LORENE
et_rot_diff_equil.C
1 /*
2  * Function Et_rot_diff::equilibrium
3  *
4  * (see file etoile.h for documentation)
5  *
6  */
7 
8 /*
9  * Copyright (c) 2001-2003 Eric Gourgoulhon
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_rot_diff_equil_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_diff_equil.C,v 1.9 2014/10/13 08:52:57 j_novak Exp $" ;
31 
32 /*
33  * $Id: et_rot_diff_equil.C,v 1.9 2014/10/13 08:52:57 j_novak Exp $
34  * $Log: et_rot_diff_equil.C,v $
35  * Revision 1.9 2014/10/13 08:52:57 j_novak
36  * Lorene classes and functions now belong to the namespace Lorene.
37  *
38  * Revision 1.8 2014/10/06 15:13:08 j_novak
39  * Modified #include directives to use c++ syntax.
40  *
41  * Revision 1.7 2005/10/05 15:15:30 j_novak
42  * Added a Param* as parameter of Etoile_rot::equilibrium
43  *
44  * Revision 1.6 2004/03/25 10:29:05 j_novak
45  * All LORENE's units are now defined in the namespace Unites (in file unites.h).
46  *
47  * Revision 1.5 2003/11/19 22:01:57 e_gourgoulhon
48  * -- Relaxation on logn and dzeta performed only if mer >= 10.
49  * -- err_grv2 is now evaluated also in the Newtonian case.
50  *
51  * Revision 1.4 2003/10/27 10:54:43 e_gourgoulhon
52  * Changed local variable name lambda_grv2 to lbda_grv2 in order not
53  * to shadow method name.
54  *
55  * Revision 1.3 2003/05/25 19:59:02 e_gourgoulhon
56  * Added the possibility to choose the factor a = R_eq / R0, instead of R0
57  * in the differential rotation law.
58  *
59  * Revision 1.2 2002/10/16 14:36:36 j_novak
60  * Reorganization of #include instructions of standard C++, in order to
61  * use experimental version 3 of gcc.
62  *
63  * Revision 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
64  * LORENE
65  *
66  * Revision 1.1 2001/10/19 08:18:16 eric
67  * Initial revision
68  *
69  *
70  * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_diff_equil.C,v 1.9 2014/10/13 08:52:57 j_novak Exp $
71  *
72  */
73 
74 
75 
76 // Headers C
77 #include <cmath>
78 
79 // Headers Lorene
80 #include "et_rot_diff.h"
81 #include "param.h"
82 
83 #include "graphique.h"
84 #include "utilitaires.h"
85 #include "unites.h"
86 
87 namespace Lorene {
88 void Et_rot_diff::equilibrium(double ent_c, double omega_c0, double fact_omega,
89  int nzadapt, const Tbl& ent_limit,
90  const Itbl& icontrol,
91  const Tbl& control, double mbar_wanted,
92  double aexp_mass, Tbl& diff, Param*) {
93 
94  // Fundamental constants and units
95  // -------------------------------
96  using namespace Unites ;
97 
98  // For the display
99  // ---------------
100  char display_bold[]="x[1m" ; display_bold[0] = 27 ;
101  char display_normal[] = "x[0m" ; display_normal[0] = 27 ;
102 
103  // Grid parameters
104  // ---------------
105 
106  const Mg3d* mg = mp.get_mg() ;
107  int nz = mg->get_nzone() ; // total number of domains
108  int nzm1 = nz - 1 ;
109 
110  // The following is required to initialize mp_prev as a Map_et:
111  Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
112 
113  // Index of the point at phi=0, theta=pi/2 at the surface of the star:
114  assert(mg->get_type_t() == SYM) ;
115  int l_b = nzet - 1 ;
116  int i_b = mg->get_nr(l_b) - 1 ;
117  int j_b = mg->get_nt(l_b) - 1 ;
118  int k_b = 0 ;
119 
120  // Value of the enthalpy defining the surface of the star
121  double ent_b = ent_limit(nzet-1) ;
122 
123  // Parameters to control the iteration
124  // -----------------------------------
125 
126  int mer_max = icontrol(0) ;
127  int mer_rot = icontrol(1) ;
128  int mer_change_omega = icontrol(2) ;
129  int mer_fix_omega = icontrol(3) ;
130  int mer_mass = icontrol(4) ;
131  int mermax_poisson = icontrol(5) ;
132  int mer_triax = icontrol(6) ;
133  int delta_mer_kep = icontrol(7) ;
134 
135  // Protections:
136  if (mer_change_omega < mer_rot) {
137  cout << "Et_rot_diff::equilibrium: mer_change_omega < mer_rot !" << endl ;
138  cout << " mer_change_omega = " << mer_change_omega << endl ;
139  cout << " mer_rot = " << mer_rot << endl ;
140  abort() ;
141  }
142  if (mer_fix_omega < mer_change_omega) {
143  cout << "Et_rot_diff::equilibrium: mer_fix_omega < mer_change_omega !"
