LORENE
et_rot_equilibrium.C
1/*
2 * Function Etoile_rot::equilibrium
3 *
4 * (see file etoile.h for documentation)
5 *
6 */
7
8/*
9 * Copyright (c) 2000-2001 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
30char et_rot_equilibrium_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_equilibrium.C,v 1.8 2014/10/13 08:52:57 j_novak Exp $" ;
31
32/*
33 * $Id: et_rot_equilibrium.C,v 1.8 2014/10/13 08:52:57 j_novak Exp $
34 * $Log: et_rot_equilibrium.C,v $
35 * Revision 1.8 2014/10/13 08:52:57 j_novak
36 * Lorene classes and functions now belong to the namespace Lorene.
37 *
38 * Revision 1.7 2014/10/06 15:13:09 j_novak
39 * Modified #include directives to use c++ syntax.
40 *
41 * Revision 1.6 2005/10/05 15:15:31 j_novak
42 * Added a Param* as parameter of Etoile_rot::equilibrium
43 *
44 * Revision 1.5 2004/03/25 10:29:06 j_novak
45 * All LORENE's units are now defined in the namespace Unites (in file unites.h).
46 *
47 * Revision 1.4 2003/11/19 21:30:57 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 1.3 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 1.2 2002/10/16 14:36:36 j_novak
56 * Reorganization of #include instructions of standard C++, in order to
57 * use experimental version 3 of gcc.
58 *
59 * Revision 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
60 * LORENE
61 *
62 * Revision 2.19 2000/11/23 15:44:10 eric
63 * Ajout de l'argument ent_limit.
64 *
65 * Revision 2.18 2000/11/19 22:34:15 eric
66 * Correction erreur ds convergence vers une masse baryonique fixee.
67 *
68 * Revision 2.17 2000/11/18 17:13:18 eric
69 * Modifs pour permettre np=1 (axisymetrie). En particulier,
70 * lambda_shift est mis a zero si np=1.
71 *
72 * Revision 2.16 2000/11/10 15:17:50 eric
73 * Ajout des arguments icontrol(7) (delta_mer_kep) et control(6) (precis_adapt)
74 * Creation des fichiers freqeuncy.d et evolution.d
75 *
76 * Revision 2.15 2000/11/08 15:21:16 eric
77 * Appel de fait_nphi() avant hydro_euler() pour le test sur u_euler.
78 *
79 * Revision 2.14 2000/10/25 15:13:36 eric
80 * omega est initialise a zero.
81 *
82 * Revision 2.13 2000/10/23 14:02:55 eric
83 * Modif de Map_et::adapt: on y rentre desormais avec nz_search
84 * dans le cas present nz_search = nzet + 1).
85 *
86 * Revision 2.12 2000/10/23 13:47:47 dorota
87 * Ajout en sortie (dans diff(7)) de vit_triax.
88 * Suppression de l'initialisation a zero de omega_ini (!)
89 *
90 * Revision 2.11 2000/10/20 13:56:43 eric
91 * Ecriture dans le fichier convergence.d de la vitesse de developpement
92 * de la perturbation triaxiale (vit_triax).
93 *
94 * Revision 2.10 2000/10/20 13:11:23 eric
95 * Ajout de l'argument nzadapt.
96 *
97 * Revision 2.9 2000/10/17 16:00:24 eric
98 * Ajout de la perturbation triaxiale.
99 *
100 * Revision 2.8 2000/10/12 15:33:22 eric
101 * Ajout de l'appel a fait_nphi() pour le calcul de tnphi et nphi.
102 * Emploi de la nouvelle version de Tenseur::set_std_base() : on n'a plus
103 * besoin de tester l'etat du tenseur avant.
104 *
105 * Revision 2.7 2000/10/11 15:14:09 eric
106 * Ajout des equations pour tggg et dzeta --> 1ere version complete !
107 *
108 * Revision 2.6 2000/10/06 15:06:14 eric
109 * Version relativiste avec le lapse et le shift uniquement.
110 * Ca converge.
111 *
112 * Revision 2.5 2000/09/18 16:15:26 eric
113 * Premiers termes relativistes.
114 *
115 * Revision 2.4 2000/08/31 15:39:02 eric
116 * Appel du nouvel operateur Cmp::mult_rsint pour le calcul de uuu.
