LORENE
star_rot_equil.C
1 /*
2  * Method Star_rot::equilibrium
3  *
4  * (see file star_h.h for documentation)
5  *
6  */
7 
8 /*
9  * Copyright (c) 2010 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 star_rot_equil_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star/star_rot_equil.C,v 1.6 2014/10/13 08:53:39 j_novak Exp $" ;
31 
32 /*
33  * $Id: star_rot_equil.C,v 1.6 2014/10/13 08:53:39 j_novak Exp $
34  * $Log: star_rot_equil.C,v $
35  * Revision 1.6 2014/10/13 08:53:39 j_novak
36  * Lorene classes and functions now belong to the namespace Lorene.
37  *
38  * Revision 1.5 2014/10/06 15:13:17 j_novak
39  * Modified #include directives to use c++ syntax.
40  *
41  * Revision 1.4 2010/01/26 16:49:53 e_gourgoulhon
42  * Reformated some outputs to the screen.
43  *
44  * Revision 1.3 2010/01/26 10:49:43 e_gourgoulhon
45  * First working version.
46  *
47  * Revision 1.2 2010/01/25 22:32:38 e_gourgoulhon
48  * Start of real implementation
49  *
50  * Revision 1.1 2010/01/25 18:15:52 e_gourgoulhon
51  * First version.
52  *
53  *
54  * $Header: /cvsroot/Lorene/C++/Source/Star/star_rot_equil.C,v 1.6 2014/10/13 08:53:39 j_novak Exp $
55  *
56  */
57 
58 // Headers C
59 #include <cmath>
60 
61 // Headers Lorene
62 #include "star_rot.h"
63 #include "param.h"
64 #include "tenseur.h"
65 
66 #include "graphique.h"
67 #include "utilitaires.h"
68 #include "unites.h"
69 
70 namespace Lorene {
71 void Star_rot::equilibrium(double ent_c, double omega0, double fact_omega,
72  int nzadapt, const Tbl& ent_limit, const Itbl& icontrol,
73  const Tbl& control, double mbar_wanted,
74  double aexp_mass, Tbl& diff, Param*) {
75 
76  // Fundamental constants and units
77  // -------------------------------
78 
79  using namespace Unites ;
80 
81  // For the display
82  // ---------------
83  char display_bold[]="x[1m" ; display_bold[0] = 27 ;
84  char display_normal[] = "x[0m" ; display_normal[0] = 27 ;
85 
86  // Grid parameters
87  // ---------------
88 
89  const Mg3d* mg = mp.get_mg() ;
90  int nz = mg->get_nzone() ; // total number of domains
91  int nzm1 = nz - 1 ;
92 
93  // The following is required to initialize mp_prev as a Map_et:
94  Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
95 
96  // Index of the point at phi=0, theta=pi/2 at the surface of the star:
97  assert(mg->get_type_t() == SYM) ;
98  int l_b = nzet - 1 ;
99  int i_b = mg->get_nr(l_b) - 1 ;
100  int j_b = mg->get_nt(l_b) - 1 ;
101  int k_b = 0 ;
102 
103  // Value of the enthalpy defining the surface of the star
104  double ent_b = ent_limit(nzet-1) ;
105 
106  // Parameters to control the iteration
107  // -----------------------------------
108 
109  int mer_max = icontrol(0) ;
110  int mer_rot = icontrol(1) ;
111  int mer_change_omega = icontrol(2) ;
112  int mer_fix_omega = icontrol(3) ;
113  int mer_mass = icontrol(4) ;
114  int mermax_poisson = icontrol(5) ;
115  int mer_triax = icontrol(6) ;
116  int delta_mer_kep = icontrol(7) ;
117 
118  // Protections:
119  if (mer_change_omega < mer_rot) {
120  cout << "Star_rot::equilibrium: mer_change_omega < mer_rot !" << endl ;
121  cout << " mer_change_omega = " << mer_change_omega << endl ;
122  cout << " mer_rot = " << mer_rot << endl ;
123  abort() ;
124  }
125  if (mer_fix_omega < mer_change_omega) {
126  cout << "Star_rot::equilibrium: mer_fix_omega < mer_change_omega !"
127  << endl ;
128  cout << " mer_fix_omega = " << mer_fix_omega << endl ;
129  cout << " mer_change_omega = " << mer_change_omega << endl ;
130  abort() ;
131  }
132 
133  // In order to converge to a given baryon mass, shall the central
134  // enthalpy be varied or Omega ?