144  << endl ;
145  cout << " mer_fix_omega = " << mer_fix_omega << endl ;
146  cout << " mer_change_omega = " << mer_change_omega << endl ;
147  abort() ;
148  }
149 
150  // In order to converge to a given baryon mass, shall the central
151  // enthalpy be varied or Omega ?
152  bool change_ent = true ;
153  if (mer_mass < 0) {
154  change_ent = false ;
155  mer_mass = abs(mer_mass) ;
156  }
157 
158  double precis = control(0) ;
159  double omega_ini = control(1) ;
160  double relax = control(2) ;
161  double relax_prev = double(1) - relax ;
162  double relax_poisson = control(3) ;
163  double thres_adapt = control(4) ;
164  double ampli_triax = control(5) ;
165  double precis_adapt = control(6) ;
166 
167 
168  // Error indicators
169  // ----------------
170 
171  diff.set_etat_qcq() ;
172  double& diff_ent = diff.set(0) ;
173  double& diff_nuf = diff.set(1) ;
174  double& diff_nuq = diff.set(2) ;
175 // double& diff_dzeta = diff.set(3) ;
176 // double& diff_ggg = diff.set(4) ;
177  double& diff_shift_x = diff.set(5) ;
178  double& diff_shift_y = diff.set(6) ;
179  double& vit_triax = diff.set(7) ;
180 
181  // Parameters for the function Map_et::adapt
182  // -----------------------------------------
183 
184  Param par_adapt ;
185  int nitermax = 100 ;
186  int niter ;
187  int adapt_flag = 1 ; // 1 = performs the full computation,
188  // 0 = performs only the rescaling by
189  // the factor alpha_r
190  int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
191  // isosurfaces
192  double alpha_r ;
193  double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
194 
195  par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
196  // locate zeros by the secant method
197  par_adapt.add_int(nzadapt, 1) ; // number of domains where the adjustment
198  // to the isosurfaces of ent is to be
199  // performed
200  par_adapt.add_int(nz_search, 2) ; // number of domains to search for
201  // the enthalpy isosurface
202  par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
203  // 0 = performs only the rescaling by
204  // the factor alpha_r
205  par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
206  // (theta_*, phi_*)
207  par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
208  // (theta_*, phi_*)
209 
210  par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
211  // the secant method
212 
213  par_adapt.add_double(precis_adapt, 0) ; // required absolute precision in
214  // the determination of zeros by
215  // the secant method
216  par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
217 
218  par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
219  // distances will be multiplied
220 
221  par_adapt.add_tbl(ent_limit, 0) ; // array of values of the field ent
222  // to define the isosurfaces.
223 
224  // Parameters for the function Map_et::poisson for nuf
225  // ----------------------------------------------------
226 
227  double precis_poisson = 1.e-16 ;
228 
229  Param par_poisson_nuf ;
230  par_poisson_nuf.add_int(mermax_poisson, 0) ; // maximum number of iterations
231  par_poisson_nuf.add_double(relax_poisson, 0) ; // relaxation parameter
232  par_poisson_nuf.add_double(precis_poisson, 1) ; // required precision
233  par_poisson_nuf.add_int_mod(niter, 0) ; // number of iterations actually used
234  par_poisson_nuf.add_cmp_mod( ssjm1_nuf ) ;
235 
236  Param par_poisson_nuq ;
237  par_poisson_nuq.add_int(mermax_poisson, 0) ; // maximum number of iterations
238  par_poisson_nuq.add_double(relax_poisson, 0) ; // relaxation parameter
239  par_poisson_nuq.add_double(precis_poisson, 1) ; // required precision
240  par_poisson_nuq.add_int_mod(niter, 0) ; // number of iterations actually used
241  par_poisson_nuq.add_cmp_mod( ssjm1_nuq ) ;
242 
243  Param par_poisson_tggg ;
244  par_poisson_tggg.add_int(mermax_poisson, 0) ; // maximum number of iterations
245  par_poisson_tggg.add_double(relax_poisson, 0) ; // relaxation parameter
246  par_poisson_tggg.add_double(precis_poisson, 1) ; // required precision
247  par_poisson_tggg.add_int_mod(niter, 0) ; // number of iterations actually used
248  par_poisson_tggg.add_cmp_mod( ssjm1_tggg ) ;
249  double lambda_tggg ;
250  par_poisson_tggg.add_double_mod( lambda_tggg ) ;
251 
252  Param par_poisson_dzeta ;
253  double lbda_grv2 ;
254  par_poisson_dzeta.add_double_mod( lbda_grv2 ) ;
255 
256  // Parameters for the function Tenseur::poisson_vect
257  // -------------------------------------------------
258 
259  Param par_poisson_vect ;
260 
261  par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of 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  // Initializations
270  // ---------------
271 
272  // Initial central angular velocity
273  double omega_c = 0 ;
274 
275  double accrois_omega = (omega_c0 - omega_ini) /
276  double(mer_fix_omega - mer_change_omega) ;
277 
278 
279  update_metric() ; // update of the metric coefficients
280 
281  equation_of_state() ; // update of the density, pressure, etc...
