ) ;
824  diff_ent = diff_ent_tbl(0) ;
825  for (int l=1; l<nzet; l++) {
826  diff_ent += diff_ent_tbl(l) ;
827  }
828  diff_ent /= nzet ;
829 
830 
831  ent_jm1 = ent ;
832 
833 
834  } // End of main loop
835 
836  //=========================================================================
837  // End of iteration
838  //=========================================================================
839 
840 
841 }
842 }
void add_tenseur_mod(Tenseur &ti, int position=0)
Adds the address of a new modifiable Tenseur to the list.
Definition: param.C:1145
const Base_vect & ref_triad
Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur &#39;s...
Definition: etoile.h:831
void dec2_dzpuis()
dzpuis -= 2 ;
Definition: tenseur.C:1146
Radial mapping of rather general form.
Definition: map.h:2783
void add_int(const int &n, int position=0)
Adds the address of a new int to the list.
Definition: param.C:249
void poisson_vect(double lambda, Param &par, Tenseur &shift, Tenseur &vect, Tenseur &scal) const
Solves the vectorial Poisson equation : .
Definition: tenseur_pde.C:121
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition: grilles.h:479
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:223
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition: tenseur.C:1186
Tenseur pot_centri
Centrifugal potential.
Definition: etoile.h:956
Cmp ssjm1_logn
Effective source at the previous step for the resolution of the Poisson equation for logn_auto by mea...
Definition: etoile.h:962
Tenseur logn_auto_regu
Regular part of the logarithm of the part of the lapse N generated principaly by the star...
Definition: etoile.h:494
Lorene prototypes.
Definition: app_hor.h:67
Standard units of space, time and mass.
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:783
double & set(int i)
Read/write of a particular element (index i) (1D case)
Definition: tbl.h:301
Tenseur nnn
Total lapse function.
Definition: etoile.h:512
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition: etoile.h:471
double ray_eq() const
Coordinate radius at , [r_unit].
virtual void adapt(const Cmp &ent, const Param &par, int nbr=0)=0
Adaptation of the mapping to a given scalar field.
Tenseur press
Fluid pressure.
Definition: etoile.h:464
Tenseur d_beta_auto
Gradient of beta_auto (Cartesian components with respect to ref_triad )
Definition: etoile.h:882
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition: cmp_math.C:507
void inc2_dzpuis()
dzpuis += 2 ;
Definition: tenseur.C:1159
Tenseur shift_auto
Part of the shift vector generated principaly by the star.
Definition: etoile.h:892
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tbl.C:364
bool irrotational
true for an irrotational star, false for a corotating one
Definition: etoile.h:825
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.
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition: tenseur.C:840
Tenseur w_shift
Vector used in the decomposition of shift_auto , following Shibata&#39;s prescription [Prog...
Definition: etoile.h:911
Tenseur u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Definition: etoile.h:477
Tenseur d_beta_comp
Gradient of beta_comp (Cartesian components with respect to ref_triad )
Definition: etoile.h:887
void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition: tenseur.C:684
Tenseur flat_scalar_prod_desal(const Tenseur &t1, const Tenseur &t2)
Same as flat_scalar_prod but with desaliasing.
Tenseur logn_comp
Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by ...
Definition: etoile.h:857
Tenseur d_logn_auto
Gradient of logn_auto (Cartesian components with respect to ref_triad )
Definition: etoile.h:862
Tenseur nbar
Baryon density in the fluid frame.
Definition: etoile.h:462
void filtre(int n)
Sets the n lasts coefficients in r to 0 in the external domain.
Definition: cmp_manip.C:77
Tenseur akcar_comp
Part of the scalar generated by shift_auto and shift_comp , i.e.
Definition: etoile.h:947
Parameter storage.
Definition: param.h:125
void add_tbl(const Tbl &ti, int position=0)
Adds the address of a new Tbl to the list.
Definition: param.C:525
Map & mp
Mapping associated with the star.
Definition: etoile.h:432
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:465
virtual void equation_of_state()
Computes the proper baryon and energy density, as well as pressure from the enthalpy.
Definition: etoile.C:569
virtual void homothetie(double lambda)
Sets a new radial scale.
Definition: map_et.C:928
Tbl max(const Cmp &)
Maximum values of a Cmp in each domain.
Definition: cmp_math.C:438
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.
Tenseur khi_shift
Scalar used in the decomposition of shift_auto , following Shibata&#39;s prescription [Prog...
Definition: etoile.h:921
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Tenseur_sym tkij_auto
Part of the extrinsic curvature tensor generated by shift_auto .
Definition: etoile.h:928
virtual void resize(int l, double lambda)=0
Rescales the outer boundary of one domain.
int nzet
Number of domains of *mp occupied by the star.
Definition: etoile.h:435
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition: grilles.h:469
Tenseur a_car
Total conformal factor .
Definition: etoile.h:518
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one. ...
Definition: etoile.h:440
Multi-domain grid.
Definition: grilles.h:279
double ray_pole() const
Coordinate radius at [r_unit].
Cmp ssjm1_beta
Effective source at the previous step for the resolution of the Poisson equation for beta_auto by mea...
Definition: etoile.h:968
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.
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
Tenseur logn_auto
Total of the logarithm of the part of the lapse N generated principaly by the star.
Definition: etoile.h:487
Tenseur loggam
Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Definition: etoile.h:852
Tenseur ent
Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case)
Definition: etoile.h:460
Cmp abs(const Cmp &)
Absolute value.
Definition: cmp_math.C:413
void add_double(const double &x, int position=0)
Adds the the address of a new double to the list.
Definition: param.C:318
double velocity_potential(int mermax, double precis, double relax)
Computes the non-translational part of the velocity scalar potential by solving the continuity equat...
Basic array class.
Definition: tbl.h:164
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition: grilles.h:474
Tenseur beta_auto
Logarithm of the part of the product AN generated principaly by by the star.
Definition: etoile.h:509
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tenseur.C:652
void add_cmp_mod(Cmp &ti, int position=0)
Adds the address of a new modifiable Cmp to the list.
Definition: param.C:1007
Tenseur akcar_auto
Part of the scalar generated by shift_auto , i.e.
Definition: etoile.h:941
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition: etoile.h:468
Tenseur d_logn_comp
Gradient of logn_comp (Cartesian components with respect to ref_triad )
Definition: etoile.h:872
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
const Tenseur & gradient() const
Returns the gradient of *this (Cartesian coordinates)
Definition: tenseur.C:1558
Cmp ssjm1_khi
Effective source at the previous step for the resolution of the Poisson equation for the scalar by m...
Definition: etoile.h:976
virtual void hydro_euler()
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid fram...
Definition: et_bin_hydro.C:109
Tenseur ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for by means...
Definition: etoile.h:986