LORENE
et_bin_equil_regu.C
1 /*
2  * Method of class Etoile_bin to compute an equilibrium configuration
3  * by regularizing source.
4  *
5  * (see file etoile.h for documentation).
6  *
7  */
8 
9 /*
10  * Copyright (c) 2000-2001 Eric Gourgoulhon
11  * Copyright (c) 2000-2001 Keisuke Taniguchi
12  *
13  * This file is part of LORENE.
14  *
15  * LORENE is free software; you can redistribute it and/or modify
16  * it under the terms of the GNU General Public License as published by
17  * the Free Software Foundation; either version 2 of the License, or
18  * (at your option) any later version.
19  *
20  * LORENE is distributed in the hope that it will be useful,
21  * but WITHOUT ANY WARRANTY; without even the implied warranty of
22  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
23  * GNU General Public License for more details.
24  *
25  * You should have received a copy of the GNU General Public License
26  * along with LORENE; if not, write to the Free Software
27  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
28  *
29  */
30 
31 
32 char et_bin_equil_regu_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_equil_regu.C,v 1.8 2014/10/13 08:52:55 j_novak Exp $" ;
33 
34 /*
35  * $Id: et_bin_equil_regu.C,v 1.8 2014/10/13 08:52:55 j_novak Exp $
36  * $Log: et_bin_equil_regu.C,v $
37  * Revision 1.8 2014/10/13 08:52:55 j_novak
38  * Lorene classes and functions now belong to the namespace Lorene.
39  *
40  * Revision 1.7 2014/10/06 15:13:08 j_novak
41  * Modified #include directives to use c++ syntax.
42  *
43  * Revision 1.6 2009/06/15 09:26:57 k_taniguchi
44  * Improved the rescaling of the domains.
45  *
46  * Revision 1.5 2004/03/25 10:29:03 j_novak
47  * All LORENE's units are now defined in the namespace Unites (in file unites.h).
48  *
49  * Revision 1.4 2003/09/01 06:48:08 k_taniguchi
50  * Change of the domain which should be resized.
51  *
52  * Revision 1.3 2003/08/31 05:35:38 k_taniguchi
53  * Addition of the specification of the domain
54  * which is resized.
55  *
56  * Revision 1.2 2002/12/11 12:51:26 k_taniguchi
57  * Change the multiplication "*" to "%"
58  * and flat_scalar_prod to flat_scalar_prod_desal.
59  *
60  * Revision 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
61  * LORENE
62  *
63  * Revision 2.17 2001/08/07 09:49:00 keisuke
64  * Change of the method to set the longest radius of a star
65  * on the first domain.
66  * Addition of a new argument in Etoile_bin::equil_regular : Tbl fact.
67  *
68  * Revision 2.16 2001/06/22 08:54:53 keisuke
69  * Set the inner values of the second domain of ent
70  * by using the outer ones of the first domain.
71  *
72  * Revision 2.15 2001/05/17 12:22:26 keisuke
73  * Change of the method to calculate chi from setting position in map
74  * to val_point.
75  *
76  * Revision 2.14 2001/02/07 09:47:28 eric
77  * unsgam1 est desormais donne par Eos::der_nbar_ent (cas newtonien)
78  * ou Eos::der_ener_ent (cas relativiste).
79  *
80  * Revision 2.13 2001/01/16 17:02:32 keisuke
81  * *** empty log message ***
82  *
83  * Revision 2.12 2001/01/16 16:58:08 keisuke
84  * Change the method to set the values on the surface.
85  *
86  * Revision 2.11 2001/01/10 16:45:34 keisuke
87  * Set the inner values of the second domain of logn_auto
88  * by using the outer ones of the first domain.
89  *
90  * Revision 2.10 2000/12/20 10:33:14 eric
91  * Changement important : nz_search = nzet ---> nz_search = nzet + 1
92  *
93  * Revision 2.9 2000/10/25 14:01:03 keisuke
94  * Modif de Map_et::adapt: on y rentre desormais avec nz_search
95  * (dans le cas present nz_search = nzet).
96  *
97  * Revision 2.8 2000/10/06 15:29:01 keisuke
98  * Change poisson_vect into poisson_vect_regu.