282 
283  hydro_euler() ; // update of the hydro quantities relative to the
284  // Eulerian observer
285 
286  // Quantities at the previous step :
287  Map_et mp_prev = mp_et ;
288  Tenseur ent_prev = ent ;
289  Tenseur logn_prev = logn ;
290  Tenseur dzeta_prev = dzeta ;
291 
292  // Creation of uninitialized tensors:
293  Tenseur source_nuf(mp) ; // source term in the equation for nuf
294  Tenseur source_nuq(mp) ; // source term in the equation for nuq
295  Tenseur source_dzf(mp) ; // matter source term in the eq. for dzeta
296  Tenseur source_dzq(mp) ; // quadratic source term in the eq. for dzeta
297  Tenseur source_tggg(mp) ; // source term in the eq. for tggg
298  Tenseur source_shift(mp, 1, CON, mp.get_bvect_cart()) ;
299  // source term for shift
300  Tenseur mlngamma(mp) ; // centrifugal potential
301 
302  // Preparations for the Poisson equations:
303  // --------------------------------------
304  if (nuf.get_etat() == ETATZERO) {
305  nuf.set_etat_qcq() ;
306  nuf.set() = 0 ;
307  }
308 
309  if (relativistic) {
310  if (nuq.get_etat() == ETATZERO) {
311  nuq.set_etat_qcq() ;
312  nuq.set() = 0 ;
313  }
314 
315  if (tggg.get_etat() == ETATZERO) {
316  tggg.set_etat_qcq() ;
317  tggg.set() = 0 ;
318  }
319 
320  if (dzeta.get_etat() == ETATZERO) {
321  dzeta.set_etat_qcq() ;
322  dzeta.set() = 0 ;
323  }
324  }
325 
326  ofstream fichconv("convergence.d") ; // Output file for diff_ent
327  fichconv << "# diff_ent GRV2 max_triax vit_triax" << endl ;
328 
329  ofstream fichfreq("frequency.d") ; // Output file for omega_c
330  fichfreq << "# f [Hz]" << endl ;
331 
332  ofstream fichevol("evolution.d") ; // Output file for various quantities
333  fichevol <<
334  "# |dH/dr_eq/dH/dr_pole| r_pole/r_eq ent_c"
335  << endl ;
336 
337  diff_ent = 1 ;
338  double err_grv2 = 1 ;
339  double max_triax_prev = 0 ; // Triaxial amplitude at previous step
340 
341  //=========================================================================
342  // Start of iteration
343  //=========================================================================
344 
345  for(int mer=0 ; (diff_ent > precis) && (mer<mer_max) ; mer++ ) {
346 
347  cout << "-----------------------------------------------" << endl ;
348  cout << "step: " << mer << endl ;
349  cout << "diff_ent = " << display_bold << diff_ent << display_normal
350  << endl ;
351  cout << "err_grv2 = " << err_grv2 << endl ;
352  fichconv << mer ;
353  fichfreq << mer ;
354  fichevol << mer ;
355 
356  if (mer >= mer_rot) {
357 
358  if (mer < mer_change_omega) {
359  omega_c = omega_ini ;
360  }
361  else {
362  if (mer <= mer_fix_omega) {
363  omega_c = omega_ini + accrois_omega *
364  (mer - mer_change_omega) ;
365  }
366  }
367 
368  }
369 
370  //-----------------------------------------------
371  // Sources of the Poisson equations
372  //-----------------------------------------------
373 
374  // Source for nu
375  // -------------
376  Tenseur beta = log(bbb) ;
377  beta.set_std_base() ;
378 
379  if (relativistic) {
380  source_nuf = qpig * a_car *( ener_euler + s_euler ) ;
381 
382  source_nuq = ak_car - flat_scalar_prod(logn.gradient_spher(),
383  logn.gradient_spher() + beta.gradient_spher()) ;
384  }
385  else {
386  source_nuf = qpig * nbar ;
387 
388  source_nuq = 0 ;
389  }
390  source_nuf.set_std_base() ;
391  source_nuq.set_std_base() ;
392 
393  // Source for dzeta
394  // ----------------
395  source_dzf = 2 * qpig * a_car * (press + (ener_euler+press) * uuu*uuu ) ;
396  source_dzf.set_std_base() ;
397 
398  source_dzq = 1.5 * ak_car - flat_scalar_prod(logn.gradient_spher(),
399  logn.gradient_spher() ) ;
400  source_dzq.set_std_base() ;
401 
402  // Source for tggg
403  // ---------------
404 
405  source_tggg = 4 * qpig * nnn * a_car * bbb * press ;
406  source_tggg.set_std_base() ;
407 
408  (source_tggg.set()).mult_rsint() ;
409 
410 
411  // Source for shift
412  // ----------------
413 
414  // Matter term:
415  source_shift = (-4*qpig) * nnn * a_car * (ener_euler + press)
416  * u_euler ;
417 
418  // Quadratic terms:
419  Tenseur vtmp = 6 * beta.gradient_spher() - 2 * logn.gradient_spher() ;
420  vtmp.change_triad(mp.get_bvect_cart()) ;
421 
422  Tenseur squad = nnn * flat_scalar_prod(tkij, vtmp) ;
423 
424  // The addition of matter terms and quadratic terms is performed
425  // component by component because u_euler is contravariant,
426  // while squad is covariant.