135  bool change_ent = true ;
136  if (mer_mass < 0) {
137  change_ent = false ;
138  mer_mass = abs(mer_mass) ;
139  }
140 
141  double precis = control(0) ;
142  double omega_ini = control(1) ;
143  double relax = control(2) ;
144  double relax_prev = double(1) - relax ;
145  double relax_poisson = control(3) ;
146  double thres_adapt = control(4) ;
147  double ampli_triax = control(5) ;
148  double precis_adapt = control(6) ;
149 
150 
151  // Error indicators
152  // ----------------
153 
154  diff.set_etat_qcq() ;
155  double& diff_ent = diff.set(0) ;
156  double& diff_nuf = diff.set(1) ;
157  double& diff_nuq = diff.set(2) ;
158 // double& diff_dzeta = diff.set(3) ;
159 // double& diff_ggg = diff.set(4) ;
160  double& diff_shift_x = diff.set(5) ;
161  double& diff_shift_y = diff.set(6) ;
162  double& vit_triax = diff.set(7) ;
163 
164  // Parameters for the function Map_et::adapt
165  // -----------------------------------------
166 
167  Param par_adapt ;
168  int nitermax = 100 ;
169  int niter ;
170  int adapt_flag = 1 ; // 1 = performs the full computation,
171  // 0 = performs only the rescaling by
172  // the factor alpha_r
173  int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
174  // isosurfaces
175  double alpha_r ;
176  double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
177 
178  par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
179  // locate zeros by the secant method
180  par_adapt.add_int(nzadapt, 1) ; // number of domains where the adjustment
181  // to the isosurfaces of ent is to be
182  // performed
183  par_adapt.add_int(nz_search, 2) ; // number of domains to search for
184  // the enthalpy isosurface
185  par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
186  // 0 = performs only the rescaling by
187  // the factor alpha_r
188  par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
189  // (theta_*, phi_*)
190  par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
191  // (theta_*, phi_*)
192 
193  par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
194  // the secant method
195 
196  par_adapt.add_double(precis_adapt, 0) ; // required absolute precision in
197  // the determination of zeros by
198  // the secant method
199  par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
200 
201  par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
202  // distances will be multiplied
203 
204  par_adapt.add_tbl(ent_limit, 0) ; // array of values of the field ent
205  // to define the isosurfaces.
206 
207  // Parameters for the function Map_et::poisson for nuf
208  // ----------------------------------------------------
209 
210  double precis_poisson = 1.e-16 ;
211 
212  Cmp cssjm1_nuf(ssjm1_nuf) ;
213  Cmp cssjm1_nuq(ssjm1_nuq) ;
214  Cmp cssjm1_tggg(ssjm1_tggg) ;
215  Cmp cssjm1_khi(ssjm1_khi) ;
216  Tenseur cssjm1_wshift(mp, 1, CON, mp.get_bvect_cart() ) ;
217  cssjm1_wshift.set_etat_qcq() ;
218  for (int i=1; i<=3; i++) {
219  cssjm1_wshift.set(i-1) = ssjm1_wshift(i) ;
220  }
221 
222  Tenseur cshift(mp, 1, CON, mp.get_bvect_cart() ) ;
223  cshift.set_etat_qcq() ;
224  for (int i=1; i<=3; i++) {
225  cshift.set(i-1) = -beta(i) ;
226  }
227 
228  Tenseur cw_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
229  cw_shift.set_etat_qcq() ;
230  for (int i=1; i<=3; i++) {
231  cw_shift.set(i-1) = w_shift(i) ;
232  }
233 
234  Tenseur ckhi_shift(mp) ;
235  ckhi_shift.set_etat_qcq() ;
236  ckhi_shift.set() = khi_shift ;
237 
238  Param par_poisson_nuf ;
239  par_poisson_nuf.add_int(mermax_poisson, 0) ; // maximum number of iterations
240  par_poisson_nuf.add_double(relax_poisson, 0) ; // relaxation parameter
241  par_poisson_nuf.add_double(precis_poisson, 1) ; // required precision
242  par_poisson_nuf.add_int_mod(niter, 0) ; // number of iterations actually used
243  par_poisson_nuf.add_cmp_mod( cssjm1_nuf ) ;
244 
245  Param par_poisson_nuq ;
246  par_poisson_nuq.add_int(mermax_poisson, 0) ; // maximum number of iterations
247  par_poisson_nuq.add_double(relax_poisson, 0) ; // relaxation parameter
248  par_poisson_nuq.add_double(precis_poisson, 1) ; // required precision
249  par_poisson_nuq.add_int_mod(niter, 0) ; // number of iterations actually used
250  par_poisson_nuq.add_cmp_mod( cssjm1_nuq ) ;
251 
252  Param par_poisson_tggg ;
253  par_poisson_tggg.add_int(mermax_poisson, 0) ; // maximum number of iterations
254  par_poisson_tggg.add_double(relax_poisson, 0) ; // relaxation parameter
255  par_poisson_tggg.add_double(precis_poisson, 1) ; // required precision
256  par_poisson_tggg.add_int_mod(niter, 0) ; // number of iterations actually used
257  par_poisson_tggg.add_cmp_mod( cssjm1_tggg ) ;
258  double lambda_tggg ;
259  par_poisson_tggg.add_double_mod( lambda_tggg ) ;
260 
261  Param par_poisson_dzeta ;
262  double lbda_grv2 ;
263  par_poisson_dzeta.add_double_mod( lbda_grv2 ) ;
264 
265  // Parameters for the function Scalar::poisson_vect
266  // -------------------------------------------------
267 
268  Param par_poisson_vect ;
269 
270  par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of iterations
271  par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
272  par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
273  par_poisson_vect.add_cmp_mod( cssjm1_khi ) ;
274  par_poisson_vect.add_tenseur_mod( cssjm1_wshift ) ;
275  par_poisson_vect.add_int_mod(niter, 0) ;
276 
277 
278  // Initializations
279  // ---------------
280 
281  // Initial angular velocity
282  omega = 0 ;
283 
284  double accrois_omega = (omega0 - omega_ini) /
285  double(mer_fix_omega - mer_change_omega) ;
286 
287 
288  update_metric() ; // update of the metric coefficients
289 
290  equation_of_state() ; // update of the density, pressure, etc...
