LORENE
et_bfrot_equilibre.C
1 /*
2  * Method of class Et_rot_bifluid to compute a static spherical configuration.
3  *
4  * (see file etoile.h for documentation).
5  *
6  */
7 
8 /*
9  * Copyright (c) 2001 Jerome Novak
10  *
11  * This file is part of LORENE.
12  *
13  * LORENE is free software; you can redistribute it and/or modify
14  * it under the terms of the GNU General Public License as published by
15  * the Free Software Foundation; either version 2 of the License, or
16  * (at your option) any later version.
17  *
18  * LORENE is distributed in the hope that it will be useful,
19  * but WITHOUT ANY WARRANTY; without even the implied warranty of
20  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21  * GNU General Public License for more details.
22  *
23  * You should have received a copy of the GNU General Public License
24  * along with LORENE; if not, write to the Free Software
25  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26  *
27  */
28 
29 
30 char et_bfrot_equilibre_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bfrot_equilibre.C,v 1.20 2015/06/10 14:39:17 a_sourie Exp $" ;
31 
32 /*
33  * $Id: et_bfrot_equilibre.C,v 1.20 2015/06/10 14:39:17 a_sourie Exp $
34  * $Log: et_bfrot_equilibre.C,v $
35  * Revision 1.20 2015/06/10 14:39:17 a_sourie
36  * New class Eos_bf_tabul for tabulated 2-fluid EoSs and associated functions for the computation of rotating stars with such EoSs.
37  *
38  * Revision 1.19 2014/10/13 08:52:54 j_novak
39  * Lorene classes and functions now belong to the namespace Lorene.
40  *
41  * Revision 1.18 2014/10/06 15:13:07 j_novak
42  * Modified #include directives to use c++ syntax.
43  *
44  * Revision 1.17 2006/03/13 10:02:27 j_novak
45  * Added things for triaxial perturbations.
46  *
47  * Revision 1.16 2004/09/01 10:56:05 r_prix
48  * added option of converging baryon-mass to equilibrium_bi()
49  *
50  * Revision 1.15 2004/08/30 09:54:20 r_prix
51  * experimental version of Kepler-limit finder for 2-fluid stars
52  *
53  * Revision 1.14 2004/03/25 10:29:03 j_novak
54  * All LORENE's units are now defined in the namespace Unites (in file unites.h).
55  *
56  * Revision 1.13 2003/12/11 12:43:35 r_prix
57  * activated adaptive grid for 2-fluid star (taken from Etoile_rot)
58  *
59  * Revision 1.12 2003/12/04 14:28:26 r_prix
60  * allow for the case of "slow-rot-style" EOS inversion, in which we need to adapt
61  * the inner domain to n_outer=0 instead of mu_outer=0 ...
62  * (this should only be used for comparison to analytic slow-rot solution!)
63  *
64  * Revision 1.11 2003/11/25 12:49:44 j_novak
65  * Modified headers to compile on IRIX. Changed Mapping to be Map_af (speed
66  * enhancement).
67  *
68  * Revision 1.10 2003/11/20 14:01:25 r_prix
69  * changed member names to better conform to Lorene coding standards:
70  * J_euler -> j_euler, EpS_euler -> enerps_euler, Delta_car -> delta_car
71  *
72  * Revision 1.9 2003/11/19 22:01:57 e_gourgoulhon
73  * -- Relaxation on logn and dzeta performed only if mer >= 10.
74  * -- err_grv2 is now evaluated also in the Newtonian case.
75  *
76  * Revision 1.8 2003/11/18 18:38:11 r_prix
77  * use of new member EpS_euler: matter sources in equilibrium() and global quantities
78  * no longer distinguish Newtonian/relativistic, as all terms should have the right limit...
79  *
80  * Revision 1.7 2003/11/17 13:49:43 r_prix
81  * - moved superluminal check into hydro_euler()
82  * - removed some warnings
83  *
84  * Revision 1.6 2003/11/13 12:14:35 r_prix
85  * *) removed all use of etoile-type specific u_euler, press
86  * and use 3+1 components of Tmunu instead
87  *
88  * Revision 1.5 2002/10/16 14:36:35 j_novak
89  * Reorganization of #include instructions of standard C++, in order to
90  * use experimental version 3 of gcc.
91  *
92  * Revision 1.4 2002/04/05 09:09:36 j_novak
93  * The inversion of the EOS for 2-fluids polytrope has been modified.
94  * Some errors in the determination of the surface were corrected.
95  *
96  * Revision 1.3 2002/01/16 15:03:28 j_novak
97  * *** empty log message ***
98  *
99  * Revision 1.2 2002/01/03 15:30:28 j_novak
100  * Some comments modified.