427 
428  if (squad.get_etat() == ETATQCQ) {
429  for (int i=0; i<3; i++) {
430  source_shift.set(i) += squad(i) ;
431  }
432  }
433 
434  source_shift.set_std_base() ;
435 
436  //----------------------------------------------
437  // Resolution of the Poisson equation for nuf
438  //----------------------------------------------
439 
440  source_nuf().poisson(par_poisson_nuf, nuf.set()) ;
441 
442  cout << "Test of the Poisson equation for nuf :" << endl ;
443  Tbl err = source_nuf().test_poisson(nuf(), cout, true) ;
444  diff_nuf = err(0, 0) ;
445 
446  //---------------------------------------
447  // Triaxial perturbation of nuf
448  //---------------------------------------
449 
450  if (mer == mer_triax) {
451 
452  if ( mg->get_np(0) == 1 ) {
453  cout <<
454  "Et_rot_diff::equilibrium: np must be stricly greater than 1"
455  << endl << " to set a triaxial perturbation !" << endl ;
456  abort() ;
457  }
458 
459  const Coord& phi = mp.phi ;
460  const Coord& sint = mp.sint ;
461  Cmp perturb(mp) ;
462  perturb = 1 + ampli_triax * sint*sint * cos(2*phi) ;
463  nuf.set() = nuf() * perturb ;
464 
465  nuf.set_std_base() ; // set the bases for spectral expansions
466  // to be the standard ones for a
467  // scalar field
468 
469  }
470 
471  // Monitoring of the triaxial perturbation
472  // ---------------------------------------
473 
474  Valeur& va_nuf = nuf.set().va ;
475  va_nuf.coef() ; // Computes the spectral coefficients
476  double max_triax = 0 ;
477 
478  if ( mg->get_np(0) > 1 ) {
479 
480  for (int l=0; l<nz; l++) { // loop on the domains
481  for (int j=0; j<mg->get_nt(l); j++) {
482  for (int i=0; i<mg->get_nr(l); i++) {
483 
484  // Coefficient of cos(2 phi) :
485  double xcos2p = (*(va_nuf.c_cf))(l, 2, j, i) ;
486 
487  // Coefficient of sin(2 phi) :
488  double xsin2p = (*(va_nuf.c_cf))(l, 3, j, i) ;
489 
490  double xx = sqrt( xcos2p*xcos2p + xsin2p*xsin2p ) ;
491 
492  max_triax = ( xx > max_triax ) ? xx : max_triax ;
493  }
494  }
495  }
496 
497  }
498 
499  cout << "Triaxial part of nuf : " << max_triax << endl ;
500 
501  if (relativistic) {
502 
503  //----------------------------------------------
504  // Resolution of the Poisson equation for nuq
505  //----------------------------------------------
506 
507  source_nuq().poisson(par_poisson_nuq, nuq.set()) ;
508 
509  cout << "Test of the Poisson equation for nuq :" << endl ;
510  err = source_nuq().test_poisson(nuq(), cout, true) ;
511  diff_nuq = err(0, 0) ;
512 
513  //---------------------------------------------------------
514  // Resolution of the vector Poisson equation for the shift
515  //---------------------------------------------------------
516 
517 
518  if (source_shift.get_etat() != ETATZERO) {
519 
520  for (int i=0; i<3; i++) {
521  if(source_shift(i).dz_nonzero()) {
522  assert( source_shift(i).get_dzpuis() == 4 ) ;
523  }
524  else{
525  (source_shift.set(i)).set_dzpuis(4) ;
526  }
527  }
528 
529  }
530  //##
531  // source_shift.dec2_dzpuis() ; // dzpuis 4 -> 2
532 
533  double lambda_shift = double(1) / double(3) ;
534 
535  if ( mg->get_np(0) == 1 ) {
536  lambda_shift = 0 ;
537  }
538 
539  source_shift.poisson_vect(lambda_shift, par_poisson_vect,
540  shift, w_shift, khi_shift) ;
541 
542  cout << "Test of the Poisson equation for shift_x :" << endl ;
543  err = source_shift(0).test_poisson(shift(0), cout, true) ;
544  diff_shift_x = err(0, 0) ;
545 
546  cout << "Test of the Poisson equation for shift_y :" << endl ;
547  err = source_shift(1).test_poisson(shift(1), cout, true) ;
548  diff_shift_y = err(0, 0) ;
549 
550  // Computation of tnphi and nphi from the Cartesian components
551  // of the shift
552  // -----------------------------------------------------------
553 
554  fait_nphi() ;
555 
556  }
557 
558  //-----------------------------------------