291 
292  hydro_euler() ; // update of the hydro quantities relative to the
293  // Eulerian observer
294 
295  // Quantities at the previous step :
296  Map_et mp_prev = mp_et ;
297  Scalar ent_prev = ent ;
298  Scalar logn_prev = logn ;
299  Scalar dzeta_prev = dzeta ;
300 
301  // Creation of uninitialized tensors:
302  Scalar source_nuf(mp) ; // source term in the equation for nuf
303  Scalar source_nuq(mp) ; // source term in the equation for nuq
304  Scalar source_dzf(mp) ; // matter source term in the eq. for dzeta
305  Scalar source_dzq(mp) ; // quadratic source term in the eq. for dzeta
306  Scalar source_tggg(mp) ; // source term in the eq. for tggg
307  Vector source_shift(mp, CON, mp.get_bvect_cart()) ;
308  // source term for shift
309  Scalar mlngamma(mp) ; // centrifugal potential
310 
311 
312  ofstream fichconv("convergence.d") ; // Output file for diff_ent
313  fichconv << "# diff_ent GRV2 max_triax vit_triax" << endl ;
314 
315  ofstream fichfreq("frequency.d") ; // Output file for omega
316  fichfreq << "# f [Hz]" << endl ;
317 
318  ofstream fichevol("evolution.d") ; // Output file for various quantities
319  fichevol <<
320  "# |dH/dr_eq/dH/dr_pole| r_pole/r_eq ent_c"
321  << endl ;
322 
323  diff_ent = 1 ;
324  double err_grv2 = 1 ;
325  double max_triax_prev = 0 ; // Triaxial amplitude at previous step
326 
327  //=========================================================================
328  // Start of iteration
329  //=========================================================================
330 
331  for(int mer=0 ; (diff_ent > precis) && (mer<mer_max) ; mer++ ) {
332 
333  cout << "-----------------------------------------------" << endl ;
334  cout << "step: " << mer << endl ;
335  cout << "diff_ent = " << display_bold << diff_ent << display_normal
336  << endl ;
337  cout << "err_grv2 = " << err_grv2 << endl ;
338  fichconv << mer ;
339  fichfreq << mer ;
340  fichevol << mer ;
341 
342  if (mer >= mer_rot) {
343 
344  if (mer < mer_change_omega) {
345  omega = omega_ini ;
346  }
347  else {
348  if (mer <= mer_fix_omega) {
349  omega = omega_ini + accrois_omega *
350  (mer - mer_change_omega) ;
351  }
352  }
353 
354  }
355 
356  //-----------------------------------------------
357  // Sources of the Poisson equations
358  //-----------------------------------------------
359 
360  // Source for nu
361  // -------------
362  Scalar bet = log(bbb) ;
363  bet.std_spectral_base() ;
364 
365  Vector d_logn = logn.derive_cov( mp.flat_met_spher() ) ;
366  Vector d_bet = bet.derive_cov( mp.flat_met_spher() ) ;
367 
368  if (relativistic) {
369  source_nuf = qpig * a_car *( ener_euler + s_euler ) ;
370 
371  source_nuq = ak_car - d_logn(1)*(d_logn(1)+d_bet(1))
372  - d_logn(2)*(d_logn(2)+d_bet(2))
373  - d_logn(3)*(d_logn(3)+d_bet(3)) ;
374  }
375  else {
376  source_nuf = qpig * nbar ;
377 
378  source_nuq = 0 ;
379  }
380  source_nuf.std_spectral_base() ;
381  source_nuq.std_spectral_base() ;
382 
383  // Source for dzeta
384  // ----------------
385  source_dzf = 2 * qpig * a_car * (press + (ener_euler+press) * uuu*uuu ) ;
386  source_dzf.std_spectral_base() ;
387 
388  source_dzq = 1.5 * ak_car
389  - d_logn(1)*d_logn(1) - d_logn(2)*d_logn(2) - d_logn(3)*d_logn(3) ;
390  source_dzq.std_spectral_base() ;
391 
392  // Source for tggg
393  // ---------------
394 
395  source_tggg = 4 * qpig * nn * a_car * bbb * press ;
396  source_tggg.std_spectral_base() ;
397 
398  source_tggg.mult_rsint() ;
399 
400 
401  // Source for shift
402  // ----------------
403 
404  // Matter term:
405  source_shift = (-4*qpig) * nn * a_car * (ener_euler + press)
406  * u_euler ;
407 
408  // Quadratic terms:
409  Vector vtmp = 6 * bet.derive_con( mp.flat_met_spher() )
410  - 2 * logn.derive_con( mp.flat_met_spher() ) ;
411  vtmp.change_triad(mp.get_bvect_cart()) ;
412 
413  Vector squad = nn * contract(tkij, 1, vtmp, 0) ;
414 
415  source_shift = source_shift + squad.up(0, mp.flat_met_cart() ) ;
416 
417  //----------------------------------------------
418  // Resolution of the Poisson equation for nuf
419  //----------------------------------------------
420 
421  source_nuf.poisson(par_poisson_nuf, nuf) ;
422 
423  cout << "Test of the Poisson equation for nuf :" << endl ;
424  Tbl err = source_nuf.test_poisson(nuf, cout, true) ;
425  diff_nuf = err(0, 0) ;
426 
427  //---------------------------------------
428  // Triaxial perturbation of nuf
429  //---------------------------------------
