LORENE
hole_bhns_equilibrium.C
1/*
2 * Method of class Hole_bhns to compute black-hole metric quantities
3 * in a black hole-neutron star binary
4 *
5 * (see file hole_bhns.h for documentation).
6 *
7 */
8
9/*
10 * Copyright (c) 2005-2007 Keisuke Taniguchi
11 *
12 * This file is part of LORENE.
13 *
14 * LORENE is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU General Public License version 2
16 * as published by the Free Software Foundation.
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
31/*
32 * $Id: hole_bhns_equilibrium.C,v 1.5 2016/12/05 16:17:55 j_novak Exp $
33 * $Log: hole_bhns_equilibrium.C,v $
34 * Revision 1.5 2016/12/05 16:17:55 j_novak
35 * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
36 *
37 * Revision 1.4 2014/10/13 08:53:00 j_novak
38 * Lorene classes and functions now belong to the namespace Lorene.
39 *
40 * Revision 1.3 2014/10/06 15:13:10 j_novak
41 * Modified #include directives to use c++ syntax.
42 *
43 * Revision 1.2 2008/05/15 19:05:12 k_taniguchi
44 * Change of some parameters.
45 *
46 * Revision 1.1 2007/06/22 01:24:36 k_taniguchi
47 * *** empty log message ***
48 *
49 *
50 * $Header: /cvsroot/Lorene/C++/Source/Hole_bhns/hole_bhns_equilibrium.C,v 1.5 2016/12/05 16:17:55 j_novak Exp $
51 *
52 */
53
54// C++ headers
55//#include <>
56
57// C headers
58#include <cmath>
59
60// Lorene headers
61#include "hole_bhns.h"
62#include "cmp.h"
63#include "tenseur.h"
64#include "param.h"
65#include "eos.h"
66#include "unites.h"
67#include "proto.h"
68#include "utilitaires.h"
69//#include "graphique.h"
70
71namespace Lorene {
72void Hole_bhns::equilibrium_bhns(int mer, int mermax_bh,
73 int filter_r, int filter_r_s, int filter_p_s,
74 double x_rot, double y_rot, double precis,
75 double omega_orb, double resize_bh,
76 const Tbl& fact_resize, Tbl& diff) {
77
78 // Fundamental constants and units
79 // -------------------------------
80 using namespace Unites ;
81
82 // Initializations
83 // ---------------
84
85 const Mg3d* mg = mp.get_mg() ;
86 int nz = mg->get_nzone() ; // total number of domains
87
88 // Re-adjustment of the boundary of domains
89 // ----------------------------------------
90
91 double rr_in_1 = mp.val_r(1, -1., M_PI/2, 0.) ;
92
93 /*
94 // Three shells outside the shell including NS
95 // -------------------------------------------
96
97 // Resize of the outer boundary of the shell including the NS
98 double rr_out_nm5 = mp.val_r(nz-5, 1., M_PI/2., 0.) ;
99 mp.resize(nz-5, rr_in_1/rr_out_nm5 * fact_resize(1)) ;
100
101 // Resize of the innner boundary of the shell including the NS
102 double rr_out_nm6 = mp.val_r(nz-6, 1., M_PI/2., 0.) ;
103 mp.resize(nz-6, rr_in_1/rr_out_nm6 * fact_resize(0)) ;
104
105 if (mer % 2 == 0) {
106
107 // Resize of the domain N-2
108 double rr_out_nm2 = mp.val_r(nz-2, 1., M_PI/2., 0.) ;
109 mp.resize(nz-2, 8. * rr_in_1 * fact_resize(1) / rr_out_nm2) ;
110
111 // Resize of the domain N-3
112 double rr_out_nm3 = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
113 mp.resize(nz-3, 4. * rr_in_1 * fact_resize(1) / rr_out_nm3) ;
114
115 // Resize of the domain N-4