559  // Determination of the fluid velociy U
560  //-----------------------------------------
561 
562  if (mer > mer_fix_omega + delta_mer_kep) {
563 
564  omega_c *= fact_omega ; // Increase of the angular velocity if
565  } // fact_omega != 1
566 
567 
568  bool omega_trop_grand = false ;
569  bool kepler = true ;
570 
571  while ( kepler ) {
572 
573  // Possible decrease of Omega to ensure a velocity < c
574 
575  bool superlum = true ;
576 
577  while ( superlum ) {
578 
579  // Computation of Omega(r,theta)
580 
581  if (omega_c == 0.) {
582  omega_field = 0 ;
583  }
584  else {
585  par_frot.set(0) = omega_c ;
586  if (par_frot(2) != double(0)) { // fixed a = R_eq / R_0
587  par_frot.set(1) = ray_eq() / par_frot(2) ;
588  }
589  double omeg_min = 0 ;
590  double omeg_max = omega_c ;
591  double precis1 = 1.e-14 ;
592  int nitermax1 = 100 ;
593 
594  fait_omega_field(omeg_min, omeg_max, precis1, nitermax1) ;
595  }
596 
597  // New fluid velocity U :
598 
599  Cmp tmp = omega_field() - nphi() ;
600  tmp.annule(nzm1) ;
601  tmp.std_base_scal() ;
602 
603  tmp.mult_rsint() ; // Multiplication by r sin(theta)
604 
605  uuu = bbb() / nnn() * tmp ;
606 
607  if (uuu.get_etat() == ETATQCQ) {
608  // Same basis as (Omega -N^phi) r sin(theta) :
609  ((uuu.set()).va).set_base( (tmp.va).base ) ;
610  }
611 
612 
613  // Is the new velocity larger than c in the equatorial plane ?
614 
615  superlum = false ;
616 
617  for (int l=0; l<nzet; l++) {
618  for (int i=0; i<mg->get_nr(l); i++) {
619 
620  double u1 = uuu()(l, 0, j_b, i) ;
621  if (u1 >= 1.) { // superluminal velocity
622  superlum = true ;
623  cout << "U > c for l, i : " << l << " " << i
624  << " U = " << u1 << endl ;
625  }
626  }
627  }
628  if ( superlum ) {
629  cout << "**** VELOCITY OF LIGHT REACHED ****" << endl ;
630  omega_c /= fact_omega ; // Decrease of Omega_c
631  cout << "New central rotation frequency : "
632  << omega/(2.*M_PI) * f_unit << " Hz" << endl ;
633  omega_trop_grand = true ;
634  }
635  } // end of while ( superlum )
636 
637 
638  // New computation of U (which this time is not superluminal)
639  // as well as of gam_euler, ener_euler, etc...
640  // -----------------------------------
641 
642  hydro_euler() ;
643 
644 
645  //------------------------------------------------------
646  // First integral of motion
647  //------------------------------------------------------
648 
649  // Centrifugal potential :
650  if (relativistic) {
651  mlngamma = - log( gam_euler ) ;
652  }
653  else {
654  mlngamma = - 0.5 * uuu*uuu ;
655  }
656 
657  // Equatorial values of various potentials :
658  double nuf_b = nuf()(l_b, k_b, j_b, i_b) ;
659  double nuq_b = nuq()(l_b, k_b, j_b, i_b) ;
660  double mlngamma_b = mlngamma()(l_b, k_b, j_b, i_b) ;
661  double primf_b = prim_field()(l_b, k_b, j_b, i_b) ;
662 
663 
664  // Central values of various potentials :
665  double nuf_c = nuf()(0,0,0,0) ;
666  double nuq_c = nuq()(0,0,0,0) ;
667  double mlngamma_c = 0 ;
668  double primf_c = prim_field()(0,0,0,0) ;
669 
670  // Scale factor to ensure that the enthalpy is equal to ent_b at
671  // the equator
672  double alpha_r2 = ( ent_c - ent_b + mlngamma_c - mlngamma_b
673  + nuq_c - nuq_b + primf_c - primf_b)
674  / ( nuf_b - nuf_c ) ;
675  alpha_r = sqrt(alpha_r2) ;
676  cout << "alpha_r = " << alpha_r << endl ;
677 
678  // Readjustment of nu :
679  // -------------------
680 
681  logn = alpha_r2 * nuf + nuq ;
682  double nu_c = logn()(0,0,0,0) ;
683 
684  // First integral --> enthalpy in all space
685  //-----------------
686 
687  ent = (ent_c + nu_c + mlngamma_c) - logn - mlngamma - prim_field ;
688 
689  // Test: is the enthalpy negative somewhere in the equatorial plane
690  // inside the star ? If yes, this means that the Keplerian velocity
691  // has been overstep.