117 *
118 * Revision 2.3 2000/08/25 12:27:55 eric
119 * modifs mineures (fichconv).
120 *
121 * Revision 2.2 2000/08/18 14:01:24 eric
122 * Premiere version operationnelle (testee en spherique Newtonien)
123 *
124 * Revision 2.1 2000/08/17 12:39:47 eric
125 * *** empty log message ***
126 *
127 * Revision 2.0 2000/07/21 16:30:32 eric
128 * *** empty log message ***
129 *
130 *
131 * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_equilibrium.C,v 1.8 2014/10/13 08:52:57 j_novak Exp $
132 *
133 */
134
135// Headers C
136#include <cmath>
137
138// Headers Lorene
139#include "etoile.h"
140#include "param.h"
141
142#include "graphique.h"
143#include "utilitaires.h"
144#include "unites.h"
145
146namespace Lorene {
147void Etoile_rot::equilibrium(double ent_c, double omega0, double fact_omega,
148 int nzadapt, const Tbl& ent_limit, const Itbl& icontrol,
149 const Tbl& control, double mbar_wanted,
150 double aexp_mass, Tbl& diff, Param*) {
151
152 // Fundamental constants and units
153 // -------------------------------
154
155 using namespace Unites ;
156
157 // For the display
158 // ---------------
159 char display_bold[]="x[1m" ; display_bold[0] = 27 ;
160 char display_normal[] = "x[0m" ; display_normal[0] = 27 ;
161
162 // Grid parameters
163 // ---------------
164
165 const Mg3d* mg = mp.get_mg() ;
166 int nz = mg->get_nzone() ; // total number of domains
167 int nzm1 = nz - 1 ;
168
169 // The following is required to initialize mp_prev as a Map_et:
170 Map_et& mp_et = dynamic_cast<Map_et&>(mp) ;
171
172 // Index of the point at phi=0, theta=pi/2 at the surface of the star:
173 assert(mg->get_type_t() == SYM) ;
174 int l_b = nzet - 1 ;
175 int i_b = mg->get_nr(l_b) - 1 ;
176 int j_b = mg->get_nt(l_b) - 1 ;
177 int k_b = 0 ;
178
179 // Value of the enthalpy defining the surface of the star
180 double ent_b = ent_limit(nzet-1) ;
181
182 // Parameters to control the iteration
183 // -----------------------------------
184
185 int mer_max = icontrol(0) ;
186 int mer_rot = icontrol(1) ;
187 int mer_change_omega = icontrol(2) ;
188 int mer_fix_omega = icontrol(3) ;
189 int mer_mass = icontrol(4) ;
190 int mermax_poisson = icontrol(5) ;
191 int mer_triax = icontrol(6) ;
192 int delta_mer_kep = icontrol(7) ;
193
194 // Protections:
195 if (mer_change_omega < mer_rot) {
196 cout << "Etoile_rot::equilibrium: mer_change_omega < mer_rot !" << endl ;
197 cout << " mer_change_omega = " << mer_change_omega << endl ;
198 cout << " mer_rot = " << mer_rot << endl ;
199 abort() ;
200 }
201 if (mer_fix_omega < mer_change_omega) {
202 cout << "Etoile_rot::equilibrium: mer_fix_omega < mer_change_omega !"
203 << endl ;
204 cout << " mer_fix_omega = " << mer_fix_omega << endl ;
205 cout << " mer_change_omega = " << mer_change_omega << endl ;
206 abort() ;
207 }
208
209 // In order to converge to a given baryon mass, shall the central
210 // enthalpy be varied or Omega ?