116 double rr_out_nm4 = mp.val_r(nz-4, 1., M_PI/2., 0.) ;
117 mp.resize(nz-4, 2. * rr_in_1 * fact_resize(1) / rr_out_nm4) ;
118
119 if (nz > 7) {
120
121 // Resize of the domain 1
122 double rr_out_1 = mp.val_r(1, 1., M_PI/2., 0.) ;
123 mp.resize(1, rr_in_1/rr_out_1 * resize_bh) ;
124
125 if (nz > 8) {
126
127 // Resize of the domain from 2 to N-7
128 double rr_out_1_new = mp.val_r(1, 1., M_PI/2., 0.) ;
129 double rr_out_nm6_new = mp.val_r(nz-6, 1., M_PI/2., 0.) ;
130 double dr = (rr_out_nm6_new - rr_out_1_new) / double(nz - 7) ;
131
132 for (int i=1; i<nz-7; i++) {
133
134 double rr = rr_out_1_new + i * dr ;
135 double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
136 mp.resize(i+1, rr/rr_out_ip1) ;
137
138 }
139
140 }
141
142 }
143
144 }
145 */
146
147 /*
148 // Two shells outside the shell including NS
149 // -----------------------------------------
150
151 // Resize of the outer boundary of the shell including the NS
152 double rr_out_nm4 = mp.val_r(nz-4, 1., M_PI/2., 0.) ;
153 mp.resize(nz-4, rr_in_1/rr_out_nm4 * fact_resize(1)) ;
154
155 // Resize of the innner boundary of the shell including the NS
156 double rr_out_nm5 = mp.val_r(nz-5, 1., M_PI/2., 0.) ;
157 mp.resize(nz-5, rr_in_1/rr_out_nm5 * fact_resize(0)) ;
158
159 // if (mer % 2 == 0) {
160
161 // Resize of the domain N-2
162 double rr_out_nm2 = mp.val_r(nz-2, 1., M_PI/2., 0.) ;
163 mp.resize(nz-2, 3. * rr_in_1 * fact_resize(1) / rr_out_nm2) ;
164
165 // Resize of the domain N-3
166 double rr_out_nm3 = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
167 mp.resize(nz-3, 1.5 * rr_in_1 * fact_resize(1) / rr_out_nm3) ;
168
169 if (nz > 6) {
170
171 // Resize of the domain 1
172 double rr_out_1 = mp.val_r(1, 1., M_PI/2., 0.) ;
173 mp.resize(1, rr_in_1/rr_out_1 * resize_bh) ;
174
175 if (nz > 7) {
176
177 // Resize of the domain from 2 to N-6
178 double rr_out_nm5_new = mp.val_r(nz-5, 1., M_PI/2., 0.) ;
179
180 for (int i=1; i<nz-6; i++) {
181
182 double rr_out_i = mp.val_r(i, 1., M_PI/2., 0.) ;
183
184 double rr_mid = rr_out_i
185 + (rr_out_nm5_new - rr_out_i) / double(nz - 5 - i) ;
186
187 double rr_2timesi = 2. * rr_out_i ;
188
189 if (rr_2timesi < rr_mid) {
190
191 double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
192 mp.resize(i+1, rr_2timesi / rr_out_ip1) ;
193
194 }
195 else {
196
197 double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
198 mp.resize(i+1, rr_mid / rr_out_ip1) ;
199
200 } // End of else
201
202 } // End of i loop
203
204 } // End of (nz > 7) loop
205
206 } // End of (nz > 6) loop
207
208 // } // End of (mer % 2) loop
209 */
210
211 // One shell outside the shell including NS
212 // ----------------------------------------
213
214 // Resize of the outer boundary of the shell including the NS
215 double rr_out_nm3 = mp.val_r(nz-3, 1., M_PI/2., 0.) ;
216 mp.resize(nz-3, rr_in_1/rr_out_nm3 * fact_resize(1)) ;
217
218 // Resize of the innner boundary of the shell including the NS
219 double rr_out_nm4 = mp.val_r(nz-4, 1., M_PI/2., 0.) ;
220 mp.resize(nz-4, rr_in_1/rr_out_nm4 * fact_resize(0)) ;
221
222 // if (mer % 2 == 0) {
223
224 // Resize of the domain N-2