101  *
102  * Revision 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
103  * LORENE
104  *
105  * Revision 1.1 2001/06/22 15:40:06 novak
106  * Initial revision
107  *
108  *
109  * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bfrot_equilibre.C,v 1.20 2015/06/10 14:39:17 a_sourie Exp $
110  *
111  */
112 
113 // Headers C
114 #include <cmath>
115 
116 // Headers Lorene
117 #include "et_rot_bifluid.h"
118 #include "param.h"
119 #include "unites.h"
120 
121 #include "graphique.h"
122 #include "utilitaires.h"
123 
124 namespace Lorene {
125 
126 //-------------------------------------------------------------------------
127 //-------------------------------------------------------------------------
128 
129 // Axial Equilibrium
130 
131 //-------------------------------------------------------------------------
132 //-------------------------------------------------------------------------
133 
135 (double ent_c, double ent2_c, double omega0, double omega20,
136  const Tbl& ent_limit, const Tbl& ent2_limit, const Itbl& icontrol,
137  const Tbl& control, Tbl& diff,
138  int mer_mass, double mbar1_wanted, double mbar2_wanted, double aexp_mass)
139 {
140 
141  // Fundamental constants and units
142  // -------------------------------
143  using namespace Unites ;
144 
145  // For the display
146  // ---------------
147  char display_bold[]="x[1m" ; display_bold[0] = 27 ;
148  char display_normal[] = "x[0m" ; display_normal[0] = 27 ;
149 
150  // Grid parameters
151  // ---------------
152 
153  const Mg3d* mg = mp.get_mg() ;
154  int nz = mg->get_nzone() ; // total number of domains
155 
156  // The following is required to initialize mp_prev as a Map_af
157  Map_et& mp_et = dynamic_cast<Map_et&>(mp) ; // reference
158 
159  // Index of the point at phi=0, theta=pi/2 at the surface of the star:
160  assert(mg->get_type_t() == SYM) ;
161  int l_b = nzet - 1 ;
162  int i_b = mg->get_nr(l_b) - 1 ;
163  int j_b = mg->get_nt(l_b) - 1 ;
164  int k_b = 0 ;
165 
166  // Value of the enthalpies defining the surface of each fluid
167  double ent1_b = ent_limit(nzet-1) ;
168  double ent2_b = ent2_limit(nzet-1) ;
169 
170  // This value is chosen so that the grid contain both fluids
171 // double ent_b = (ent1_b > ent2_b ? ent1_b : ent2_b) ;
172 
173  // Parameters to control the iteration
174  // -----------------------------------
175 
176  int mer_max = icontrol(0) ;
177  int mer_rot = icontrol(1) ;
178  int mer_change_omega = icontrol(2) ;
179  int mer_fix_omega = icontrol(3) ;
180  int mermax_poisson = icontrol(4) ;
181  int nzadapt = icontrol(5); // number of domains for adaptive grid
182  int kepler_fluid = icontrol(6); // fluid-index for kepler-limit (0=none,3=both)
183  int kepler_wait_steps = icontrol(7);
184  int mer_triax = icontrol(8) ;
185 
186  int niter ;
187 
188  // Protections:
189  if (mer_change_omega < mer_rot) {
190  cout << "Et_rot_bifluid::equilibrium: mer_change_omega < mer_rot !" << endl ;
191  cout << " mer_change_omega = " << mer_change_omega << endl ;
192  cout << " mer_rot = " << mer_rot << endl ;
193  abort() ;
194  }
195  if (mer_fix_omega < mer_change_omega) {
196  cout << "Et_rot_bifluid::equilibrium: mer_fix_omega < mer_change_omega !"
197  << endl ;
198  cout << " mer_fix_omega = " << mer_fix_omega << endl ;
199  cout << " mer_change_omega = " << mer_change_omega << endl ;
200  abort() ;
201  }
202 
203  double precis = control(0) ;
204  double omega_ini = control(1) ;
205  double omega2_ini = control(2) ;
206  double relax = control(3) ;
207  double relax_prev = double(1) - relax ;
208  double relax_poisson = control(4) ;
209  // some additional stuff for adaptive grid:
210  double thres_adapt = control(5) ;
211  double precis_adapt = control(6) ;
212  double kepler_factor = control(7);
213  if (kepler_factor <= 1.0)
214  {
215  cout << "ERROR: Kepler factor has to be greater than 1!!\n";
216  abort();
217  }
218  double ampli_triax = control(8) ;
219 
220  // Error indicators
221  // ----------------
222 
223  diff.set_etat_qcq() ;
224  double diff_ent ;
225  double& diff_ent1 = diff.set(0) ;
226  double& diff_ent2 = diff.set(1) ;
227  double& diff_nuf = diff.set(2) ;
228  double& diff_nuq = diff.set(3) ;
229  // double& diff_dzeta = diff.set(4) ;
230  // double& diff_ggg = diff.set(5) ;
231  double& diff_shift_x = diff.set(6) ;
232  double& diff_shift_y = diff.set(7) ;
233  double& vit_triax = diff.set(8) ;
234 
235  // Parameters for the function Map_et::adapt
236  // -----------------------------------------
237 
238  Param par_adapt ;
239  int nitermax = 100 ;
240  int adapt_flag = 1 ; // 1 = performs the full computation,
241  // 0 = performs only the rescaling by
242  // the factor alpha_r
243  int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
244  // isosurfaces
245  double alpha_r ;
246  double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
247 
248  par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
249  // locate zeros by the secant method
250  par_adapt.add_int(nzadapt, 1) ; // number of domains where the adjustment
251  // to the isosurfaces of ent is to be
252  // performed
253  par_adapt.add_int(nz_search, 2) ; // number of domains to search for
254  // the enthalpy isosurface
255  par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
256  // 0 = performs only the rescaling by
257  // the factor alpha_r
258  par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
259  // (theta_*, phi_*)
260  par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
261  // (theta_*, phi_*)
262 
263  par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
264  // the secant method
265 
266  par_adapt.add_double(precis_adapt, 0) ; // required absolute precision in
267  // the determination of zeros by
268  // the secant method
269  par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
270 
271  par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
272  // distances will be multiplied
273 
274  par_adapt.add_tbl(ent_limit, 0) ; // array of values of the field ent
275  // to define the isosurfaces.