99  *
100  * Revision 2.7 2000/09/25 15:01:10 keisuke
101  * Suppress "int" from the declaration of k_div.
102  *
103  * Revision 2.6 2000/09/22 15:51:39 keisuke
104  * d_logn_auto est desormais calcule en dehors (dans update_metric).
105  *
106  * Revision 2.5 2000/09/13 09:50:33 keisuke
107  * Minor change on change_triad.
108  *
109  * Revision 2.4 2000/09/08 15:57:31 keisuke
110  * Change the basis of d_logn_auto_div from the spherical coordinate
111  * to the Cartesian one with respect to ref_triad.
112  *
113  * Revision 2.3 2000/09/07 15:47:19 keisuke
114  * Minor change.
115  *
116  * Revision 2.2 2000/09/07 15:43:41 keisuke
117  * Add a new argument in poisson_regular and suppress logn_auto_total.
118  *
119  * Revision 2.1 2000/08/29 14:01:43 keisuke
120  * Modify the arguments of poisson_regular.
121  *
122  * Revision 2.0 2000/08/29 11:39:02 eric
123  * Version provisoire.
124  *
125  *
126  * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_equil_regu.C,v 1.8 2014/10/13 08:52:55 j_novak Exp $
127  *
128  */
129 
130 // Headers C
131 #include <cmath>
132 
133 // Headers Lorene
134 #include "etoile.h"
135 #include "param.h"
136 #include "eos.h"
137 #include "utilitaires.h"
138 #include "unites.h"
139 
140 namespace Lorene {
141 
142 //********************************************************************
143 
144 void Etoile_bin::equil_regular(double ent_c, int mermax, int mermax_poisson,
145  double relax_poisson, int mermax_potvit,
146  double relax_potvit, double thres_adapt,
147  const Tbl& fact_resize, Tbl& diff) {
148 
149  // Fundamental constants and units
150  // -------------------------------
151  using namespace Unites ;
152 
153  // Initializations
154  // ---------------
155 
156  k_div = 2 ; // Regularity parameter for poisson_regular
157 
158  const Mg3d* mg = mp.get_mg() ;
159  int nz = mg->get_nzone() ; // total number of domains
160 
161  // The following is required to initialize mp_prev as a Map_et:
162  Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
163 
164  // Domain and radial indices of points at the surface of the star:
165  int l_b = nzet - 1 ;
166  int i_b = mg->get_nr(l_b) - 1 ;
167  int k_b ;
168  int j_b ;
169 
170  // Value of the enthalpy defining the surface of the star
171  double ent_b = 0 ;
172 
173  // Error indicators
174  // ----------------
175 
176  double& diff_ent = diff.set(0) ;
177  double& diff_vel_pot = diff.set(1) ;
178  double& diff_logn = diff.set(2) ;
179  double& diff_beta = diff.set(3) ;
180  double& diff_shift_x = diff.set(4) ;
181  double& diff_shift_y = diff.set(5) ;
182  double& diff_shift_z = diff.set(6) ;
183 
184  // Parameters for the function Map_et::adapt
185  // -----------------------------------------
186 
187  Param par_adapt ;
188  int nitermax = 100 ;
189  int niter ;
190  int adapt_flag = 1 ; // 1 = performs the full computation,
191  // 0 = performs only the rescaling by
192  // the factor alpha_r
193  //## int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
194  int nz_search = nzet ; // Number of domains for searching the enthalpy
195  // isosurfaces
196 
197  double precis_secant = 1.e-14 ;
198  double alpha_r ;
199  double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
200 
201  Tbl ent_limit(nz) ;
202 
203  par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
204  // locate zeros by the secant method
205  par_adapt.add_int(nzet, 1) ; // number of domains where the adjustment
206  // to the isosurfaces of ent is to be
207  // performed
208  par_adapt.add_int(nz_search, 2) ; // number of domains to search for
209  // the enthalpy isosurface
210  par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
211  // 0 = performs only the rescaling by
212  // the factor alpha_r
213  par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
214  // (theta_*, phi_*)
215  par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
216  // (theta_*, phi_*)
217  par_adapt.add_int_mod(niter, 0) ; // number of iterations actually
218  // used in the secant method
219  par_adapt.add_double(precis_secant, 0) ; // required absolute precision in
220  // the determination of zeros by
221  // the secant method
222  par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping,
223  // 0 = contracting mapping
224  par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
225  // distances will be multiplied
226  par_adapt.add_tbl(ent_limit, 0) ; // array of values of the field ent
227  // to define the isosurfaces.