430 
431  if (mer == mer_triax) {
432 
433  if ( mg->get_np(0) == 1 ) {
434  cout <<
435  "Star_rot::equilibrium: np must be stricly greater than 1"
436  << endl << " to set a triaxial perturbation !" << endl ;
437  abort() ;
438  }
439 
440  const Coord& phi = mp.phi ;
441  const Coord& sint = mp.sint ;
442  Scalar perturb(mp) ;
443  perturb = 1 + ampli_triax * sint*sint * cos(2*phi) ;
444  nuf = nuf * perturb ;
445 
446  nuf.std_spectral_base() ; // set the bases for spectral expansions
447  // to be the standard ones for a
448  // scalar field
449 
450  }
451 
452  // Monitoring of the triaxial perturbation
453  // ---------------------------------------
454 
455  const Valeur& va_nuf = nuf.get_spectral_va() ;
456  va_nuf.coef() ; // Computes the spectral coefficients
457  double max_triax = 0 ;
458 
459  if ( mg->get_np(0) > 1 ) {
460 
461  for (int l=0; l<nz; l++) { // loop on the domains
462  for (int j=0; j<mg->get_nt(l); j++) {
463  for (int i=0; i<mg->get_nr(l); i++) {
464 
465  // Coefficient of cos(2 phi) :
466  double xcos2p = (*(va_nuf.c_cf))(l, 2, j, i) ;
467 
468  // Coefficient of sin(2 phi) :
469  double xsin2p = (*(va_nuf.c_cf))(l, 3, j, i) ;
470 
471  double xx = sqrt( xcos2p*xcos2p + xsin2p*xsin2p ) ;
472 
473  max_triax = ( xx > max_triax ) ? xx : max_triax ;
474  }
475  }
476  }
477 
478  }
479 
480  cout << "Triaxial part of nuf : " << max_triax << endl ;
481 
482  if (relativistic) {
483 
484  //----------------------------------------------
485  // Resolution of the Poisson equation for nuq
486  //----------------------------------------------
487 
488  source_nuq.poisson(par_poisson_nuq, nuq) ;
489 
490  cout << "Test of the Poisson equation for nuq :" << endl ;
491  err = source_nuq.test_poisson(nuq, cout, true) ;
492  diff_nuq = err(0, 0) ;
493 
494  //---------------------------------------------------------
495  // Resolution of the vector Poisson equation for the shift
496  //---------------------------------------------------------
497 
498 
499  for (int i=1; i<=3; i++) {
500  if(source_shift(i).get_etat() != ETATZERO) {
501  if(source_shift(i).dz_nonzero()) {
502  assert( source_shift(i).get_dzpuis() == 4 ) ;
503  }
504  else{
505  (source_shift.set(i)).set_dzpuis(4) ;
506  }
507  }
508  }
509 
510  double lambda_shift = double(1) / double(3) ;
511 
512  if ( mg->get_np(0) == 1 ) {
513  lambda_shift = 0 ;
514  }
515 
516  Tenseur csource_shift(mp, 1, CON, mp.get_bvect_cart() ) ;
517  csource_shift.set_etat_qcq() ;
518  for (int i=1; i<=3; i++) {
519  csource_shift.set(i-1) = source_shift(i) ;
520  }
521  csource_shift.set(2).set_etat_zero() ; //## bizarre...
522 
523  csource_shift.poisson_vect(lambda_shift, par_poisson_vect,
524  cshift, cw_shift, ckhi_shift) ;
525 
526  for (int i=1; i<=3; i++) {
527  beta.set(i) = - cshift(i-1) ;
528  beta.set(i).set_dzpuis(0) ; //## bizarre...
529  w_shift.set(i) = cw_shift(i-1) ;
530  }
531  khi_shift = ckhi_shift() ;
532 
533  cout << "Test of the Poisson equation for shift_x :" << endl ;
534  err = source_shift(1).test_poisson(-beta(1), cout, true) ;
535  diff_shift_x = err(0, 0) ;
536 
537  cout << "Test of the Poisson equation for shift_y :" << endl ;
538  err = source_shift(2).test_poisson(-beta(2), cout, true) ;
539  diff_shift_y = err(0, 0) ;
540 
541  // Computation of tnphi and nphi from the Cartesian components
542  // of the shift
543  // -----------------------------------------------------------
544 
545  fait_nphi() ;
546 
547  }
548 
549  //-----------------------------------------
550  // Determination of the fluid velociy U
551  //-----------------------------------------
552 
553  if (mer > mer_fix_omega + delta_mer_kep) {
554 
555  omega *= fact_omega ; // Increase of the angular velocity if
556  } // fact_omega != 1
557 
558  bool omega_trop_grand = false ;
559  bool kepler = true ;
560 
561  while ( kepler ) {
562 
563  // Possible decrease of Omega to ensure a velocity < c
564 
565  bool superlum = true ;
566 
567  while ( superlum ) {
568 
569  // New fluid velocity U :
570 
571  Scalar tmp = omega - nphi ;
572  tmp.annule_domain(nzm1) ;
573  tmp.std_spectral_base() ;
574 
575  tmp.mult_rsint() ; // Multiplication by r sin(theta)
576 
577  uuu = bbb / nn * tmp ;
578 
579  if (uuu.get_etat() == ETATQCQ) {
580  // Same basis as (Omega -N^phi) r sin(theta) :
581  (uuu.set_spectral_va()).set_base( tmp.get_spectral_va().get_base() ) ;
582  }
583 
584  // Is the new velocity larger than c in the equatorial plane ?