276 
277 
278  // Parameters for the function Map_et::poisson for nuf
279  // ----------------------------------------------------
280 
281  double precis_poisson = 1.e-16 ;
282 
283  Param par_poisson_nuf ;
284  par_poisson_nuf.add_int(mermax_poisson, 0) ; // maximum number of iterations
285  par_poisson_nuf.add_double(relax_poisson, 0) ; // relaxation parameter
286  par_poisson_nuf.add_double(precis_poisson, 1) ; // required precision
287  par_poisson_nuf.add_int_mod(niter, 0) ; // number of iterations actually used
288  par_poisson_nuf.add_cmp_mod( ssjm1_nuf ) ;
289 
290  Param par_poisson_nuq ;
291  par_poisson_nuq.add_int(mermax_poisson, 0) ; // maximum number of iterations
292  par_poisson_nuq.add_double(relax_poisson, 0) ; // relaxation parameter
293  par_poisson_nuq.add_double(precis_poisson, 1) ; // required precision
294  par_poisson_nuq.add_int_mod(niter, 0) ; // number of iterations actually used
295  par_poisson_nuq.add_cmp_mod( ssjm1_nuq ) ;
296 
297  Param par_poisson_tggg ;
298  par_poisson_tggg.add_int(mermax_poisson, 0) ; // maximum number of iterations
299  par_poisson_tggg.add_double(relax_poisson, 0) ; // relaxation parameter
300  par_poisson_tggg.add_double(precis_poisson, 1) ; // required precision
301  par_poisson_tggg.add_int_mod(niter, 0) ; // number of iterations actually used
302  par_poisson_tggg.add_cmp_mod( ssjm1_tggg ) ;
303  double lambda_tggg ;
304  par_poisson_tggg.add_double_mod( lambda_tggg ) ;
305 
306  Param par_poisson_dzeta ;
307  double lbda_grv2 ;
308  par_poisson_dzeta.add_double_mod( lbda_grv2 ) ;
309 
310  // Parameters for the function Tenseur::poisson_vect
311  // -------------------------------------------------
312 
313  Param par_poisson_vect ;
314 
315  par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of iterations
316  par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
317  par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
318  par_poisson_vect.add_cmp_mod( ssjm1_khi ) ;
319  par_poisson_vect.add_tenseur_mod( ssjm1_wshift ) ;
320  par_poisson_vect.add_int_mod(niter, 0) ;
321 
322 
323  // Initializations
324  // ---------------
325 
326  // Initial angular velocities
327  omega = 0 ;
328  omega2 = 0 ;
329 
330  double accrois_omega = (omega0 - omega_ini) /
331  double(mer_fix_omega - mer_change_omega) ;
332  double accrois_omega2 = (omega20 - omega2_ini) /
333  double(mer_fix_omega - mer_change_omega) ;
334 
335 
336  update_metric() ; // update of the metric coefficients
337 
338  equation_of_state() ; // update of the densities, pressure, etc...
339 
340  hydro_euler() ; // update of the hydro quantities relative to the
341  // Eulerian observer
342 
343  // Quantities at the previous step :
344 
345  Map_et mp_prev = mp_et;
346  Tenseur ent_prev = ent ;
347  Tenseur ent2_prev = ent2 ;
348  Tenseur logn_prev = logn ;
349  Tenseur dzeta_prev = dzeta ;
350 
351  // Creation of uninitialized tensors:
352  Tenseur source_nuf(mp) ; // source term in the equation for nuf
353  Tenseur source_nuq(mp) ; // source term in the equation for nuq
354  Tenseur source_dzf(mp) ; // matter source term in the eq. for dzeta
355  Tenseur source_dzq(mp) ; // quadratic source term in the eq. for dzeta
356  Tenseur source_tggg(mp) ; // source term in the eq. for tggg
357  Tenseur source_shift(mp, 1, CON, mp.get_bvect_cart()) ;
358  // source term for shift
359  Tenseur mlngamma(mp) ; // centrifugal potential
360  Tenseur mlngamma2(mp) ; // centrifugal potential
361 
362  Tenseur *outer_ent_p; // pointer to the enthalpy field of the outer fluid
363 
364  // Preparations for the Poisson equations:
365  // --------------------------------------
366  if (nuf.get_etat() == ETATZERO) {
367  nuf.set_etat_qcq() ;
368  nuf.set() = 0 ;
369  }
370 
371  if (relativistic) {
372  if (nuq.get_etat() == ETATZERO) {
373  nuq.set_etat_qcq() ;
374  nuq.set() = 0 ;
375  }
376 
377  if (tggg.get_etat() == ETATZERO) {
378  tggg.set_etat_qcq() ;
379  tggg.set() = 0 ;
380  }
381 
382  if (dzeta.get_etat() == ETATZERO) {
383  dzeta.set_etat_qcq() ;
384  dzeta.set() = 0 ;
385  }
386  }
387 
388  ofstream fichconv("convergence.d") ; // Output file for diff_ent
389  fichconv << "# diff_ent GRV2 max_triax vit_triax" << endl ;
390 
391  ofstream fichfreq("frequency.d") ; // Output file for omega
392  fichfreq << "# f1 [Hz] f2 [Hz]" << endl ;
393 
394  ofstream fichevol("evolution.d") ; // Output file for various quantities
395  fichevol << "# r_pole/r_eq ent_c ent2_c" << endl ;
396 
397  diff_ent = 1 ;
398  double err_grv2 = 1 ;
399  double max_triax_prev = 0 ; // Triaxial amplitude at previous step
400 