211 bool change_ent = true ;
212 if (mer_mass < 0) {
213 change_ent = false ;
214 mer_mass = abs(mer_mass) ;
215 }
216
217 double precis = control(0) ;
218 double omega_ini = control(1) ;
219 double relax = control(2) ;
220 double relax_prev = double(1) - relax ;
221 double relax_poisson = control(3) ;
222 double thres_adapt = control(4) ;
223 double ampli_triax = control(5) ;
224 double precis_adapt = control(6) ;
225
226
227 // Error indicators
228 // ----------------
229
230 diff.set_etat_qcq() ;
231 double& diff_ent = diff.set(0) ;
232 double& diff_nuf = diff.set(1) ;
233 double& diff_nuq = diff.set(2) ;
234// double& diff_dzeta = diff.set(3) ;
235// double& diff_ggg = diff.set(4) ;
236 double& diff_shift_x = diff.set(5) ;
237 double& diff_shift_y = diff.set(6) ;
238 double& vit_triax = diff.set(7) ;
239
240 // Parameters for the function Map_et::adapt
241 // -----------------------------------------
242
243 Param par_adapt ;
244 int nitermax = 100 ;
245 int niter ;
246 int adapt_flag = 1 ; // 1 = performs the full computation,
247 // 0 = performs only the rescaling by
248 // the factor alpha_r
249 int nz_search = nzet + 1 ; // Number of domains for searching the enthalpy
250 // isosurfaces
251 double alpha_r ;
252 double reg_map = 1. ; // 1 = regular mapping, 0 = contracting mapping
253
254 par_adapt.add_int(nitermax, 0) ; // maximum number of iterations to
255 // locate zeros by the secant method
256 par_adapt.add_int(nzadapt, 1) ; // number of domains where the adjustment
257 // to the isosurfaces of ent is to be
258 // performed
259 par_adapt.add_int(nz_search, 2) ; // number of domains to search for
260 // the enthalpy isosurface
261 par_adapt.add_int(adapt_flag, 3) ; // 1 = performs the full computation,
262 // 0 = performs only the rescaling by
263 // the factor alpha_r
264 par_adapt.add_int(j_b, 4) ; // theta index of the collocation point
265 // (theta_*, phi_*)
266 par_adapt.add_int(k_b, 5) ; // theta index of the collocation point
267 // (theta_*, phi_*)
268
269 par_adapt.add_int_mod(niter, 0) ; // number of iterations actually used in
270 // the secant method
271
272 par_adapt.add_double(precis_adapt, 0) ; // required absolute precision in
273 // the determination of zeros by
274 // the secant method
275 par_adapt.add_double(reg_map, 1) ; // 1. = regular mapping, 0 = contracting mapping
276
277 par_adapt.add_double(alpha_r, 2) ; // factor by which all the radial
278 // distances will be multiplied
279
280 par_adapt.add_tbl(ent_limit, 0) ; // array of values of the field ent
281 // to define the isosurfaces.
282
283 // Parameters for the function Map_et::poisson for nuf
284 // ----------------------------------------------------
285
286 double precis_poisson = 1.e-16 ;
287
288 Param par_poisson_nuf ;
289 par_poisson_nuf.add_int(mermax_poisson, 0) ; // maximum number of iterations
290 par_poisson_nuf.add_double(relax_poisson, 0) ; // relaxation parameter
291 par_poisson_nuf.add_double(precis_poisson, 1) ; // required precision
292 par_poisson_nuf.add_int_mod(niter, 0) ; // number of iterations actually used
293 par_poisson_nuf.add_cmp_mod( ssjm1_nuf ) ;
294
295 Param par_poisson_nuq ;
296 par_poisson_nuq.add_int(mermax_poisson, 0) ; // maximum number of iterations
297 par_poisson_nuq.add_double(relax_poisson, 0) ; // relaxation parameter
298 par_poisson_nuq.add_double(precis_poisson, 1) ; // required precision
299 par_poisson_nuq.add_int_mod(niter, 0) ; // number of iterations actually used
300 par_poisson_nuq.add_cmp_mod( ssjm1_nuq ) ;
301
302 Param par_poisson_tggg ;
303 par_poisson_tggg.add_int(mermax_poisson, 0) ; // maximum number of iterations
304 par_poisson_tggg.add_double(relax_poisson, 0) ; // relaxation parameter
305 par_poisson_tggg.add_double(precis_poisson, 1) ; // required precision
306 par_poisson_tggg.add_int_mod(niter, 0) ; // number of iterations actually used
307 par_poisson_tggg.add_cmp_mod( ssjm1_tggg ) ;
308 double lambda_tggg ;
309 par_poisson_tggg.add_double_mod( lambda_tggg ) ;
310
311 Param par_poisson_dzeta ;
312 double lbda_grv2 ;
313 par_poisson_dzeta.add_double_mod( lbda_grv2 ) ;
314
315 // Parameters for the function Tenseur::poisson_vect
316 // -------------------------------------------------
317
318 Param par_poisson_vect ;
319
320 par_poisson_vect.add_int(mermax_poisson, 0) ; // maximum number of iterations
321 par_poisson_vect.add_double(relax_poisson, 0) ; // relaxation parameter
322 par_poisson_vect.add_double(precis_poisson, 1) ; // required precision
323 par_poisson_vect.add_cmp_mod( ssjm1_khi ) ;
324 par_poisson_vect.add_tenseur_mod( ssjm1_wshift ) ;
325 par_poisson_vect.add_int_mod(niter, 0) ;
326
327
328 // Initializations
329 // ---------------
330
331 // Initial angular velocity
332 omega = 0 ;
333
334 double accrois_omega = (omega0 - omega_ini) /
335 double(mer_fix_omega - mer_change_omega) ;
336
337
338 update_metric() ; // update of the metric coefficients
339
340 equation_of_state() ; // update of the density, pressure, etc...