585 
586  superlum = false ;
587 
588  for (int l=0; l<nzet; l++) {
589  for (int i=0; i<mg->get_nr(l); i++) {
590 
591  double u1 = uuu.val_grid_point(l, 0, j_b, i) ;
592  if (u1 >= 1.) { // superluminal velocity
593  superlum = true ;
594  cout << "U > c for l, i : " << l << " " << i
595  << " U = " << u1 << endl ;
596  }
597  }
598  }
599  if ( superlum ) {
600  cout << "**** VELOCITY OF LIGHT REACHED ****" << endl ;
601  omega /= fact_omega ; // Decrease of Omega
602  cout << "New rotation frequency : "
603  << omega/(2.*M_PI) * f_unit << " Hz" << endl ;
604  omega_trop_grand = true ;
605  }
606  } // end of while ( superlum )
607 
608 
609  // New computation of U (which this time is not superluminal)
610  // as well as of gam_euler, ener_euler, etc...
611  // -----------------------------------
612 
613  hydro_euler() ;
614 
615 
616  //------------------------------------------------------
617  // First integral of motion
618  //------------------------------------------------------
619 
620  // Centrifugal potential :
621  if (relativistic) {
622  mlngamma = - log( gam_euler ) ;
623  }
624  else {
625  mlngamma = - 0.5 * uuu*uuu ;
626  }
627 
628  // Equatorial values of various potentials :
629  double nuf_b = nuf.val_grid_point(l_b, k_b, j_b, i_b) ;
630  double nuq_b = nuq.val_grid_point(l_b, k_b, j_b, i_b) ;
631  double mlngamma_b = mlngamma.val_grid_point(l_b, k_b, j_b, i_b) ;
632 
633  // Central values of various potentials :
634  double nuf_c = nuf.val_grid_point(0,0,0,0) ;
635  double nuq_c = nuq.val_grid_point(0,0,0,0) ;
636  double mlngamma_c = 0 ;
637 
638  // Scale factor to ensure that the enthalpy is equal to ent_b at
639  // the equator
640  double alpha_r2 = ( ent_c - ent_b + mlngamma_c - mlngamma_b
641  + nuq_c - nuq_b) / ( nuf_b - nuf_c ) ;
642  alpha_r = sqrt(alpha_r2) ;
643  cout << "alpha_r = " << alpha_r << endl ;
644 
645  // Readjustment of nu :
646  // -------------------
647 
648  logn = alpha_r2 * nuf + nuq ;
649  double nu_c = logn.val_grid_point(0,0,0,0) ;
650 
651  // First integral --> enthalpy in all space
652  //-----------------
653 
654  ent = (ent_c + nu_c + mlngamma_c) - logn - mlngamma ;
655 
656  // Test: is the enthalpy negative somewhere in the equatorial plane
657  // inside the star ? If yes, this means that the Keplerian velocity
658  // has been overstep.
659 
660  kepler = false ;
661  for (int l=0; l<nzet; l++) {
662  int imax = mg->get_nr(l) - 1 ;
663  if (l == l_b) imax-- ; // The surface point is skipped
664  for (int i=0; i<imax; i++) {
665  if ( ent.val_grid_point(l, 0, j_b, i) < 0. ) {
666  kepler = true ;
667  cout << "ent < 0 for l, i : " << l << " " << i
668  << " ent = " << ent.val_grid_point(l, 0, j_b, i) << endl ;
669  }
670  }
671  }
672 
673  if ( kepler ) {
674  cout << "**** KEPLERIAN VELOCITY REACHED ****" << endl ;
675  omega /= fact_omega ; // Omega is decreased
676  cout << "New rotation frequency : "
677  << omega/(2.*M_PI) * f_unit << " Hz" << endl ;
678  omega_trop_grand = true ;
679  }
680 
681  } // End of while ( kepler )
682 
683  if ( omega_trop_grand ) { // fact_omega is decreased for the
684  // next step
685  fact_omega = sqrt( fact_omega ) ;
686  cout << "**** New fact_omega : " << fact_omega << endl ;
687  }
688 
689  //----------------------------------------------------
690  // Adaptation of the mapping to the new enthalpy field
691  //----------------------------------------------------
692 
693  // Shall the adaptation be performed (cusp) ?