228 
229  // Parameters for the function Map_et::poisson_regular for logn_auto
230  // -----------------------------------------------------------------
231 
232  double precis_poisson = 1.e-16 ;
233 
234  Param par_poisson1 ;
235 
236  par_poisson1.add_int(mermax_poisson, 0) ; // maximum number of iterations
237  par_poisson1.add_double(relax_poisson, 0) ; // relaxation parameter
238  par_poisson1.add_double(precis_poisson, 1) ; // required precision
239  par_poisson1.add_int_mod(niter, 0) ; // number of iterations actually
240  // used
241  par_poisson1.add_cmp_mod( ssjm1_logn ) ;
242 
243  // Parameters for the function Map_et::poisson for beta_auto
244  // ---------------------------------------------------------
245 
246  Param par_poisson2 ;
247 
248  par_poisson2.add_int(mermax_poisson, 0) ; // maximum number of iterations
249  par_poisson2.add_double(relax_poisson, 0) ; // relaxation parameter
250  par_poisson2.add_double(precis_poisson, 1) ; // required precision
251  par_poisson2.add_int_mod(niter, 0) ; // number of iterations actually
252  // used
253  par_poisson2.add_cmp_mod( ssjm1_beta ) ;
254 
255  // Parameters for the function Tenseur::poisson_vect_regu
256  // ------------------------------------------------------
257 
258  Param par_poisson_vect ;
259 
260  par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of
261  // iterations
262  par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
263  par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
264  par_poisson_vect.add_cmp_mod( ssjm1_khi ) ;
265  par_poisson_vect.add_tenseur_mod( ssjm1_wshift ) ;
266  par_poisson_vect.add_int_mod(niter, 0) ;
267 
268 
269  // External potential
270  // ------------------
271 
272  Tenseur pot_ext = logn_comp + pot_centri + loggam ;
273 //##
274 // des_coupe_z(pot_ext(), 0., 1, "pot_ext", &(ent()) ) ;
275 //##
276 
277  Tenseur ent_jm1 = ent ; // Enthalpy at previous step
278 
279  Tenseur source(mp) ; // source term in the equation for logn_auto
280  // and beta_auto
281 
282  Tenseur source_shift(mp, 1, CON, ref_triad) ; // source term in the
283  // equation for shift_auto
284 
285  Cmp source_regu(mp) ;
286  Cmp source_div(mp) ;
287 
288  //=========================================================================
289  // Start of iteration
290  //=========================================================================
291 
292  for(int mer=0 ; mer<mermax ; mer++ ) {
293 
294  cout << "-----------------------------------------------" << endl ;
295  cout << "step: " << mer << endl ;
296  cout << "diff_ent = " << diff_ent << endl ;
297 
298  //-----------------------------------------------------
299  // Resolution of the elliptic equation for the velocity
300  // scalar potential
301  //-----------------------------------------------------
302 
303  if (irrotational) {
304 
305  diff_vel_pot = velocity_potential(mermax_potvit, precis_poisson,
306  relax_potvit) ;
307 
308  }
309 
310  //-----------------------------------------------------
311  // Computation of the new radial scale
312  //-----------------------------------------------------
313 
314  // alpha_r (r = alpha_r r') is determined so that the enthalpy
315  // takes the requested value ent_b at the stellar surface
316 
317  // Values at the center of the star:
318  double logn_auto_c = logn_auto()(0, 0, 0, 0) ;
319  double pot_ext_c = pot_ext()(0, 0, 0, 0) ;
320 
321  // Search for the reference point (theta_*, phi_*) [notation of