692 
693  kepler = false ;
694  for (int l=0; l<nzet; l++) {
695  int imax = mg->get_nr(l) - 1 ;
696  if (l == l_b) imax-- ; // The surface point is skipped
697  for (int i=0; i<imax; i++) {
698  if ( ent()(l, 0, j_b, i) < 0. ) {
699  kepler = true ;
700  cout << "ent < 0 for l, i : " << l << " " << i
701  << " ent = " << ent()(l, 0, j_b, i) << endl ;
702  }
703  }
704  }
705 
706  if ( kepler ) {
707  cout << "**** KEPLERIAN VELOCITY REACHED ****" << endl ;
708  omega_c /= fact_omega ; // Omega is decreased
709  cout << "New central rotation frequency : "
710  << omega_c/(2.*M_PI) * f_unit << " Hz" << endl ;
711  omega_trop_grand = true ;
712  }
713 
714  } // End of while ( kepler )
715 
716  if ( omega_trop_grand ) { // fact_omega is decreased for the
717  // next step
718  fact_omega = sqrt( fact_omega ) ;
719  cout << "**** New fact_omega : " << fact_omega << endl ;
720  }
721 
722 
723  //----------------------------------------------------
724  // Adaptation of the mapping to the new enthalpy field
725  //----------------------------------------------------
726 
727  // Shall the adaptation be performed (cusp) ?
728  // ------------------------------------------
729 
730  double dent_eq = ent().dsdr()(l_b, k_b, j_b, i_b) ;
731  double dent_pole = ent().dsdr()(l_b, k_b, 0, i_b) ;
732  double rap_dent = fabs( dent_eq / dent_pole ) ;
733  cout << "| dH/dr_eq / dH/dr_pole | = " << rap_dent << endl ;
734 
735  if ( rap_dent < thres_adapt ) {
736  adapt_flag = 0 ; // No adaptation of the mapping
737  cout << "******* FROZEN MAPPING *********" << endl ;
738  }
739  else{
740  adapt_flag = 1 ; // The adaptation of the mapping is to be
741  // performed
742  }
743 
744  mp_prev = mp_et ;
745 
746  mp.adapt(ent(), par_adapt) ;
747 
748  //----------------------------------------------------
749  // Computation of the enthalpy at the new grid points
750  //----------------------------------------------------
751 
752  mp_prev.homothetie(alpha_r) ;
753 
754  mp.reevaluate(&mp_prev, nzet+1, ent.set()) ;
755 
756 
757  //----------------------------------------------------
758  // Equation of state
759  //----------------------------------------------------
760 
761  equation_of_state() ; // computes new values for nbar (n), ener (e)
762  // and press (p) from the new ent (H)
763 
764  //---------------------------------------------------------
765  // Matter source terms in the gravitational field equations
766  //---------------------------------------------------------
767 
768  //## Computation of tnphi and nphi from the Cartesian components
769  // of the shift for the test in hydro_euler():
770 
771  fait_nphi() ;
772 
773  hydro_euler() ; // computes new values for ener_euler (E),
774  // s_euler (S) and u_euler (U^i)
775 
776  if (relativistic) {
777 
778  //-------------------------------------------------------
779  // 2-D Poisson equation for tggg
780  //-------------------------------------------------------
781 
782  mp.poisson2d(source_tggg(), mp.cmp_zero(), par_poisson_tggg,
783  tggg.set()) ;
784 
785  //-------------------------------------------------------
786  // 2-D Poisson equation for dzeta
787  //-------------------------------------------------------
788 
789  mp.poisson2d(source_dzf(), source_dzq(), par_poisson_dzeta,
790  dzeta.set()) ;
791 
792  err_grv2 = lbda_grv2 - 1;
793  cout << "GRV2: " << err_grv2 << endl ;
794 
795  }
796  else {
797  err_grv2 = grv2() ;
798  }
799 
800 
801  //---------------------------------------
802  // Computation of the metric coefficients (except for N^phi)
803  //---------------------------------------
804 
805  // Relaxations on nu and dzeta :
806 
807  if (mer >= 10) {
808  logn = relax * logn + relax_prev * logn_prev ;
809 
810  dzeta = relax * dzeta + relax_prev * dzeta_prev ;
811  }
812 
813  // Update of the metric coefficients N, A, B and computation of K_ij :
814 
815  update_metric() ;
816 
817  //-----------------------
818  // Informations display
819  //-----------------------