694  // ------------------------------------------
695 
696  double dent_eq = ent.dsdr().val_grid_point(l_b, k_b, j_b, i_b) ;
697  double dent_pole = ent.dsdr().val_grid_point(l_b, k_b, 0, i_b) ;
698  double rap_dent = fabs( dent_eq / dent_pole ) ;
699  cout << "| dH/dr_eq / dH/dr_pole | = " << rap_dent << endl ;
700 
701  if ( rap_dent < thres_adapt ) {
702  adapt_flag = 0 ; // No adaptation of the mapping
703  cout << "******* FROZEN MAPPING *********" << endl ;
704  }
705  else{
706  adapt_flag = 1 ; // The adaptation of the mapping is to be
707  // performed
708  }
709 
710  mp_prev = mp_et ;
711 
712  Cmp cent(ent) ;
713  mp.adapt(cent, par_adapt) ;
714 
715  //----------------------------------------------------
716  // Computation of the enthalpy at the new grid points
717  //----------------------------------------------------
718 
719  mp_prev.homothetie(alpha_r) ;
720 
721  mp.reevaluate(&mp_prev, nzet+1, cent) ;
722  ent = cent ;
723 
724  //----------------------------------------------------
725  // Equation of state
726  //----------------------------------------------------
727 
728  equation_of_state() ; // computes new values for nbar (n), ener (e)
729  // and press (p) from the new ent (H)
730 
731  //---------------------------------------------------------
732  // Matter source terms in the gravitational field equations
733  //---------------------------------------------------------
734 
735  //## Computation of tnphi and nphi from the Cartesian components
736  // of the shift for the test in hydro_euler():
737 
738  fait_nphi() ;
739 
740  hydro_euler() ; // computes new values for ener_euler (E),
741  // s_euler (S) and u_euler (U^i)
742 
743  if (relativistic) {
744 
745  //-------------------------------------------------------
746  // 2-D Poisson equation for tggg
747  //-------------------------------------------------------
748 
749  Cmp csource_tggg(source_tggg) ;
750  Cmp ctggg(tggg) ;
751  mp.poisson2d(csource_tggg, mp.cmp_zero(), par_poisson_tggg,
752  ctggg) ;
753  tggg = ctggg ;
754 
755 
756  //-------------------------------------------------------
757  // 2-D Poisson equation for dzeta
758  //-------------------------------------------------------
759 
760  Cmp csource_dzf(source_dzf) ;
761  Cmp csource_dzq(source_dzq) ;
762  Cmp cdzeta(dzeta) ;
763  mp.poisson2d(csource_dzf, csource_dzq, par_poisson_dzeta,
764  cdzeta) ;
765  dzeta = cdzeta ;
766 
767  err_grv2 = lbda_grv2 - 1;
768  cout << "GRV2: " << err_grv2 << endl ;
769 
770  }
771  else {
772  err_grv2 = grv2() ;
773  }
774 
775 
776  //---------------------------------------
777  // Computation of the metric coefficients (except for N^phi)
778  //---------------------------------------
779 
780  // Relaxations on nu and dzeta :
781 
782  if (mer >= 10) {
783  logn = relax * logn + relax_prev * logn_prev ;
784 
785  dzeta = relax * dzeta + relax_prev * dzeta_prev ;
786  }
787 
788  // Update of the metric coefficients N, A, B and computation of K_ij :
789 
790  update_metric() ;
791 
792  //-----------------------
793  // Informations display
794  //-----------------------
795 
796  partial_display(cout) ;
797  fichfreq << " " << omega / (2*M_PI) * f_unit ;
798  fichevol << " " << rap_dent ;
799  fichevol << " " << ray_pole() / ray_eq() ;
800  fichevol << " " << ent_c ;
801 
802  //-----------------------------------------
803  // Convergence towards a given baryon mass
804  //-----------------------------------------
805 
806  if (mer > mer_mass) {
807 
808  double xx ;
809  if (mbar_wanted > 0.) {
810  xx = mass_b() / mbar_wanted - 1. ;
811  cout << "Discrep. baryon mass <-> wanted bar. mass : " << xx
812  << endl ;
813  }
814  else{
815  xx = mass_g() / fabs(mbar_wanted) - 1. ;
816  cout << "Discrep. grav. mass <-> wanted grav. mass : " << xx
817  << endl ;
818  }
819  double xprog = ( mer > 2*mer_mass) ? 1. :
820  double(mer-mer_mass)/double(mer_mass) ;
821  xx *= xprog ;
822  double ax = .5 * ( 2. + xx ) / (1. + xx ) ;
823  double fact = pow(ax, aexp_mass) ;
824  cout << " xprog, xx, ax, fact : " << xprog << " " <<
825  xx << " " << ax << " " << fact << endl ;
826 
827  if ( change_ent ) {
828  ent_c *= fact ;
829  }
830  else {
831  if (mer%4 == 0) omega *= fact ;
832  }
833  }
834 
835 
836  //------------------------------------------------------------
837  // Relative change in enthalpy with respect to previous step
838  //------------------------------------------------------------
839 
840  Tbl diff_ent_tbl = diffrel( ent, ent_prev ) ;
841  diff_ent = diff_ent_tbl(0) ;
842  for (int l=1; l<nzet; l++) {
843  diff_ent += diff_ent_tbl(l) ;
844  }
845  diff_ent /= nzet ;
846 
847  fichconv << " " << log10( fabs(diff_ent) + 1.e-16 ) ;
848  fichconv << " " << log10( fabs(err_grv2) + 1.e-16 ) ;
849  fichconv << " " << log10( fabs(max_triax) + 1.e-16 ) ;
850 
851  vit_triax = 0 ;
852  if ( (mer > mer_triax+1) && (max_triax_prev > 1e-13) ) {
853  vit_triax = (max_triax - max_triax_prev) / max_triax_prev ;
854  }
855 
856  fichconv << " " << vit_triax ;
857 
858  //------------------------------
859  // Recycling for the next step
860  //------------------------------
861 
862  ent_prev = ent ;
863  logn_prev = logn ;
864  dzeta_prev = dzeta ;
865  max_triax_prev = max_triax ;
866 
867  fichconv << endl ;
868  fichfreq << endl ;
869  fichevol << endl ;
870  fichconv.flush() ;
871  fichfreq.flush() ;
872  fichevol.flush() ;
873 
874  } // End of main loop
875 
876  //=========================================================================
877  // End of iteration
878  //=========================================================================
879 
880  ssjm1_nuf = cssjm1_nuf ;
881  ssjm1_nuq = cssjm1_nuq ;
882  ssjm1_tggg = cssjm1_tggg ;
883  ssjm1_khi = cssjm1_khi ;
884  for (int i=1; i<=3; i++) {
885  ssjm1_wshift.set(i) = cssjm1_wshift(i-1) ;
886  }
887 
888  fichconv.close() ;
889  fichfreq.close() ;
890  fichevol.close() ;
891 
892 }
893 }
Lorene::Map_et
Radial mapping of rather general form.