225 double rr_out_nm2 = mp.val_r(nz-2, 1., M_PI/2., 0.) ;
226 mp.resize(nz-2, 2. * rr_in_1 * fact_resize(1) / rr_out_nm2) ;
227
228 if (nz > 5) {
229
230 // Resize of the domain 1
231 double rr_out_1 = mp.val_r(1, 1., M_PI/2., 0.) ;
232 mp.resize(1, rr_in_1/rr_out_1 * resize_bh) ;
233
234 if (nz > 6) {
235
236 // Resize of the domain from 2 to N-5
237 double rr_out_nm4_new = mp.val_r(nz-4, 1., M_PI/2., 0.) ;
238
239 for (int i=1; i<nz-5; i++) {
240
241 double rr_out_i = mp.val_r(i, 1., M_PI/2., 0.) ;
242
243 double rr_mid = rr_out_i
244 + (rr_out_nm4_new - rr_out_i) / double(nz - 4 - i) ;
245
246 double rr_2timesi = 2. * rr_out_i ;
247
248 if (rr_2timesi < rr_mid) {
249
250 double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
251 mp.resize(i+1, rr_2timesi / rr_out_ip1) ;
252
253 }
254 else {
255
256 double rr_out_ip1 = mp.val_r(i+1, 1., M_PI/2., 0.) ;
257 mp.resize(i+1, rr_mid / rr_out_ip1) ;
258
259 } // End of else
260
261 } // End of i loop
262
263 } // End of (nz > 6) loop
264
265 } // End of (nz > 5) loop
266
267 // } // End of (mer % 2) loop
268
269
270 // Inner boundary condition
271 // ------------------------
272
273 Valeur bc_lapc(mg->get_angu()) ;
274 Valeur bc_conf(mg->get_angu()) ;
275
276 Valeur bc_shif_x(mg->get_angu()) ;
277 Valeur bc_shif_y(mg->get_angu()) ;
278 Valeur bc_shif_z(mg->get_angu()) ;
279
280 // Error indicators
281 // ----------------
282
283 double& diff_lapconf = diff.set(0) ;
284 double& diff_confo = diff.set(1) ;
285 double& diff_shift_x = diff.set(2) ;
286 double& diff_shift_y = diff.set(3) ;
287 double& diff_shift_z = diff.set(4) ;
288
289 Scalar lapconf_jm1 = lapconf_auto_rs ; // Lapconf function at previous step
290 Scalar confo_jm1 = confo_auto_rs ; // Conformal factor at preious step
291 Vector shift_jm1 = shift_auto_rs ; // Shift vector at previous step
292
293 // Auxiliary quantities
294 // --------------------
295
296 Scalar source_lapconf(mp) ;
297 Scalar source_confo(mp) ;
298 Vector source_shift(mp, CON, mp.get_bvect_cart()) ;
299
300 Scalar lapconf_m1(mp) ; // = lapconf_auto_rs + 0.5
301 Scalar confo_m1(mp) ; // = confo_auto_rs + 0.5
302
303 double mass = ggrav * mass_bh ;
304
305 Scalar rr(mp) ;
306 rr = mp.r ;
307 rr.std_spectral_base() ;
308 Scalar st(mp) ;
309 st = mp.sint ;
310 st.std_spectral_base() ;
311 Scalar ct(mp) ;
312 ct = mp.cost ;
313 ct.std_spectral_base() ;
314 Scalar sp(mp) ;
315 sp = mp.sinp ;
316 sp.std_spectral_base() ;
317 Scalar cp(mp) ;
318 cp = mp.cosp ;
319 cp.std_spectral_base() ;
320
321 Vector ll(mp, CON, mp.get_bvect_cart()) ;
322 ll.set_etat_qcq() ;
323 ll.set(1) = st % cp ;
324 ll.set(2) = st % sp ;
325 ll.set(3) = ct ;
326 ll.std_spectral_base() ;
327
328 Vector dlappsi(mp, COV, mp.get_bvect_cart()) ;
329 for (int i=1; i<=3; i++) {
330 dlappsi.set(i) = lapconf_auto_rs.deriv(i) + d_lapconf_comp(i)
331 - 7. * lapconf_tot % (confo_auto_rs.deriv(i) + d_confo_comp(i))
332 / confo_tot ;
333 }
334
335 dlappsi.std_spectral_base() ;
336
337 //======================================//
338 // Start of iteration //
339 //======================================//
340
341 for (int mer_bh=0; mer_bh<mermax_bh; mer_bh++) {