322  // Bonazzola, Gourgoulhon & Marck PRD 58, 104020 (1998)]
323  // at the surface of the star
324  // ------------------------------------------------------------
325  double alpha_r2 = 0 ;
326  for (int k=0; k<mg->get_np(l_b); k++) {
327  for (int j=0; j<mg->get_nt(l_b); j++) {
328 
329  double pot_ext_b = pot_ext()(l_b, k, j, i_b) ;
330  double logn_auto_b = logn_auto()(l_b, k, j, i_b) ;
331 
332  double alpha_r2_jk = ( ent_c - ent_b + pot_ext_c - pot_ext_b) /
333  ( logn_auto_b - logn_auto_c ) ;
334 
335 // cout << "k, j, alpha_r2_jk : " << k << " " << j << " "
336 // << alpha_r2_jk << endl ;
337 
338  if (alpha_r2_jk > alpha_r2) {
339  alpha_r2 = alpha_r2_jk ;
340  k_b = k ;
341  j_b = j ;
342  }
343 
344  }
345  }
346 
347  alpha_r = sqrt(alpha_r2) ;
348 
349  cout << "k_b, j_b, alpha_r: " << k_b << " " << j_b << " "
350  << alpha_r << endl ;
351 
352  // New value of logn_auto
353  // ----------------------
354 
355  logn_auto = alpha_r2 * logn_auto ;
356  logn_auto_regu = alpha_r2 * logn_auto_regu ;
357  logn_auto_c = logn_auto()(0, 0, 0, 0) ;
358 
359 
360  //------------------------------------------------------------
361  // Change the values of the inner points of the second domain
362  // by those of the outer points of the first domain
363  //------------------------------------------------------------
364 
365  (logn_auto().va).smooth(nzet, (logn_auto.set()).va) ;
366 
367 
368  //--------------------
369  // First integral --> enthalpy in all space
370  //--------------------
371 
372  ent = (ent_c + logn_auto_c + pot_ext_c) - logn_auto - pot_ext ;
373 
374  (ent().va).smooth(nzet, (ent.set()).va) ;
375 
376  //----------------------------------------------------
377  // Adaptation of the mapping to the new enthalpy field
378  //----------------------------------------------------
379 
380  // Shall the adaptation be performed (cusp) ?
381  // ------------------------------------------
382 
383  double dent_eq = ent().dsdr().val_point(ray_eq(),M_PI/2.,0.) ;
384  double dent_pole = ent().dsdr().val_point(ray_pole(),0.,0.) ;
385  double rap_dent = fabs( dent_eq / dent_pole ) ;
386  cout << "| dH/dr_eq / dH/dr_pole | = " << rap_dent << endl ;
387 
388  if ( rap_dent < thres_adapt ) {
389  adapt_flag = 0 ; // No adaptation of the mapping
390  cout << "******* FROZEN MAPPING *********" << endl ;
391  }
392  else{
393  adapt_flag = 1 ; // The adaptation of the mapping is to be
394  // performed
395  }
396 
397 
398  ent_limit.set_etat_qcq() ;
399  for (int l=0; l<nzet; l++) { // loop on domains inside the star
400  ent_limit.set(l) = ent()(l, k_b, j_b, i_b) ;
401  }
402  ent_limit.set(nzet-1) = ent_b ;
403 
404  Map_et mp_prev = mp_et ;
405 
406 //##
407 // des_coupe_z(ent(), 0., 1, "ent before adapt", &(ent()) ) ;
408 //##
409 
410  mp.adapt(ent(), par_adapt) ;
411 
412  // Readjustment of the external boundary of domain l=nzet
413  // to keep a fixed ratio with respect to star's surface
414 
415  double rr_in_1 = mp.val_r(nzet, -1., M_PI/2., 0.) ;
416 
417  // Resizes the outer boundary of the shell including the comp. NS
418  double rr_out_nm2 = mp.val_r(nz-2, 1., M_PI/2., 0.) ;
419 
420  mp.resize(nz-2, rr_in_1/rr_out_nm2 * fact_resize(1)) ;
421 
422  // Resizes the inner boundary of the shell including the comp. NS
423  double rr_out_nm3 = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
424 
425  mp.resize(nz-3, rr_in_1/rr_out_nm3 * fact_resize(0)) ;
426 