341
342 hydro_euler() ; // update of the hydro quantities relative to the
343 // Eulerian observer
344
345 // Quantities at the previous step :
346 Map_et mp_prev = mp_et ;
347 Tenseur ent_prev = ent ;
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
361 // Preparations for the Poisson equations:
362 // --------------------------------------
363 if (nuf.get_etat() == ETATZERO) {
364 nuf.set_etat_qcq() ;
365 nuf.set() = 0 ;
366 }
367
368 if (relativistic) {
369 if (nuq.get_etat() == ETATZERO) {
370 nuq.set_etat_qcq() ;
371 nuq.set() = 0 ;
372 }
373
374 if (tggg.get_etat() == ETATZERO) {
375 tggg.set_etat_qcq() ;
376 tggg.set() = 0 ;
377 }
378
379 if (dzeta.get_etat() == ETATZERO) {
381 dzeta.set() = 0 ;
382 }
383 }
384
385 ofstream fichconv("convergence.d") ; // Output file for diff_ent
386 fichconv << "# diff_ent GRV2 max_triax vit_triax" << endl ;
387
388 ofstream fichfreq("frequency.d") ; // Output file for omega
389 fichfreq << "# f [Hz]" << endl ;
390
391 ofstream fichevol("evolution.d") ; // Output file for various quantities
392 fichevol <<
393 "# |dH/dr_eq/dH/dr_pole| r_pole/r_eq ent_c"
394 << endl ;
395
396 diff_ent = 1 ;
397 double err_grv2 = 1 ;
398 double max_triax_prev = 0 ; // Triaxial amplitude at previous step
399
400 //=========================================================================
401 // Start of iteration
402 //=========================================================================
403
404 for(int mer=0 ; (diff_ent > precis) && (mer<mer_max) ; mer++ ) {
405
406 cout << "-----------------------------------------------" << endl ;
407 cout << "step: " << mer << endl ;
408 cout << "diff_ent = " << display_bold << diff_ent << display_normal
409 << endl ;
410 cout << "err_grv2 = " << err_grv2 << endl ;
411 fichconv << mer ;
412 fichfreq << mer ;
413 fichevol << mer ;
414
415 if (mer >= mer_rot) {
416
417 if (mer < mer_change_omega) {
418 omega = omega_ini ;
419 }
420 else {
421 if (mer <= mer_fix_omega) {
422 omega = omega_ini + accrois_omega *
423 (mer - mer_change_omega) ;
424 }
425 }
426
427 }
428
429 //-----------------------------------------------
430 // Sources of the Poisson equations
431 //-----------------------------------------------
432
433 // Source for nu
434 // -------------
435 Tenseur beta = log(bbb) ;
436 beta.set_std_base() ;
437
438 if (relativistic) {
439 source_nuf = qpig * a_car *( ener_euler + s_euler ) ;
440
441 source_nuq = ak_car - flat_scalar_prod(logn.gradient_spher(),
442 logn.gradient_spher() + beta.gradient_spher()) ;
443 }
444 else {
445 source_nuf = qpig * nbar ;
446
447 source_nuq = 0 ;
448 }
449 source_nuf.set_std_base() ;
450 source_nuq.set_std_base() ;
451
452 // Source for dzeta
453 // ----------------
454 source_dzf = 2 * qpig * a_car * (press + (ener_euler+press) * uuu*uuu ) ;
455 source_dzf.set_std_base() ;
456
457 source_dzq = 1.5 * ak_car - flat_scalar_prod(logn.gradient_spher(),
458 logn.gradient_spher() ) ;
459 source_dzq.set_std_base() ;
460
461 // Source for tggg
462 // ---------------
463
464 source_tggg = 4 * qpig * nnn * a_car * bbb * press ;
465 source_tggg.set_std_base() ;
466
467 (source_tggg.set()).mult_rsint() ;
468
469
470 // Source for shift
471 // ----------------
472
473 // Matter term:
474 source_shift = (-4*qpig) * nnn * a_car * (ener_euler + press)