820 
821  partial_display(cout) ;
822  fichfreq << " " << omega_c / (2*M_PI) * f_unit ;
823  fichevol << " " << rap_dent ;
824  fichevol << " " << ray_pole() / ray_eq() ;
825  fichevol << " " << ent_c ;
826 
827  //-----------------------------------------
828  // Convergence towards a given baryon mass
829  //-----------------------------------------
830 
831  if (mer > mer_mass) {
832 
833  double xx ;
834  if (mbar_wanted > 0.) {
835  xx = mass_b() / mbar_wanted - 1. ;
836  cout << "Discrep. baryon mass <-> wanted bar. mass : " << xx
837  << endl ;
838  }
839  else{
840  xx = mass_g() / fabs(mbar_wanted) - 1. ;
841  cout << "Discrep. grav. mass <-> wanted grav. mass : " << xx
842  << endl ;
843  }
844  double xprog = ( mer > 2*mer_mass) ? 1. :
845  double(mer-mer_mass)/double(mer_mass) ;
846  xx *= xprog ;
847  double ax = .5 * ( 2. + xx ) / (1. + xx ) ;
848  double fact = pow(ax, aexp_mass) ;
849  cout << " xprog, xx, ax, fact : " << xprog << " " <<
850  xx << " " << ax << " " << fact << endl ;
851 
852  if ( change_ent ) {
853  ent_c *= fact ;
854  }
855  else {
856  if (mer%4 == 0) omega_c *= fact ;
857  }
858  }
859 
860 
861  //------------------------------------------------------------
862  // Relative change in enthalpy with respect to previous step
863  //------------------------------------------------------------
864 
865  Tbl diff_ent_tbl = diffrel( ent(), ent_prev() ) ;
866  diff_ent = diff_ent_tbl(0) ;
867  for (int l=1; l<nzet; l++) {
868  diff_ent += diff_ent_tbl(l) ;
869  }
870  diff_ent /= nzet ;
871 
872  fichconv << " " << log10( fabs(diff_ent) + 1.e-16 ) ;
873  fichconv << " " << log10( fabs(err_grv2) + 1.e-16 ) ;
874  fichconv << " " << log10( fabs(max_triax) + 1.e-16 ) ;
875 
876  vit_triax = 0 ;
877  if ( (mer > mer_triax+1) && (max_triax_prev > 1e-13) ) {
878  vit_triax = (max_triax - max_triax_prev) / max_triax_prev ;
879  }
880 
881  fichconv << " " << vit_triax ;
882 
883  //------------------------------
884  // Recycling for the next step
885  //------------------------------
886 
887  ent_prev = ent ;
888  logn_prev = logn ;
889  dzeta_prev = dzeta ;
890  max_triax_prev = max_triax ;
891 
892  fichconv << endl ;
893  fichfreq << endl ;
894  fichevol << endl ;
895  fichconv.flush() ;
896  fichfreq.flush() ;
897  fichevol.flush() ;
898 
899  } // End of main loop
900 
901  //=========================================================================
902  // End of iteration
903  //=========================================================================
904 
905  fichconv.close() ;
906  fichfreq.close() ;
907  fichevol.close() ;
908 
909 
910 }
911 }
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:446
void mult_rsint()
Multiplication by .
Definition: cmp_r_manip.C:116
Valeur va
The numerical value of the Cmp
Definition: cmp.h:464
void std_base_scal()
Sets the spectral bases of the Valeur va to the standard ones for a scalar.
Definition: cmp.C:644
void annule(int l)
Sets the Cmp to zero in a given domain.
Definition: cmp.C:348
Active physical coordinates and mapping derivatives.
Definition: coord.h:90
void fait_omega_field(double omeg_min, double omeg_max, double precis, int nitermax)
Computes (member omega_field ).
Tenseur prim_field
Field .
Definition: et_rot_diff.h:111
virtual void hydro_euler()
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid fram...
Tenseur omega_field
Field .
Definition: et_rot_diff.h:105
Tbl par_frot
Parameters of the function .
Definition: et_rot_diff.h:102
virtual void equilibrium(double ent_c, double omega0, double fact_omega, int nzadapt, const Tbl &ent_limit, const Itbl &icontrol, const Tbl &control, double mbar_wanted, double aexp_mass, Tbl &diff, Param *=0x0)
Computes an equilibrium configuration.
Tenseur ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for .
Definition: etoile.h:1625
Tenseur uuu
Norm of u_euler.
Definition: etoile.h:1518
double omega
Rotation angular velocity ([f_unit] )
Definition: etoile.h:1501
Tenseur & logn
Metric potential = logn_auto.