401  //=========================================================================
402  // Start of iteration
403  //=========================================================================
404 
405  for(int mer=0 ; (diff_ent > precis) && (mer<mer_max) ; mer++ ) {
406 
407  cout << "-----------------------------------------------" << endl ;
408  cout << "step: " << mer << endl ;
409  cout << "diff_ent = " << display_bold << diff_ent << display_normal
410  << endl ;
411  cout << "err_grv2 = " << err_grv2 << endl ;
412  fichconv << mer ;
413  fichfreq << mer ;
414  fichevol << mer ;
415 
416  if (mer >= mer_rot) {
417 
418  if (mer < mer_change_omega) {
419  omega = omega_ini ;
420  omega2 = omega2_ini ;
421  }
422  else {
423  if (mer <= mer_fix_omega) {
424  omega = omega_ini + accrois_omega *
425  (mer - mer_change_omega) ;
426  omega2 = omega2_ini + accrois_omega2 *
427  (mer - mer_change_omega) ;
428  }
429  }
430 
431  }
432 
433  //-----------------------------------------------
434  // Sources of the Poisson equations
435  //-----------------------------------------------
436 
437  // Source for nu
438  // -------------
439  Tenseur beta = log(bbb) ;
440  beta.set_std_base() ;
441 
442  // common source term for relativistic and Newtonian ! (enerps_euler has the right limit)
443  source_nuf = qpig * a_car * enerps_euler;
444 
445  if (relativistic)
446  source_nuq = ak_car - flat_scalar_prod(logn.gradient_spher(),logn.gradient_spher() + beta.gradient_spher()) ;
447  else
448  source_nuq = 0 ;
449 
450  source_nuf.set_std_base() ;
451  source_nuq.set_std_base() ;
452 
453  if (relativistic) {
454  // Source for dzeta
455  // ----------------
456  source_dzf = 2 * qpig * a_car * sphph_euler;
457  source_dzf.set_std_base() ;
458 
459  source_dzq = 1.5 * ak_car - flat_scalar_prod(logn.gradient_spher(),logn.gradient_spher() ) ;
460  source_dzq.set_std_base() ;
461 
462  // Source for tggg
463  // ---------------
464 
465  source_tggg = 2 * qpig * nnn * a_car * bbb * (s_euler - sphph_euler);
466  source_tggg.set_std_base() ;
467 
468  (source_tggg.set()).mult_rsint() ;
469 
470 
471  // Source for shift
472  // ----------------
473 
474  // Matter term
475  source_shift = (-4*qpig) * nnn * a_car * j_euler;
476 
477  // Quadratic terms:
478  Tenseur vtmp = 3 * beta.gradient_spher() - logn.gradient_spher() ;
479  vtmp.change_triad(mp.get_bvect_cart()) ;
480 
481  Tenseur squad = 2 * nnn * flat_scalar_prod(tkij, vtmp) ;
482 
483  // The addition of matter terms and quadratic terms is performed
484  // component by component because u_euler is contravariant,
485  // while squad is covariant.
486 
487  if (squad.get_etat() == ETATQCQ) {
488  for (int i=0; i<3; i++) {
489  source_shift.set(i) += squad(i) ;
490  }
491  }
492 
493  source_shift.set_std_base() ;
494  }
495  //----------------------------------------------
496  // Resolution of the Poisson equation for nuf
497  //----------------------------------------------
498 
499  source_nuf().poisson(par_poisson_nuf, nuf.set()) ;
500 
501 // cout << "Test of the Poisson equation for nuf :" << endl ;
502 // Tbl err = source_nuf().test_poisson(nuf(), cout, true) ;
503 // diff_nuf = err(0, 0) ;
504  diff_nuf = 0 ;
505 
506  //---------------------------------------
507  // Triaxial perturbation of nuf
508  //---------------------------------------
509 
510  if (mer == mer_triax) {
511 
512  if ( mg->get_np(0) == 1 ) {
513  cout <<
514  "Et_rot_bifluid::equilibrium: np must be stricly greater than 1"
515  << endl << " to set a triaxial perturbation !" << endl ;
516  abort() ;
517  }
518 
519  const Coord& phi = mp.phi ;
520  const Coord& sint = mp.sint ;
521  Cmp perturb(mp) ;
522  perturb = 1 + ampli_triax * sint*sint * cos(2*phi) ;
523  nuf.set() = nuf() * perturb ;
524 
525  nuf.set_std_base() ; // set the bases for spectral expansions
526  // to be the standard ones for a
527  // scalar field
528 
529  }
530 
531  // Monitoring of the triaxial perturbation
532  // ---------------------------------------
533 
534  Valeur& va_nuf = nuf.set().va ;
535  va_nuf.coef() ; // Computes the spectral coefficients
536  double max_triax = 0 ;
537 
538  if ( mg->get_np(0) > 1 ) {
539 
540  for (int l=0; l<nz; l++) { // loop on the domains
541  for (int j=0; j<mg->get_nt(l); j++) {
542  for (int i=0; i<mg->get_nr(l); i++) {
543 
544  // Coefficient of cos(2 phi) :
545  double xcos2p = (*(va_nuf.c_cf))(l, 2, j, i) ;
546 
547  // Coefficient of sin(2 phi) :
548  double xsin2p = (*(va_nuf.c_cf))(l, 3, j, i) ;
549 
550  double xx = sqrt( xcos2p*xcos2p + xsin2p*xsin2p ) ;
551 
552  max_triax = ( xx > max_triax ) ? xx : max_triax ;
553  }