427  if (nz > nzet+3) {
428 
429  // Resize of the domain from 1(nzet) to N-4
430  double rr_out_nm3_new = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
431 
432  for (int i=nzet-1; i<nz-4; i++) {
433 
434  double rr_out_i = mp.val_r(i, 1., M_PI/2., 0.) ;
435 
436  double rr_mid = rr_out_i
437  + (rr_out_nm3_new - rr_out_i) / double(nz - 3 - i) ;
438 
439  double rr_2timesi = 2. * rr_out_i ;
440 
441  if (rr_2timesi < rr_mid) {
442 
443  double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
444 
445  mp.resize(i+1, rr_2timesi / rr_out_ip1) ;
446 
447  }
448  else {
449 
450  double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
451 
452  mp.resize(i+1, rr_mid / rr_out_ip1) ;
453 
454  } // End of else
455 
456  } // End of i loop
457 
458  } // End of (nz > nzet+3) loop
459 
460 //##
461 // des_coupe_z(ent(), 0., 1, "ent after adapt", &(ent()) ) ;
462 //##
463  //----------------------------------------------------
464  // Computation of the enthalpy at the new grid points
465  //----------------------------------------------------
466 
467  mp_prev.homothetie(alpha_r) ;
468 
469  mp.reevaluate_symy(&mp_prev, nzet+1, ent.set()) ;
470 
471 // des_coupe_z(ent(), 0., 1, "ent after reevaluate", &(ent()) ) ;
472 
473  double ent_s_max = -1 ;
474  int k_s_max = -1 ;
475  int j_s_max = -1 ;
476  for (int k=0; k<mg->get_np(l_b); k++) {
477  for (int j=0; j<mg->get_nt(l_b); j++) {
478  double xx = fabs( ent()(l_b, k, j, i_b) ) ;
479  if (xx > ent_s_max) {
480  ent_s_max = xx ;
481  k_s_max = k ;
482  j_s_max = j ;
483  }
484  }
485  }
486  cout << "Max. abs(enthalpy) at the boundary between domains nzet-1"
487  << " and nzet : " << endl ;
488  cout << " " << ent_s_max << " reached for k = " << k_s_max <<
489  " and j = " << j_s_max << endl ;
490 
491  //----------------------------------------------------
492  // Equation of state
493  //----------------------------------------------------
494 
495  equation_of_state() ; // computes new values for nbar (n), ener (e)
496  // and press (p) from the new ent (H)
497 
498  //---------------------------------------------------------
499  // Matter source terms in the gravitational field equations
500  //---------------------------------------------------------
501 
502  hydro_euler() ; // computes new values for ener_euler (E),
503  // s_euler (S) and u_euler (U^i)
504 
505  //--------------------------------------------------------
506  // Poisson equation for logn_auto (nu_auto)
507  //--------------------------------------------------------
508 
509  // Source
510  // ------
511 
512  double unsgam1 ; // effective power of H in the source
513  // close to the surface
514 
515  if (relativistic) {
516  source = qpig * a_car % (ener_euler + s_euler)
520 
521  // 1/(gam-1) = dln(e)/dln(H) close to the surface :
522  unsgam1 = eos.der_ener_ent_p(ent_b + 1e-10*(ent_c-ent_b)) ;
523 
524  }
525  else {
526  source = qpig * nbar ;
527 
528  // 1/(gam-1) = dln(n)/dln(H) close to the surface :
529  unsgam1 = eos.der_nbar_ent_p(ent_b + 1e-10*(ent_c-ent_b)) ;
530  }
531 
532  source.set_std_base() ;
533 
534  // Resolution of the Poisson equation
535  // ----------------------------------
536 
540 
541  source_regu.std_base_scal() ;
542  source_div.std_base_scal() ;
543 
544  source().poisson_regular(k_div, nzet, unsgam1, par_poisson1,
546  logn_auto_div.set(),
548  source_regu, source_div) ;
549 
550  // Check: has the Poisson equation been correctly solved ?