475 * u_euler ;
476
477 // Quadratic terms:
478 Tenseur vtmp = 6 * beta.gradient_spher() - 2 * logn.gradient_spher() ;
480
481 Tenseur squad = 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
505 //---------------------------------------
506 // Triaxial perturbation of nuf
507 //---------------------------------------
508
509 if (mer == mer_triax) {
510
511 if ( mg->get_np(0) == 1 ) {
512 cout <<
513 "Etoile_rot::equilibrium: np must be stricly greater than 1"
514 << endl << " to set a triaxial perturbation !" << endl ;
515 abort() ;
516 }
517
518 const Coord& phi = mp.phi ;
519 const Coord& sint = mp.sint ;
520 Cmp perturb(mp) ;
521 perturb = 1 + ampli_triax * sint*sint * cos(2*phi) ;
522 nuf.set() = nuf() * perturb ;
523
524 nuf.set_std_base() ; // set the bases for spectral expansions
525 // to be the standard ones for a
526 // scalar field
527
528 }
529
530 // Monitoring of the triaxial perturbation
531 // ---------------------------------------
532
533 Valeur& va_nuf = nuf.set().va ;
534 va_nuf.coef() ; // Computes the spectral coefficients
535 double max_triax = 0 ;
536
537 if ( mg->get_np(0) > 1 ) {
538
539 for (int l=0; l<nz; l++) { // loop on the domains
540 for (int j=0; j<mg->get_nt(l); j++) {
541 for (int i=0; i<mg->get_nr(l); i++) {
542
543 // Coefficient of cos(2 phi) :
544 double xcos2p = (*(va_nuf.c_cf))(l, 2, j, i) ;
545
546 // Coefficient of sin(2 phi) :
547 double xsin2p = (*(va_nuf.c_cf))(l, 3, j, i) ;
548
549 double xx = sqrt( xcos2p*xcos2p + xsin2p*xsin2p ) ;
550
551 max_triax = ( xx > max_triax ) ? xx : max_triax ;
552 }
553 }
554 }
555
556 }
557
558 cout << "Triaxial part of nuf : " << max_triax << endl ;
559
560 if (relativistic) {
561
562 //----------------------------------------------
563 // Resolution of the Poisson equation for nuq
564 //----------------------------------------------
565
566 source_nuq().poisson(par_poisson_nuq, nuq.set()) ;
567
568 cout << "Test of the Poisson equation for nuq :" << endl ;
569 err = source_nuq().test_poisson(nuq(), cout, true) ;
570 diff_nuq = err(0, 0) ;
571
572 //---------------------------------------------------------
573 // Resolution of the vector Poisson equation for the shift
574 //---------------------------------------------------------
575
576
577 if (source_shift.get_etat() != ETATZERO) {
578
579 for (int i=0; i<3; i++) {
580 if(source_shift(i).dz_nonzero()) {
581 assert( source_shift(i).get_dzpuis() == 4 ) ;
582 }
583 else{
584 (source_shift.set(i)).set_dzpuis(4) ;
585 }
586 }
587
588 }
589 //##
590 // source_shift.dec2_dzpuis() ; // dzpuis 4 -> 2
591
592 double lambda_shift = double(1) / double(3) ;
593
594 if ( mg->get_np(0) == 1 ) {
595 lambda_shift = 0 ;
596 }
597
598 source_shift.poisson_vect(lambda_shift, par_poisson_vect,
600
601 cout << "Test of the Poisson equation for shift_x :" << endl ;
602 err = source_shift(0).test_poisson(shift(0), cout, true) ;
603 diff_shift_x = err(0, 0) ;
604
605 cout << "Test of the Poisson equation for shift_y :" << endl ;
606 err = source_shift(1).test_poisson(shift(1), cout, true) ;
607 diff_shift_y = err(0, 0) ;
608
609 // Computation of tnphi and nphi from the Cartesian components
610 // of the shift
611 // -----------------------------------------------------------
612
613 fait_nphi() ;
614
615 //## cout.precision(10) ;