554  }
555  }
556  }
557  cout << "Triaxial part of nuf : " << max_triax << endl ;
558 
559  if (relativistic) {
560 
561  //----------------------------------------------
562  // Resolution of the Poisson equation for nuq
563  //----------------------------------------------
564 
565  source_nuq().poisson(par_poisson_nuq, nuq.set()) ;
566 
567 // cout << "Test of the Poisson equation for nuq :" << endl ;
568 // err = source_nuq().test_poisson(nuq(), cout, true) ;
569 // diff_nuq = err(0, 0) ;
570  diff_nuq = 0 ;
571 
572  //---------------------------------------------------------
573  // Resolution of the vector Poisson equation for the shift
574  //---------------------------------------------------------
575 
576  if (source_shift.get_etat() != ETATZERO) {
577 
578  for (int i=0; i<3; i++) {
579  if(source_shift(i).dz_nonzero()) {
580  assert( source_shift(i).get_dzpuis() == 4 ) ;
581  }
582  else{
583  (source_shift.set(i)).set_dzpuis(4) ;
584  }
585  }
586 
587  }
588 
589  double lambda_shift = double(1) / double(3) ;
590 
591  if ( mg->get_np(0) == 1 ) {
592  lambda_shift = 0 ;
593  }
594 
595  source_shift.poisson_vect(lambda_shift, par_poisson_vect,
596  shift, w_shift, khi_shift) ;
597 
598 // cout << "Test of the Poisson equation for shift_x :" << endl ;
599 // err = source_shift(0).test_poisson(shift(0), cout, true) ;
600 // diff_shift_x = err(0, 0) ;
601  diff_shift_x = 0 ;
602 
603 // cout << "Test of the Poisson equation for shift_y :" << endl ;
604 // err = source_shift(1).test_poisson(shift(1), cout, true) ;
605 // diff_shift_y = err(0, 0) ;
606  diff_shift_y = 0 ;
607 
608  // Computation of tnphi and nphi from the Cartesian components
609  // of the shift
610  // -----------------------------------------------------------
611 
612  fait_nphi() ;
613 
614  }
615 
616 
617  //----------------------------------------
618  // Shall we search for the Kepler limit?
619  //----------------------------------------
620  bool kepler = false;
621  bool too_fast = false;
622 
623  if ( (kepler_fluid > 0) && (mer > mer_fix_omega + kepler_wait_steps) )
624  {
625  if (kepler_fluid & 0x01)
626  omega *= kepler_factor;
627  if (kepler_fluid & 0x02)
628  omega2 *= kepler_factor;
629  }
630 
631 
632  // ============================================================
633  kepler = true;
634  while (kepler)
635  {
636 
637  // New computation of delta_car, gam_euler, enerps_euler etc...
638  // ------------------------------------------------------
639  hydro_euler() ;
640 
641 
642  //------------------------------------------------------
643  // First integral of motion
644  //------------------------------------------------------
645 
646  // Centrifugal potential :
647  if (relativistic) {
648  mlngamma = - log( gam_euler ) ;
649  mlngamma2 = - log( gam_euler2) ;
650  }
651  else {
652  mlngamma = - 0.5 * uuu*uuu ;
653  mlngamma2 = -0.5 * uuu2*uuu2 ;
654  }
655 
656  // Central values of various potentials :
657  double nuf_c = nuf()(0,0,0,0) ;
658  double nuq_c = nuq()(0,0,0,0) ;
659 
660  // Scale factor to ensure that the enthalpy is equal to ent_b at
661  // the equator for the "outer" fluid
662  double alpha_r2 = 0;
663 
664  int j=j_b;
665 
666  // Boundary values of various potentials :
667  double nuf_b = nuf()(l_b, k_b, j, i_b) ;
668  double nuq_b = nuq()(l_b, k_b, j, i_b) ;
669  double mlngamma_b = mlngamma()(l_b, k_b, j, i_b) ;
670  double mlngamma2_b = mlngamma2()(l_b, k_b, j, i_b) ;
671 
672 
673  // RP: "hack": adapt the radius correctly if using "slow-rot-style" EOS inversion
674  //
675  if ( eos.identify() == 2 ) // only applies to Eos_bf_poly_newt
676  {
677  const Eos_bf_poly_newt &eos0 = dynamic_cast<const Eos_bf_poly_newt&>(eos);
678  if (eos0.get_typeos() == 5)
679  {
680  double vn_b = uuu()(l_b, k_b, j, i_b);
681  double vp_b = uuu2()(l_b, k_b, j, i_b);
682  double D2_b = (vp_b - vn_b)*(vp_b - vn_b);
683  double kdet = eos0.get_kap3() + eos0.get_beta()*D2_b;
684  double kaps1 = kdet / ( eos0.get_kap2() - kdet );
685  double kaps2 = kdet / ( eos0.get_kap1() - kdet );
686 
687  ent1_b = kaps1 * ( ent2_c - ent_c - mlngamma2_b + mlngamma_b );
688  ent2_b = kaps2 * ( ent_c - ent2_c - mlngamma_b + mlngamma2_b );
689 
690  cout << "**********************************************************************\n";
691  cout << "DEBUG: Rescaling domain for slow-rot-style EOS inversion \n";
692  cout << "DEBUG: ent1_b = " << ent1_b << "; ent2_b = " << ent2_b << endl;
693  cout << "**********************************************************************\n";
694 
695  adapt_flag = 0; // don't do adaptive-grid if using slow-rot-style inversion!