551  // -----------------------------------------------------
552 
553  Tbl tdiff_logn = diffrel(logn_auto().laplacien(), source()) ;
554  cout <<
555  "Relative error in the resolution of the equation for logn_auto : "
556  << endl ;
557  for (int l=0; l<nz; l++) {
558  cout << tdiff_logn(l) << " " ;
559  }
560  cout << endl ;
561  diff_logn = max(abs(tdiff_logn)) ;
562 
563 
564  if (relativistic) {
565 
566  //--------------------------------------------------------
567  // Poisson equation for beta_auto
568  //--------------------------------------------------------
569 
570  // Source
571  // ------
572 
573  source = qpig * a_car % s_euler
574  + .75 * ( akcar_auto + akcar_comp )
579 
580  source.set_std_base() ;
581 
582  // Resolution of the Poisson equation
583  // ----------------------------------
584 
585  source().poisson(par_poisson2, beta_auto.set()) ;
586 
587 
588  // Check: has the Poisson equation been correctly solved ?
589  // -----------------------------------------------------
590 
591  Tbl tdiff_beta = diffrel(beta_auto().laplacien(), source()) ;
592  cout <<
593  "Relative error in the resolution of the equation for beta_auto : "
594  << endl ;
595  for (int l=0; l<nz; l++) {
596  cout << tdiff_beta(l) << " " ;
597  }
598  cout << endl ;
599  diff_beta = max(abs(tdiff_beta)) ;
600 
601  //--------------------------------------------------------
602  // Vector Poisson equation for shift_auto
603  //--------------------------------------------------------
604 
605  // Source
606  // ------
607 
608  Tenseur vtmp = 6. * ( d_beta_auto + d_beta_comp )
609  -8. * ( d_logn_auto + d_logn_comp ) ;
610 
611  source_shift = (-4.*qpig) * nnn % a_car % (ener_euler + press)
612  % u_euler
614 
615  source_shift.set_std_base() ;
616 
617  // Resolution of the Poisson equation
618  // ----------------------------------
619 
620  // Filter for the source of shift vector
621 
622  for (int i=0; i<3; i++) {
623 
624  if (source_shift(i).get_etat() != ETATZERO)
625  source_shift.set(i).filtre(4) ;
626 
627  }
628 
629  // For Tenseur::poisson_vect_regu,
630  // the triad must be the mapping triad,
631  // not the reference one:
632 
633  source_shift.change_triad( mp.get_bvect_cart() ) ;
634 
635  for (int i=0; i<3; i++) {
636  if(source_shift(i).dz_nonzero()) {
637  assert( source_shift(i).get_dzpuis() == 4 ) ;
638  }
639  else{
640  (source_shift.set(i)).set_dzpuis(4) ;
641  }
642  }
643 
644  //##
645  // source_shift.dec2_dzpuis() ; // dzpuis 4 -> 2
646 
647  double lambda_shift = double(1) / double(3) ;
648 
649  source_shift.poisson_vect_regu(k_div, nzet, unsgam1,
650  lambda_shift, par_poisson_vect,
652 
653 
654  // Check: has the equation for shift_auto been correctly solved ?