Definition: map.h:2752
Lorene::Star_rot::khi_shift
Scalar khi_shift
Scalar used in the decomposition of shift , following Shibata's prescription [Prog.
Definition: star_rot.h:160
Lorene::Star::nbar
Scalar nbar
Baryon density in the fluid frame.
Definition: star.h:192
Lorene::Star::logn
Scalar logn
Logarithm of the lapse N .
Definition: star.h:222
Lorene::Star_rot::partial_display
virtual void partial_display(ostream &) const
Printing of some informations, excluding all global quantities.
Definition: star_rot.C:590
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::Star_rot::ssjm1_khi
Scalar ssjm1_khi
Effective source at the previous step for the resolution of the Poisson equation for the scalar by m...
Definition: star_rot.h:216
Lorene::Tenseur
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition: tenseur.h:301
Lorene::Tensor::up
Tensor up(int ind, const Metric &gam) const
Computes a new tensor by raising an index of *this.
Definition: tensor_calculus.C:225
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition: valeur.h:287
Lorene::Star_rot::mass_g
virtual double mass_g() const
Gravitational mass.
Definition: star_rot_global.C:124
Lorene::Star::ray_eq
double ray_eq() const
Coordinate radius at , [r_unit].
Definition: star_global.C:108
Lorene::Star_rot::equilibrium
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.
Definition: star_rot_equil.C:71
Lorene::Mg3d
Multi-domain grid.
Definition: grilles.h:273
Lorene::Star_rot::update_metric
void update_metric()
Computes metric coefficients from known potentials.
Definition: star_rot_upmetr.C:51
Lorene::Star::gam_euler
Scalar gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition: star.h:204
Lorene::Tenseur::set
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition: tenseur.C:824
Lorene::Scalar::dsdr
const Scalar & dsdr() const
Returns of *this .
Definition: scalar_deriv.C:113
Lorene::Star_rot::omega
double omega
Rotation angular velocity ([f_unit] )
Definition: star_rot.h:101
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::Scalar::mult_rsint
void mult_rsint()
Multiplication by everywhere; dzpuis is not changed.
Definition: scalar_r_manip.C:281
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::Map::cmp_zero
const Cmp & cmp_zero() const
Returns the null Cmp defined on *this.
Definition: map.h:807
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::Star::press
Scalar press
Fluid pressure.
Definition: star.h:194
Lorene::Star::nzet
int nzet
Number of domains of *mp occupied by the star.
Definition: star.h:183
Lorene::Star_rot::nuf
Scalar nuf
Part of the Metric potential = logn generated by the matter terms.
Definition: star_rot.h:126
Lorene::Star_rot::bbb
Scalar bbb
Metric factor B.
Definition: star_rot.h:107
Lorene::Map::get_mg
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:765
Lorene::Map::flat_met_spher
const Metric_flat & flat_met_spher() const
Returns the flat metric associated with the spherical coordinates and with components expressed in th...
Definition: map.C:321
Lorene::Star_rot::relativistic
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition: star_rot.h:94
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::Scalar::derive_cov
const Vector & derive_cov(const Metric &gam) const
Returns the gradient (1-form = covariant vector) of *this
Definition: scalar_deriv.C:390
Lorene::Map::sint
Coord sint
Definition: map.h:721
Lorene::Star_rot::nphi
Scalar nphi
Metric coefficient .
Definition: star_rot.h:113
Lorene::Star_rot::grv2
virtual double grv2() const
Error on the virial identity GRV2.
Definition: star_rot_global.C:204
Lorene::Map::adapt
virtual void adapt(const Cmp &ent, const Param &par, int nbr=0)=0
Adaptation of the mapping to a given scalar field.
Lorene::abs
Cmp abs(const Cmp &)
Absolute value.
Definition: cmp_math.C:410
Lorene::Cmp::set_etat_zero
void set_etat_zero()
Sets the logical state to ETATZERO (zero).
Definition: cmp.C:289
Lorene::Itbl
Basic integer array class.
Definition: itbl.h:122
Lorene::Scalar
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:387
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::Star::nn
Scalar nn
Lapse function N .
Definition: star.h:225
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition: cmp_math.C:348
Lorene::Star_rot::nuq
Scalar nuq
Part of the Metric potential = logn generated by the quadratic terms.
Definition: star_rot.h:131
Lorene::Star_rot::mass_b
virtual double mass_b() const
Baryon mass.
Definition: star_rot_global.C:98
Lorene::Tensor::annule_domain
void annule_domain(int l)
Sets the Tensor to zero in a given domain.