696  }
697  }
698 
699  double alpha1_r2 = ( ent_c - ent1_b - mlngamma_b + nuq_c - nuq_b) / ( nuf_b - nuf_c ) ;
700  double alpha2_r2 = ( ent2_c - ent2_b - mlngamma2_b + nuq_c - nuq_b) / ( nuf_b - nuf_c ) ;
701 
702  cout << "DEBUG: j= "<< j<<" ; alpha1 = " << alpha1_r2 <<" ; alpha2 = " << alpha2_r2 << endl;
703 
704  int outer_fluid = (alpha1_r2 > alpha2_r2) ? 1 : 2; // index of 'outer' fluid (at equator!)
705 
706  outer_ent_p = (outer_fluid == 1) ? (&ent) : (&ent2);
707 
708  alpha_r2 = (outer_fluid == 1) ? alpha1_r2 : alpha2_r2 ;
709 
710  alpha_r = sqrt(alpha_r2);
711 
712  cout << "alpha_r = " << alpha_r << endl ;
713 
714  // Readjustment of nu :
715  // -------------------
716 
717  logn = alpha_r2 * nuf + nuq ;
718  double nu_c = logn()(0,0,0,0) ;
719 
720 
721  // First integral --> enthalpy in all space
722  //-----------------
723 
724  ent = (ent_c + nu_c) - logn - mlngamma ;
725  ent2 = (ent2_c + nu_c) - logn - mlngamma2 ;
726 
727 
728  // now let's try to figure out if we have overstepped the Kepler-limit
729  // (FIXME) we assume that the enthalpy of the _outer_ fluid being negative
730  // inside the star
731  kepler = false;
732  for (int l=0; l<nzet; l++) {
733  int imax = mg->get_nr(l) - 1 ;
734  if (l == l_b) imax-- ; // The surface point is skipped
735  for (int i=0; i<imax; i++) {
736  if ( (*outer_ent_p)()(l, 0, j_b, i) < 0. ) {
737  kepler = true;
738  cout << "(outer) ent < 0 for l, i : " << l << " " << i
739  << " ent = " << (*outer_ent_p)()(l, 0, j_b, i) << endl ;
740  }
741  }
742  }
743 
744  if ( kepler )
745  {
746  cout << "**** KEPLERIAN VELOCITY REACHED ****" << endl ;
747  if (kepler_fluid & 0x01)
748  omega /= kepler_factor ; // Omega is decreased
749  if (kepler_fluid & 0x02)
750  omega2 /= kepler_factor;
751 
752  cout << "New rotation frequencies : "
753  << "Omega = " << omega/(2.*M_PI) * f_unit << " Hz; "
754  << "Omega2 = " << omega2/(2.*M_PI) * f_unit << endl ;
755 
756  too_fast = true;
757  }
758 
759  } /* while kepler */
760 
761 
762  if ( too_fast )
763  { // fact_omega is decreased for the next step
764  kepler_factor = sqrt( kepler_factor ) ;
765  cout << "**** New fact_omega : " << kepler_factor << endl ;
766  }
767  // ============================================================
768 
769 
770  // Cusp-check: shall the adaptation still be performed?
771  // ------------------------------------------
772  double dent_eq = (*outer_ent_p)().dsdr()(l_b, k_b, j_b, i_b) ;
773  double dent_pole = (*outer_ent_p)().dsdr()(l_b, k_b, 0, i_b) ;
774  double rap_dent = fabs( dent_eq / dent_pole ) ;
775  cout << "| dH/dr_eq / dH/dr_pole | = " << rap_dent << endl ;
776 
777  if ( rap_dent < thres_adapt ) {
778  adapt_flag = 0 ; // No adaptation of the mapping
779  cout << "******* FROZEN MAPPING *********" << endl ;
780  }
781 
782  // Rescaling of the grid and adaption to (outer) enthalpy surface
783  //---------------------------------------
784  if (adapt_flag && (nzadapt > 0) )
785  {
786  mp_prev = mp_et ;
787 
788  mp.adapt( (*outer_ent_p)(), par_adapt) ;
789 
790  mp_prev.homothetie(alpha_r) ;
791 
792  mp.reevaluate(&mp_prev, nzet+1, ent.set()) ;
793  mp.reevaluate(&mp_prev, nzet+1, ent2.set()) ;
794  }
795  else
796  mp.homothetie (alpha_r);
797 
798 
799  //----------------------------------------------------
800  // Equation of state
801  //----------------------------------------------------
802 
803  equation_of_state() ; // computes new values for nbar1,2 , ener (e)
804  // and press (p) from the new ent,ent2
805 
806  //---------------------------------------------------------
807  // Matter source terms in the gravitational field equations
808  //---------------------------------------------------------
809 
810  //## Computation of tnphi and nphi from the Cartesian components
811  // of the shift for the test in hydro_euler():
812 
813  fait_nphi() ;
814 
815  hydro_euler() ; // computes new values for ener_euler (E),
816  // s_euler (S) and u_euler (U^i)
817 
818  if (relativistic) {
819 
820  //-------------------------------------------------------
821  // 2-D Poisson equation for tggg
822  //-------------------------------------------------------
823 
824  mp.poisson2d(source_tggg(), mp.cmp_zero(), par_poisson_tggg, tggg.set()) ;
825 
826  //-------------------------------------------------------
827  // 2-D Poisson equation for dzeta
828  //-------------------------------------------------------
829 
830  mp.poisson2d(source_dzf(), source_dzq(), par_poisson_dzeta, dzeta.set()) ;
831 
832  err_grv2 = lbda_grv2 - 1;
833  cout << "GRV2: " << err_grv2 << endl ;
834 
835  }
836  else {
837  err_grv2 = grv2() ;
838  }
839 
840 
841  //---------------------------------------
842  // Computation of the metric coefficients (except for N^phi)
843  //---------------------------------------
844 
845  // Relaxations on nu and dzeta :
846 
847  if (mer >= 10) {
848  logn = relax * logn + relax_prev * logn_prev ;
849 
850  dzeta = relax * dzeta + relax_prev * dzeta_prev ;
851  }
852 
853  // Update of the metric coefficients N, A, B and computation of K_ij :
854 
855  update_metric() ;
856 
857  //-----------------------
858  // Informations display
859  //-----------------------
860 
861  // partial_display(cout) ;
862  fichfreq << " " << omega / (2*M_PI) * f_unit ;
863  fichfreq << " " << omega2 / (2*M_PI) * f_unit ;
864  fichevol << " " << ray_pole() / ray_eq() ;
865  fichevol << " " << ent_c ;
866  fichevol << " " << ent2_c ;
867 
868 
869  //-----------------------------------------
870  // Convergence towards given baryon masses (if mer_mass > 0)
871  //-----------------------------------------
872 
873  // If we want to impose baryonic masses for both fluids.