655  // --------------------------------------------------------------
656 
657  // Divergence of shift_auto :
658  Tenseur divn = contract(shift_auto.gradient(), 0, 1) ;
659  divn.dec2_dzpuis() ; // dzpuis 2 -> 0
660 
661  // Grad(div) :
662  Tenseur graddivn = divn.gradient() ;
663  graddivn.inc2_dzpuis() ; // dzpuis 2 -> 4
664 
665  // Full operator :
666  Tenseur lap_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
667  lap_shift.set_etat_qcq() ;
668  for (int i=0; i<3; i++) {
669  lap_shift.set(i) = shift_auto(i).laplacien()
670  + lambda_shift * graddivn(i) ;
671  }
672 
673  Tbl tdiff_shift_x = diffrel(lap_shift(0), source_shift(0)) ;
674  Tbl tdiff_shift_y = diffrel(lap_shift(1), source_shift(1)) ;
675  Tbl tdiff_shift_z = diffrel(lap_shift(2), source_shift(2)) ;
676 
677  cout <<
678  "Relative error in the resolution of the equation "
679  "for shift_auto : "
680  << endl ;
681  cout << "x component : " ;
682  for (int l=0; l<nz; l++) {
683  cout << tdiff_shift_x(l) << " " ;
684  }
685  cout << endl ;
686  cout << "y component : " ;
687  for (int l=0; l<nz; l++) {
688  cout << tdiff_shift_y(l) << " " ;
689  }
690  cout << endl ;
691  cout << "z component : " ;
692  for (int l=0; l<nz; l++) {
693  cout << tdiff_shift_z(l) << " " ;
694  }
695  cout << endl ;
696 
697  diff_shift_x = max(abs(tdiff_shift_x)) ;
698  diff_shift_y = max(abs(tdiff_shift_y)) ;
699  diff_shift_z = max(abs(tdiff_shift_z)) ;
700 
701  // Final result
702  // ------------
703  // The output of Tenseur::poisson_vect is on the mapping triad,
704  // it should therefore be transformed to components on the
705  // reference triad :
706 
708 
709 
710  } // End of relativistic equations
711 
712 
713  //-------------------------------------------------
714  // Relative change in enthalpy
715  //-------------------------------------------------
716 
717  Tbl diff_ent_tbl = diffrel( ent(), ent_jm1() ) ;
718  diff_ent = diff_ent_tbl(0) ;
719  for (int l=1; l<nzet; l++) {
720  diff_ent += diff_ent_tbl(l) ;
721  }
722  diff_ent /= nzet ;
723 
724  ent_jm1 = ent ;
725 
726 
727  } // End of main loop
728 
729  //=========================================================================
730  // End of iteration
731  //=========================================================================
732 
733 
734 }
735 
736 }
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:446
void std_base_scal()
Sets the spectral bases of the Valeur va to the standard ones for a scalar.
Definition: cmp.C:644
void filtre(int n)
Sets the n lasts coefficients in r to 0 in the external domain.
Definition: cmp_manip.C:74
virtual double der_ener_ent_p(double ent, const Param *par=0x0) const =0
Computes the logarithmic derivative from the log-enthalpy with extra parameters (virtual function im...
virtual double der_nbar_ent_p(double ent, const Param *par=0x0) const =0
Computes the logarithmic derivative from the log-enthalpy and extra parameters (virtual function imp...
Tenseur d_beta_auto
Gradient of beta_auto (Cartesian components with respect to ref_triad )
Definition: etoile.h:879
Tenseur d_logn_auto
Gradient of logn_auto (Cartesian components with respect to ref_triad )
Definition: etoile.h:859
Tenseur akcar_comp
Part of the scalar generated by shift_auto and shift_comp , i.e.
Definition: etoile.h:944
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
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 Base_vect & ref_triad
Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's...
Definition: etoile.h:828
bool irrotational
true for an irrotational star, false for a corotating one
Definition: etoile.h:822
Tenseur w_shift
Vector used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Definition: etoile.h:908
Tenseur logn_comp
Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by ...
Definition: etoile.h:854
Tenseur d_logn_comp
Gradient of logn_comp (Cartesian components with respect to ref_triad )
Definition: etoile.h:869
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
Tenseur ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for by means...
Definition: etoile.h:983
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
Tenseur pot_centri
Centrifugal potential.
Definition: etoile.h:953
void equil_regular(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)
Computes an equilibrium configuration by regularizing the diverging source.
Tenseur loggam
Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Definition: etoile.h:849
Tenseur shift_auto
Part of the shift vector generated principaly by the star.
Definition: etoile.h:889
Tenseur_sym tkij_auto
Part of the extrinsic curvature tensor generated by shift_auto .
Definition: etoile.h:925
Tenseur akcar_auto
Part of the scalar generated by shift_auto , i.e.
Definition: etoile.h:938
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
Tenseur d_beta_comp
Gradient of beta_comp (Cartesian components with respect to ref_triad )
Definition: etoile.h:884
Tenseur khi_shift
Scalar used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Definition: etoile.h:918
Tenseur logn_auto_div
Divergent part (if k_div!=0 ) of the logarithm of the part of the lapse N generated principaly by t...