616 // cout << "nphi : " << nphi()(0, 0, 0, 0)
617 // << " " << nphi()(l_b, k_b, j_b, i_b/2)
618 // << " " << nphi()(l_b, k_b, j_b, i_b) << endl ;
619
620 }
621
622 //-----------------------------------------
623 // Determination of the fluid velociy U
624 //-----------------------------------------
625
626 if (mer > mer_fix_omega + delta_mer_kep) {
627
628 omega *= fact_omega ; // Increase of the angular velocity if
629 } // fact_omega != 1
630
631 bool omega_trop_grand = false ;
632 bool kepler = true ;
633
634 while ( kepler ) {
635
636 // Possible decrease of Omega to ensure a velocity < c
637
638 bool superlum = true ;
639
640 while ( superlum ) {
641
642 // New fluid velocity U :
643
644 Cmp tmp = omega - nphi() ;
645 tmp.annule(nzm1) ;
646 tmp.std_base_scal() ;
647
648 tmp.mult_rsint() ; // Multiplication by r sin(theta)
649
650 uuu = bbb() / nnn() * tmp ;
651
652 if (uuu.get_etat() == ETATQCQ) {
653 // Same basis as (Omega -N^phi) r sin(theta) :
654 ((uuu.set()).va).set_base( (tmp.va).base ) ;
655 }
656
657
658 // Is the new velocity larger than c in the equatorial plane ?
659
660 superlum = false ;
661
662 for (int l=0; l<nzet; l++) {
663 for (int i=0; i<mg->get_nr(l); i++) {
664
665 double u1 = uuu()(l, 0, j_b, i) ;
666 if (u1 >= 1.) { // superluminal velocity
667 superlum = true ;
668 cout << "U > c for l, i : " << l << " " << i
669 << " U = " << u1 << endl ;
670 }
671 }
672 }
673 if ( superlum ) {
674 cout << "**** VELOCITY OF LIGHT REACHED ****" << endl ;
675 omega /= fact_omega ; // Decrease of Omega
676 cout << "New rotation frequency : "
677 << omega/(2.*M_PI) * f_unit << " Hz" << endl ;
678 omega_trop_grand = true ;
679 }
680 } // end of while ( superlum )
681
682
683 // New computation of U (which this time is not superluminal)
684 // as well as of gam_euler, ener_euler, etc...
685 // -----------------------------------
686
687 hydro_euler() ;
688
689
690 //------------------------------------------------------
691 // First integral of motion
692 //------------------------------------------------------
693
694 // Centrifugal potential :
695 if (relativistic) {
696 mlngamma = - log( gam_euler ) ;
697 }
698 else {
699 mlngamma = - 0.5 * uuu*uuu ;
700 }
701
702 // Equatorial values of various potentials :
703 double nuf_b = nuf()(l_b, k_b, j_b, i_b) ;
704 double nuq_b = nuq()(l_b, k_b, j_b, i_b) ;
705 double mlngamma_b = mlngamma()(l_b, k_b, j_b, i_b) ;
706
707 // Central values of various potentials :
708 double nuf_c = nuf()(0,0,0,0) ;
709 double nuq_c = nuq()(0,0,0,0) ;
710 double mlngamma_c = 0 ;
711
712 // Scale factor to ensure that the enthalpy is equal to ent_b at
713 // the equator
714 double alpha_r2 = ( ent_c - ent_b + mlngamma_c - mlngamma_b
715 + nuq_c - nuq_b) / ( nuf_b - nuf_c ) ;
716 alpha_r = sqrt(alpha_r2) ;
717 cout << "alpha_r = " << alpha_r << endl ;
718
719 // Readjustment of nu :
720 // -------------------
721
722 logn = alpha_r2 * nuf + nuq ;
723 double nu_c = logn()(0,0,0,0) ;
724
725 // First integral --> enthalpy in all space
726 //-----------------
727
728 ent = (ent_c + nu_c + mlngamma_c) - logn - mlngamma ;
729
730 // Test: is the enthalpy negative somewhere in the equatorial plane
731 // inside the star ? If yes, this means that the Keplerian velocity
732 // has been overstep.