342
343 cout << "--------------------------------------------------" << endl ;
344 cout << "step: " << mer_bh << endl ;
345 cout << "diff_lapconf = " << diff_lapconf << endl ;
346 cout << "diff_confo = " << diff_confo << endl ;
347 cout << "diff_shift : x = " << diff_shift_x
348 << " y = " << diff_shift_y << " z = " << diff_shift_z << endl ;
349
350 if (kerrschild) {
351
352 cout << "!!!!! WARNING: Not yet available !!!!!" << endl ;
353 abort() ;
354
355 } // End of Kerr-Schild
356 else { // Isotropic coordinates with the maximal slicing
357
358 // Sets C/M^2 for each case of the lapse boundary condition
359 // --------------------------------------------------------
360 double cc ;
361
362 if (bc_lapconf_nd) { // Neumann boundary condition
363 if (bc_lapconf_fs) { // First condition
364 // d(\alpha \psi)/dr = 0
365 // ---------------------
366 cc = 2. * (sqrt(13.) - 1.) / 3. ;
367 }
368 else { // Second condition
369 // d(\alpha \psi)/dr = (\alpha \psi)/(2 rah)
370 // -----------------------------------------
371 cc = 4. / 3. ;
372 }
373 }
374 else { // Dirichlet boundary condition
375 if (bc_lapconf_fs) { // First condition
376 // (\alpha \psi) = 1/2
377 // -------------------
378 cout << "!!!!! WARNING: Not yet prepared !!!!!" << endl ;
379 abort() ;
380 }
381 else { // Second condition
382 // (\alpha \psi) = 1/sqrt(2.) \psi_KS
383 // ----------------------------------
384 cout << "!!!!! WARNING: Not yet prepared !!!!!" << endl ;
385 abort() ;
386 // cc = 2. * sqrt(2.) ;
387 }
388 }
389
390 Scalar r_are(mp) ;
391 r_are = r_coord(bc_lapconf_nd, bc_lapconf_fs) ;
392 r_are.std_spectral_base() ;
393
394 Scalar lapbh_iso(mp) ;
395 lapbh_iso = sqrt(1. - 2.*mass/r_are/rr
396 + cc*cc*pow(mass/r_are/rr,4.)) ;
397 lapbh_iso.std_spectral_base() ;
398 lapbh_iso.annule_domain(0) ;
399 lapbh_iso.raccord(1) ;
400
401 Scalar psibh_iso(mp) ;
402 psibh_iso = sqrt(r_are) ;
403 psibh_iso.std_spectral_base() ;
404 psibh_iso.annule_domain(0) ;
405 psibh_iso.raccord(1) ;
406
407 Scalar dlapbh_iso(mp) ;
408 dlapbh_iso = mass/r_are/rr - 2.*cc*cc*pow(mass/r_are/rr,4.) ;
409 dlapbh_iso.std_spectral_base() ;
410 dlapbh_iso.annule_domain(0) ;
411 dlapbh_iso.raccord(1) ;
412
413 //---------------------------------------------------------------//
414 // Resolution of the Poisson equation for the lapconf function //
415 //---------------------------------------------------------------//
416
417 // Source term
418 // -----------
419
420 Scalar tmpl1(mp) ;
421 tmpl1 = 0.875 * lapconf_tot % taij_quad_auto
422 / pow(confo_tot, 8.) ;
423 tmpl1.std_spectral_base() ; // dzpuis = 4
424 tmpl1.annule_domain(0) ;
425 tmpl1.raccord(1) ;
426
427 Scalar tmpl2(mp) ;
428 tmpl2 = 0.875 * (lapconf_comp+0.5) * taij_quad_comp
429 * (pow(confo_tot/(confo_comp+0.5),6.)*(lapconf_comp+0.5)
430 /lapconf_tot - 1.)
431 / pow(confo_comp+0.5,8.) ;
432 tmpl2.std_spectral_base() ;
433 tmpl2.annule_domain(0) ; // dzpuis = 4
434 tmpl2.raccord(1) ;
435
436 Scalar tmpl3(mp) ;
437 tmpl3 = 5.25 * cc * cc * pow(mass,4.) * lapbh_iso
438 * (pow(confo_tot,6.)*lapbh_iso/lapconf_tot - pow(psibh_iso,5.))