Definition: etoile.h:497
int nzet
Number of domains of *mp occupied by the star.
Definition: etoile.h:432
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
int k_div
Index of regularity of the gravitational potential logn_auto .
Definition: etoile.h:449
double ray_eq() const
Coordinate radius at , [r_unit].
Tenseur nnn
Total lapse function.
Definition: etoile.h:509
Tenseur logn_auto
Total of the logarithm of the part of the lapse N generated principaly by the star.
Definition: etoile.h:484
Tenseur nbar
Baryon density in the fluid frame.
Definition: etoile.h:459
const Eos & eos
Equation of state of the stellar matter.
Definition: etoile.h:451
virtual void equation_of_state()
Computes the proper baryon and energy density, as well as pressure from the enthalpy.
Definition: etoile.C:566
Tenseur u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Definition: etoile.h:474
Map & mp
Mapping associated with the star.
Definition: etoile.h:429
Tenseur d_logn_auto_div
Gradient of logn_auto_div (if k_div!=0 )
Definition: etoile.h:501
Tenseur press
Fluid pressure.
Definition: etoile.h:461
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition: etoile.h:437
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition: etoile.h:465
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition: etoile.h:468
Tenseur ent
Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case)
Definition: etoile.h:457
Tenseur beta_auto
Logarithm of the part of the product AN generated principaly by by the star.
Definition: etoile.h:506
Tenseur a_car
Total conformal factor .
Definition: etoile.h:515
double ray_pole() const
Coordinate radius at [r_unit].
Radial mapping of rather general form.
Definition: map.h:2752
virtual void homothetie(double lambda)
Sets a new radial scale.
Definition: map_et.C:905
virtual void resize(int l, double lambda)=0
Rescales the outer boundary of one domain.
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:765
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.
virtual void adapt(const Cmp &ent, const Param &par, int nbr=0)=0
Adaptation of the mapping to a given scalar field.
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
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.
Multi-domain grid.
Definition: grilles.h:273
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition: grilles.h:462
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition: grilles.h:457
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:448
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition: grilles.h:452
Parameter storage.
Definition: param.h:125
void add_double(const double &x, int position=0)
Adds the the address of a new double to the list.
Definition: param.C:315
void add_cmp_mod(Cmp &ti, int position=0)
Adds the address of a new modifiable Cmp to the list.
Definition: param.C:1004
void add_int_mod(int &n, int position=0)
Adds the address of a new modifiable int to the list.
Definition: param.C:385
void add_tenseur_mod(Tenseur &ti, int position=0)
Adds the address of a new modifiable Tenseur to the list.
Definition: param.C:1142
void add_int(const int &n, int position=0)
Adds the address of a new int to the list.
Definition: param.C:246
void add_tbl(const Tbl &ti, int position=0)
Adds the address of a new Tbl to the list.
Definition: param.C:522
Basic array class.
Definition: tbl.h:161
double & set(int i)
Read/write of a particular element (index i) (1D case)
Definition: tbl.h:281
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tbl.C:361
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition: tenseur.h:301
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition: tenseur.C:824
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tenseur.C:636
void dec2_dzpuis()
dzpuis -= 2 ;
Definition: tenseur.C:1130
const Tenseur & gradient() const
Returns the gradient of *this (Cartesian coordinates)
Definition: tenseur.C:1542
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition: tenseur.C:1170
void inc2_dzpuis()
dzpuis += 2 ;
Definition: tenseur.C:1143
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
void poisson_vect_regu(int k_div, int nzet, double unsgam1, double lambda, Param &par, Tenseur &shift, Tenseur &vect, Tenseur &scal) const
Solves the vectorial Poisson equation : .
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition: cmp_math.C:504
Tbl max(const Cmp &)
Maximum values of a Cmp in each domain.
Definition: cmp_math.C:435
Cmp abs(const Cmp &)
Absolute value.
Definition: cmp_math.C:410
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Tenseur flat_scalar_prod_desal(const Tenseur &t1, const Tenseur &t2)
Same as flat_scalar_prod but with desaliasing.
Lorene prototypes.
Definition: app_hor.h:64
Standard units of space, time and mass.