733
734 kepler = false ;
735 for (int l=0; l<nzet; l++) {
736 int imax = mg->get_nr(l) - 1 ;
737 if (l == l_b) imax-- ; // The surface point is skipped
738 for (int i=0; i<imax; i++) {
739 if ( ent()(l, 0, j_b, i) < 0. ) {
740 kepler = true ;
741 cout << "ent < 0 for l, i : " << l << " " << i
742 << " ent = " << ent()(l, 0, j_b, i) << endl ;
743 }
744 }
745 }
746
747 if ( kepler ) {
748 cout << "**** KEPLERIAN VELOCITY REACHED ****" << endl ;
749 omega /= fact_omega ; // Omega is decreased
750 cout << "New rotation frequency : "
751 << omega/(2.*M_PI) * f_unit << " Hz" << endl ;
752 omega_trop_grand = true ;
753 }
754
755 } // End of while ( kepler )
756
757 if ( omega_trop_grand ) { // fact_omega is decreased for the
758 // next step
759 fact_omega = sqrt( fact_omega ) ;
760 cout << "**** New fact_omega : " << fact_omega << endl ;
761 }
762
763//## if (mer >= mer_triax) {
764// des_coupe_y(ent(), 0., 1, "ent before adapt", &(ent()) ) ;
765// des_coupe_z(ent(), 0., 1, "ent before adapt (EQUAT)", &(ent()) ) ;
766//## }
767
768 //----------------------------------------------------
769 // Adaptation of the mapping to the new enthalpy field
770 //----------------------------------------------------
771
772 // Shall the adaptation be performed (cusp) ?
773 // ------------------------------------------
774
775 double dent_eq = ent().dsdr()(l_b, k_b, j_b, i_b) ;
776 double dent_pole = ent().dsdr()(l_b, k_b, 0, i_b) ;
777 double rap_dent = fabs( dent_eq / dent_pole ) ;
778 cout << "| dH/dr_eq / dH/dr_pole | = " << rap_dent << endl ;
779
780 if ( rap_dent < thres_adapt ) {
781 adapt_flag = 0 ; // No adaptation of the mapping
782 cout << "******* FROZEN MAPPING *********" << endl ;
783 }
784 else{
785 adapt_flag = 1 ; // The adaptation of the mapping is to be
786 // performed
787 }
788
789 mp_prev = mp_et ;
790
791 mp.adapt(ent(), par_adapt) ;
792
793//## if (mer >= mer_triax) {
794// des_coupe_y(ent(), 0., 1, "ent after adapt", &(ent()) ) ;
795// des_coupe_z(ent(), 0., 1, "ent after adapt (EQUAT)", &(ent()) ) ;
796//## }
797
798 //----------------------------------------------------
799 // Computation of the enthalpy at the new grid points
800 //----------------------------------------------------
801
802 mp_prev.homothetie(alpha_r) ;
803
804 mp.reevaluate(&mp_prev, nzet+1, ent.set()) ;
805
806//## if (mer >= mer_triax) {
807// des_coupe_y(ent(), 0., 1, "ent after reevaluate", &(ent()) ) ;
808// des_coupe_z(ent(), 0., 1, "ent after reevaluate (EQUAT)", &(ent()) ) ;
809//## }
810
811
812 //----------------------------------------------------
813 // Equation of state
814 //----------------------------------------------------
815
816 equation_of_state() ; // computes new values for nbar (n), ener (e)
817 // and press (p) from the new ent (H)
818
819 //---------------------------------------------------------
820 // Matter source terms in the gravitational field equations
821 //---------------------------------------------------------
822
823 //## Computation of tnphi and nphi from the Cartesian components
824 // of the shift for the test in hydro_euler():
825
826 fait_nphi() ;
827
828 hydro_euler() ; // computes new values for ener_euler (E),
829 // s_euler (S) and u_euler (U^i)
830
831 if (relativistic) {
832
833 //-------------------------------------------------------
834 // 2-D Poisson equation for tggg
835 //-------------------------------------------------------
836
837 mp.poisson2d(source_tggg(), mp.cmp_zero(), par_poisson_tggg,
838 tggg.set()) ;
839
840 //-------------------------------------------------------
841 // 2-D Poisson equation for dzeta
842 //-------------------------------------------------------
843
844 mp.poisson2d(source_dzf(), source_dzq(), par_poisson_dzeta,
845 dzeta.set()) ;
846
847 err_grv2 = lbda_grv2 - 1;
848 cout << "GRV2: " << err_grv2 << endl ;
849
850 }
851 else {
852 err_grv2 = grv2() ;
853 }
854
855
856 //---------------------------------------
857 // Computation of the metric coefficients (except for N^phi)
858 //---------------------------------------
859
860 // Relaxations on nu and dzeta :
861
862 if (mer >= 10) {
863 logn = relax * logn + relax_prev * logn_prev ;