Definition: tensor.C:666
Lorene::Vector::change_triad
virtual void change_triad(const Base_vect &)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition: vector_change_triad.C:75
Lorene::Valeur::coef
void coef() const
Computes the coeffcients of *this.
Definition: valeur_coef.C:148
Lorene::Scalar::get_spectral_va
const Valeur & get_spectral_va() const
Returns va (read only version)
Definition: scalar.h:601
Lorene::Scalar::set_spectral_va
Valeur & set_spectral_va()
Returns va (read/write version)
Definition: scalar.h:604
Lorene::Star::u_euler
Vector u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Definition: star.h:207
Lorene::Star_rot::ssjm1_tggg
Scalar ssjm1_tggg
Effective source at the previous step for the resolution of the Poisson equation for tggg .
Definition: star_rot.h:208
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::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::Star_rot::tkij
Sym_tensor tkij
Tensor related to the extrinsic curvature tensor by .
Definition: star_rot.h:167
Lorene::Coord
Active physical coordinates and mapping derivatives.
Definition: coord.h:90
Lorene::Star::equation_of_state
void equation_of_state()
Computes the proper baryon and energy density, as well as pressure from the enthalpy.
Definition: star.C:462
Lorene::Star::mp
Map & mp
Mapping associated with the star.
Definition: star.h:180
Lorene::Vector::set
Scalar & set(int)
Read/write access to a component.
Definition: vector.C:296
Lorene::Star_rot::hydro_euler
virtual void hydro_euler()
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid fram...
Definition: star_rot_hydro.C:57
Lorene::Map::reevaluate
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.
Lorene::Map::poisson2d
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.
Lorene::Star_rot::ssjm1_nuf
Scalar ssjm1_nuf
Effective source at the previous step for the resolution of the Poisson equation for nuf by means of ...
Definition: star_rot.h:192
Lorene::Star::ener_euler
Scalar ener_euler
Total energy density in the Eulerian frame.
Definition: star.h:198
Lorene::Star::ent
Scalar ent
Log-enthalpy.
Definition: star.h:190
Lorene::Cmp
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:446
Lorene::Star_rot::ssjm1_nuq
Scalar ssjm1_nuq
Effective source at the previous step for the resolution of the Poisson equation for nuq by means of ...
Definition: star_rot.h:198
Lorene::Tbl
Basic array class.
Definition: tbl.h:161
Lorene::Map::flat_met_cart
const Metric_flat & flat_met_cart() const
Returns the flat metric associated with the Cartesian coordinates and with components expressed in th...
Definition: map.C:331
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::Map::get_bvect_cart
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping,...
Definition: map.h:791
Lorene::Map::phi
Coord phi
coordinate centered on the grid
Definition: map.h:720
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
Lorene::Scalar::set_dzpuis
void set_dzpuis(int)
Modifies the dzpuis flag.
Definition: scalar.C:808
Lorene::Vector
Tensor field of valence 1.
Definition: vector.h:188
Lorene::Scalar::get_etat
int get_etat() const
Returns the logical state ETATNONDEF (undefined), ETATZERO (null) or ETATQCQ (ordinary).
Definition: scalar.h:554
Lorene::Tenseur::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tenseur.C:636
Lorene::Scalar::derive_con
const Vector & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of *this with respect to some metric , by raising the index of...
Definition: scalar_deriv.C:402
Lorene::Scalar::test_poisson
Tbl test_poisson(const Scalar &uu, ostream &ostr, bool detail=false) const
Checks if a Poisson equation with *this as a source has been correctly solved.
Definition: scalar_test_poisson.C:60
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::Scalar::std_spectral_base
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field.
Definition: scalar.C:784
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::Star_rot::ak_car
Scalar ak_car
Scalar .
Definition: star_rot.h:186
Lorene::Scalar::poisson
Scalar poisson() const
Solves the scalar Poisson equation with *this as a source.
Definition: scalar_pde.C:136
Lorene::Star_rot::w_shift
Vector w_shift
Vector used in the decomposition of shift , following Shibata's prescription [Prog.
Definition: star_rot.h:150
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::Star::s_euler
Scalar s_euler
Trace of the stress scalar in the Eulerian frame.
Definition: star.h:201
Lorene::Star_rot::uuu
Scalar uuu
Norm of u_euler.
Definition: star_rot.h:121
Lorene::Scalar::val_grid_point
double val_grid_point(int l, int k, int j, int i) const
Returns the value of the field at a specified grid point.
Definition: scalar.h:637
Lorene::Star::ray_pole
double ray_pole() const
Coordinate radius at [r_unit].
Definition: star_global.C:278
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::Star_rot::a_car
Scalar a_car
Square of the metric factor A.
Definition: star_rot.h:104
Lorene::Star_rot::dzeta
Scalar dzeta
Metric potential .
Definition: star_rot.h:134
Lorene::Star_rot::tggg
Scalar tggg
Metric potential .
Definition: star_rot.h:137
Lorene::Star_rot::fait_nphi
void fait_nphi()
Computes tnphi and nphi from the Cartesian components of the shift, stored in shift .
Definition: star_rot.C:748
Lorene::Star_rot::ssjm1_wshift
Vector ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for .
Definition: star_rot.h:225
Lorene::contract
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Definition: tenseur_operateur.C:279
Lorene::Star::beta
Vector beta
Shift vector.
Definition: star.h:228
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