874  //Be careful, the code acts on mu_n and mu_p (at the center)
875  // -> beta equilibrium can be not verified
876  cout << "DEBUG MODE : mbar1_wanted : " << mbar1_wanted << endl ;
877  cout << "DEBUG MODE : mbar2_wanted : " << mbar2_wanted << endl ;
878  if (mbar2_wanted != 0 )
879 
880  {
881  if ((mer_mass>0) && (mer > mer_mass)) {
882 
883  double xx, xprog, ax, fact;
884 
885  // fluid 1
886  xx = mass_b1() / mbar1_wanted - 1. ;
887  cout << "Discrep. baryon mass1 <-> wanted bar. mass1 : " << xx << endl ;
888 
889  xprog = ( mer > 2*mer_mass) ? 1. : double(mer - mer_mass)/double(mer_mass) ;
890  xx *= xprog ;
891  ax = 0.5 * ( 2. + xx ) / (1. + xx ) ;
892  fact = pow(ax, aexp_mass) ;
893  cout << "Fluid1: xprog, xx, ax, fact : " << xprog << " " << xx << " " << ax << " " << fact << endl ;
894  ent_c *= fact ;
895 
896  // fluid 2
897  xx = mass_b2() / mbar2_wanted - 1. ;
898  cout << "Discrep. baryon mass2 <-> wanted bar. mass2 : " << xx << endl ;
899 
900  xprog = ( mer > 2*mer_mass) ? 1. : double(mer - mer_mass)/double(mer_mass) ;
901  xx *= xprog ;
902  ax = 0.5 * ( 2. + xx ) / (1. + xx ) ;
903  fact = pow(ax, aexp_mass) ;
904  cout << "Fluid2: xprog, xx, ax, fact : " << xprog << " " << xx << " " << ax << " " << fact << endl ;
905  ent2_c *= fact ;
906  cout << "H1c = " << ent_c << " H2c = " << ent2_c << endl ;
907  }
908  }
909 
910  else {
911  // If we want to impose Mb_tot and beta equilibrium
912  // In this case : mbar1_wanted = total baryonic mass wanted
913  // mbar2_wanted must be set to -1 and is not used.
914 
915  if ((mer_mass>0) && (mer > mer_mass)) {
916 
917  double xx, xprog, ax, fact;
918 
919  // total mass
920  xx = mass_b() / mbar1_wanted - 1. ; // mbar1_wanted = " mbar_wanted"
921  cout << "Discrep. baryon mass <-> wanted bar. mass : " << xx << endl ;
922 
923  xprog = ( mer > 2*mer_mass) ? 1. : double(mer - mer_mass)/double(mer_mass) ;
924  xx *= xprog ;
925  ax = 0.5 * ( 2. + xx ) / (1. + xx ) ;
926  fact = pow(ax, aexp_mass) ;
927  cout << "Fluid1: xprog, xx, ax, fact : " << xprog << " " << xx << " " << ax << " " << fact << endl ;
928  ent_c *= fact ;
929 
930  double m1 = 1.009000285 ;
931  double m2 = 1.008160139 ;
932  ent2_c = ent_c + log(m1/m2); // to ensure beta_equilibrium
933  cout << "DEBUG MODE : ent_c " << ent_c << endl ;
934  cout << "DEBUG MODE : ent2_c " << ent2_c << endl ;
935  cout << "H1c = " << ent_c << " H2c = " << ent2_c << endl ;
936 
937  }
938 
939  } /* if mer > mer_mass */
940 
941 
942 
943 
944 
945  //-------------------------------------------------------------
946  // Relative change in enthalpies with respect to previous step
947  //-------------------------------------------------------------
948 
949  Tbl diff_ent_tbl = diffrel( ent(), ent_prev() ) ;
950  diff_ent1 = diff_ent_tbl(0) ;
951  for (int l=1; l<nzet; l++) {
952  diff_ent1 += diff_ent_tbl(l) ;
953  }
954  diff_ent1 /= nzet ;
955  diff_ent_tbl = diffrel( ent2(), ent2_prev() ) ;
956  diff_ent2 = diff_ent_tbl(0) ;
957  for (int l=1; l<nzet; l++) {
958  diff_ent2 += diff_ent_tbl(l) ;
959  }
960  diff_ent2 /= nzet ;
961  diff_ent = 0.5*(diff_ent1 + diff_ent2) ;
962 
963  fichconv << " " << log10( fabs(diff_ent) + 1.e-16 ) ;
964  fichconv << " " << log10( fabs(err_grv2) + 1.e-16 ) ;
965  fichconv << " " << log10( fabs(max_triax) + 1.e-16 ) ;
966 
967  vit_triax = 0 ;
968  if ( (mer > mer_triax+1) && (max_triax_prev > 1e-13) ) {
969  vit_triax = (max_triax - max_triax_prev) / max_triax_prev ;
970  }
971 
972  fichconv << " " << vit_triax ;
973 
974  //------------------------------
975  // Recycling for the next step
976  //------------------------------
977 
978  ent_prev = ent ;
979  ent2_prev = ent2 ;
980  logn_prev = logn ;
981  dzeta_prev = dzeta ;
982  max_triax_prev = max_triax ;
983 
984  fichconv << endl ;
985  fichfreq << endl ;
986  fichevol << endl ;
987  fichconv.flush() ;
988  fichfreq.flush() ;
989  fichevol.flush() ;
990 
991  } // End of main loop
992 
993  //=========================================================================
994  // End of iteration
995  //=========================================================================
996 
997  fichconv.close() ;