864
865 dzeta = relax * dzeta + relax_prev * dzeta_prev ;
866 }
867
868 // Update of the metric coefficients N, A, B and computation of K_ij :
869
870 update_metric() ;
871
872 //-----------------------
873 // Informations display
874 //-----------------------
875
876 partial_display(cout) ;
877 fichfreq << " " << omega / (2*M_PI) * f_unit ;
878 fichevol << " " << rap_dent ;
879 fichevol << " " << ray_pole() / ray_eq() ;
880 fichevol << " " << ent_c ;
881
882 //-----------------------------------------
883 // Convergence towards a given baryon mass
884 //-----------------------------------------
885
886 if (mer > mer_mass) {
887
888 double xx ;
889 if (mbar_wanted > 0.) {
890 xx = mass_b() / mbar_wanted - 1. ;
891 cout << "Discrep. baryon mass <-> wanted bar. mass : " << xx
892 << endl ;
893 }
894 else{
895 xx = mass_g() / fabs(mbar_wanted) - 1. ;
896 cout << "Discrep. grav. mass <-> wanted grav. mass : " << xx
897 << endl ;
898 }
899 double xprog = ( mer > 2*mer_mass) ? 1. :
900 double(mer-mer_mass)/double(mer_mass) ;
901 xx *= xprog ;
902 double ax = .5 * ( 2. + xx ) / (1. + xx ) ;
903 double fact = pow(ax, aexp_mass) ;
904 cout << " xprog, xx, ax, fact : " << xprog << " " <<
905 xx << " " << ax << " " << fact << endl ;
906
907 if ( change_ent ) {
908 ent_c *= fact ;
909 }
910 else {
911 if (mer%4 == 0) omega *= fact ;
912 }
913 }
914
915
916 //------------------------------------------------------------
917 // Relative change in enthalpy with respect to previous step
918 //------------------------------------------------------------
919
920 Tbl diff_ent_tbl = diffrel( ent(), ent_prev() ) ;
921 diff_ent = diff_ent_tbl(0) ;
922 for (int l=1; l<nzet; l++) {
923 diff_ent += diff_ent_tbl(l) ;
924 }
925 diff_ent /= nzet ;
926
927 fichconv << " " << log10( fabs(diff_ent) + 1.e-16 ) ;
928 fichconv << " " << log10( fabs(err_grv2) + 1.e-16 ) ;
929 fichconv << " " << log10( fabs(max_triax) + 1.e-16 ) ;
930
931 vit_triax = 0 ;
932 if ( (mer > mer_triax+1) && (max_triax_prev > 1e-13) ) {
933 vit_triax = (max_triax - max_triax_prev) / max_triax_prev ;
934 }
935
936 fichconv << " " << vit_triax ;
937
938 //------------------------------
939 // Recycling for the next step
940 //------------------------------
941
942 ent_prev = ent ;
943 logn_prev = logn ;
944 dzeta_prev = dzeta ;
945 max_triax_prev = max_triax ;
946
947 fichconv << endl ;
948 fichfreq << endl ;
949 fichevol << endl ;
950 fichconv.flush() ;
951 fichfreq.flush() ;
952 fichevol.flush() ;
953
954 } // End of main loop
955
956 //=========================================================================
957 // End of iteration
958 //=========================================================================
959
960 fichconv.close() ;
961 fichfreq.close() ;
962 fichevol.close() ;
963
964
965}
966}
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
void mult_rsint()
Multiplication by .
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
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
virtual void hydro_euler()
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid fram...
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.
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
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_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
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping,...
Definition map.h:791
virtual 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
virtual void adapt(const Cmp &ent, const Param &par, int nbr=0)=0
Adaptation of the mapping to a given scalar field.
const Cmp & cmp_zero() const
Returns the null Cmp defined on *this.
Definition map.h:807
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 Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition map.h:765
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
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tbl.C:361
double & set(int i)
Read/write of a particular element (index i) (1D case)
Definition tbl.h:281
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 : .
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.
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.