Definition: etoile.h:1521
Tenseur nuq
Part of the Metric potential = logn generated by the quadratic terms.
Definition: etoile.h:1531
virtual double mass_g() const
Gravitational mass.
Tenseur khi_shift
Scalar used in the decomposition of shift , following Shibata's prescription [Prog.
Definition: etoile.h:1560
Tenseur tggg
Metric potential .
Definition: etoile.h:1537
Tenseur nuf
Part of the Metric potential = logn generated by the matter terms.
Definition: etoile.h:1526
Cmp ssjm1_tggg
Effective source at the previous step for the resolution of the Poisson equation for tggg .
Definition: etoile.h:1608
Tenseur nphi
Metric coefficient .
Definition: etoile.h:1510
virtual double mass_b() const
Baryon mass.
Tenseur bbb
Metric factor B.
Definition: etoile.h:1504
void update_metric()
Computes metric coefficients from known potentials.
Definition: et_rot_upmetr.C:69
Tenseur ak_car
Scalar .
Definition: etoile.h:1586
Tenseur & dzeta
Metric potential = beta_auto.
Definition: etoile.h:1534
Cmp ssjm1_nuf
Effective source at the previous step for the resolution of the Poisson equation for nuf by means of ...
Definition: etoile.h:1592
virtual double grv2() const
Error on the virial identity GRV2.
void fait_nphi()
Computes tnphi and nphi from the Cartesian components of the shift, stored in shift .
Definition: etoile_rot.C:781
Cmp ssjm1_khi
Effective source at the previous step for the resolution of the Poisson equation for the scalar by m...
Definition: etoile.h:1616
Tenseur_sym tkij
Tensor related to the extrinsic curvature tensor by .
Definition: etoile.h:1567
Cmp ssjm1_nuq
Effective source at the previous step for the resolution of the Poisson equation for nuq by means of ...
Definition: etoile.h:1598
Tenseur w_shift
Vector used in the decomposition of shift , following Shibata's prescription [Prog.
Definition: etoile.h:1550
virtual void partial_display(ostream &) const
Printing of some informations, excluding all global quantities.
Definition: etoile_rot.C:630
int nzet
Number of domains of *mp occupied by the star.
Definition: etoile.h:432
double ray_eq() const
Coordinate radius at , [r_unit].
Tenseur nnn
Total lapse function.
Definition: etoile.h:509
Tenseur nbar
Baryon density in the fluid frame.
Definition: etoile.h:459
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
Tenseur gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition: etoile.h:471
Map & mp
Mapping associated with the star.
Definition: etoile.h:429
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 shift
Total shift vector.
Definition: etoile.h:512
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 a_car
Total conformal factor .
Definition: etoile.h:515
double ray_pole() const
Coordinate radius at [r_unit].
Basic integer array class.
Definition: itbl.h:122
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 reevaluate(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.
Coord sint
Definition: map.h:721
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:765
virtual void adapt(const Cmp &ent, const Param &par, int nbr=0)=0
Adaptation of the mapping to a given scalar field.
virtual void poisson2d(const Cmp &source_mat, const Cmp &source_quad, Param &par, Cmp &uu) const =0
Computes the solution of a 2-D Poisson equation.
Coord phi
coordinate centered on the grid
Definition: map.h:720
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
const Cmp & cmp_zero() const
Returns the null Cmp defined on *this.
Definition: map.h:807
Multi-domain grid.
Definition: grilles.h:273
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
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_double_mod(double &x, int position=0)
Adds the address of a new modifiable double to the list.
Definition: param.C:453
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 set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition: tenseur.C:1170
const Tenseur & gradient_spher() const
Returns the gradient of *this (Spherical coordinates) (scalar field only).
Definition: tenseur.C:1548
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(double lambda, Param &par, Tenseur &shift, Tenseur &vect, Tenseur &scal) const
Solves the vectorial Poisson equation : .
Definition: tenseur_pde.C:118
int get_etat() const
Returns the logical state.
Definition: tenseur.h:707
Values and coefficients of a (real-value) function.
Definition: valeur.h:287
Mtbl_cf * c_cf
Coefficients of the spectral expansion of the function.
Definition: valeur.h:302
void coef() const
Computes the coeffcients of *this.
Definition: valeur_coef.C:148
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
Cmp log10(const Cmp &)
Basis 10 logarithm.
Definition: cmp_math.C:322
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition: cmp_math.C:504
Cmp pow(const Cmp &, int)
Power .
Definition: cmp_math.C:348
Cmp cos(const Cmp &)
Cosine.
Definition: cmp_math.C:94
Cmp abs(const Cmp &)
Absolute value.
Definition: cmp_math.C:410
Cmp log(const Cmp &)
Neperian logarithm.
Definition: cmp_math.C:296
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...
Lorene prototypes.
Definition: app_hor.h:64
Standard units of space, time and mass.