998  fichfreq.close() ;
999  fichevol.close() ;
1000 
1001 
1002 }
1003 
1004 }
Lorene::Map_et
Radial mapping of rather general form.
Definition: map.h:2752
Lorene::Et_rot_bifluid::equilibrium_bi
void equilibrium_bi(double ent_c, double ent_c2, double omega0, double omega20, const Tbl &ent_limit, const Tbl &ent2_limit, const Itbl &icontrol, const Tbl &control, Tbl &diff, int mer_mass, double mbar1_wanted, double mbar2_wanted, double aexp_mass)
Computes an equilibrium configuration.
Definition: et_bfrot_equilibre.C:135
Lorene::Eos_bf_poly::get_beta
double get_beta() const
Returns the coefficient [unit: ], where .
Definition: eos_bifluid.h:1050
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::Tenseur
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition: tenseur.h:301
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition: valeur.h:287
Lorene::Mg3d
Multi-domain grid.
Definition: grilles.h:273
Lorene::Eos_bf_poly::get_kap3
double get_kap3() const
Returns the pressure coefficient [unit: ], where .
Definition: eos_bifluid.h:1044
Lorene::Tenseur::set
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition: tenseur.C:824
Lorene::log
Cmp log(const Cmp &)
Neperian logarithm.
Definition: cmp_math.C:296
Lorene::Valeur::c_cf
Mtbl_cf * c_cf
Coefficients of the spectral expansion of the function.
Definition: valeur.h:302
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::Eos_bf_poly::get_kap2
double get_kap2() const
Returns the pressure coefficient [unit: ], where .
Definition: eos_bifluid.h:1038
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::Tenseur::gradient_spher
const Tenseur & gradient_spher() const
Returns the gradient of *this (Spherical coordinates) (scalar field only).
Definition: tenseur.C:1548
Lorene::Itbl
Basic integer array class.
Definition: itbl.h:122
Lorene::Param::add_double_mod
void add_double_mod(double &x, int position=0)
Adds the address of a new modifiable double to the list.
Definition: param.C:453
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition: cmp_math.C:348
Lorene::Valeur::coef
void coef() const
Computes the coeffcients of *this.
Definition: valeur_coef.C:148
Lorene::Tenseur::get_etat
int get_etat() const
Returns the logical state.
Definition: tenseur.h:707
Unites
Standard units of space, time and mass.
Lorene::Tbl::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tbl.C:361
Lorene::Map_et::adapt
virtual void adapt(const Cmp &ent, const Param &par, int nbr_filtre=0)
Adaptation of the mapping to a given scalar field.
Definition: map_et_adapt.C:108
Lorene::Mg3d::get_type_t
int get_type_t() const
Returns the type of sampling in the direction: SYM : : symmetry with respect to the equatorial pl...
Definition: grilles.h:485
Lorene::Coord
Active physical coordinates and mapping derivatives.
Definition: coord.h:90
Lorene::Eos_bf_poly_newt
Analytic equation of state for two fluids (Newtonian case).
Definition: eos_bifluid.h:1258
Lorene::Cmp
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:446
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::flat_scalar_prod
Tenseur flat_scalar_prod(const Tenseur &t1, const Tenseur &t2)
Scalar product of two Tenseur when the metric is : performs the contraction of the last index of t1 w...
Definition: tenseur_operateur.C:653
Lorene::Mg3d::get_nzone
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:448
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::log10
Cmp log10(const Cmp &)
Basis 10 logarithm.
Definition: cmp_math.C:322
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
Lorene::Tenseur::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tenseur.C:636
Lorene::cos
Cmp cos(const Cmp &)
Cosine.
Definition: cmp_math.C:94
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::Eos_bf_poly::get_kap1
double get_kap1() const
Returns the pressure coefficient [unit: ], where .
Definition: eos_bifluid.h:1032
Lorene::Valeur::set
Tbl & set(int l)
Read/write of the value in a given domain (configuration space).
Definition: valeur.h:363
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::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::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