439 / pow(r_are*rr,6.) ;
440 tmpl3.std_spectral_base() ;
441 tmpl3.annule_domain(0) ;
442 tmpl3.raccord(1) ;
443
444 tmpl3.inc_dzpuis(4) ; // dzpuis : 0 -> 4
445
446 source_lapconf = tmpl1 + tmpl2 + tmpl3 ;
447 source_lapconf.std_spectral_base() ;
448
449 source_lapconf.annule_domain(0) ;
450 source_lapconf.raccord(1) ;
451 /*
452 if (source_lapconf.get_dzpuis() != 4) {
453 source_lapconf.set_dzpuis(4) ;
454 }
455 source_lapconf.std_spectral_base() ;
456 */
457 if (filter_r != 0) {
458 if (source_lapconf.get_etat() != ETATZERO) {
459 source_lapconf.filtre(filter_r) ;
460 }
461 }
462
463 bc_lapc = bc_lapconf() ;
464
465 lapconf_m1.set_etat_qcq() ;
466
467 if (bc_lapconf_nd) {
468 lapconf_m1 = source_lapconf.poisson_neumann(bc_lapc, 0) ;
469 }
470 else {
471 lapconf_m1 = source_lapconf.poisson_dirichlet(bc_lapc, 0) ;
472 }
473
474 // Re-construction of the lapconf function
475 // ---------------------------------------
476
477 lapconf_auto_rs = lapconf_m1 - 0.5 ;
478 lapconf_auto_rs.annule_domain(0) ;
479 lapconf_auto_rs.raccord(1) ;
480
481 lapconf_auto = lapconf_auto_rs + lapconf_auto_bh ;
482 lapconf_auto.annule_domain(0) ; // lapconf_auto,_comp->0.5 (r->inf)
483 lapconf_auto.raccord(1) ; // lapconf_tot -> 1 (r->inf)
484
485
486 //---------------------------------------------------------------//
487 // Resolution of the Poisson equation for the conformal factor //
488 //---------------------------------------------------------------//
489
490 // Source term
491 // -----------
492
493 Scalar tmpc1 = - 0.125 * taij_quad_auto / pow(confo_tot, 7.) ;
494 tmpc1.std_spectral_base() ; // dzpuis = 4
495 tmpc1.annule_domain(0) ;
496 tmpc1.raccord(1) ;
497
498 Scalar tmpc2 = 0.75 * cc * cc * pow(mass,4.)
499 * (pow(psibh_iso,5.)
500 - pow(confo_tot,7.)*lapbh_iso*lapbh_iso
501 /lapconf_tot/lapconf_tot)
502 / pow(r_are*rr,6.) ;
503 tmpc2.std_spectral_base() ;
504 tmpc2.annule_domain(0) ;
505 tmpc2.raccord(1) ;
506
507 tmpc2.inc_dzpuis(4) ; // dzpuis : 0 -> 4
508
509 Scalar tmpc3 = 0.125 * taij_quad_comp
510 * (1. - pow(confo_tot/(confo_comp+0.5),7.)
511 *pow((lapconf_comp+0.5)/lapconf_tot,2.))
512 / pow(confo_comp+0.5, 7.) ;
513 tmpc3.std_spectral_base() ; // dzpuis = 4
514 tmpc3.annule_domain(0) ;
515 tmpc3.raccord(1) ;
516
517 source_confo = tmpc1 + tmpc2 + tmpc3 ;
518 source_confo.std_spectral_base() ;
519
520 source_confo.annule_domain(0) ;
521 source_confo.raccord(1) ;
522 /*
523 if (source_confo.get_dzpuis() != 4) {
524 source_confo.set_dzpuis(4) ;
525 }
526 source_confo.std_spectral_base() ;
527 */
528 if (filter_r != 0) {
529 if (source_confo.get_etat() != ETATZERO) {
530 source_confo.filtre(filter_r) ;
531 }
532 }
533
534 bc_conf = bc_confo(omega_orb, x_rot, y_rot) ;
535
536 confo_m1.set_etat_qcq() ;
537
538 confo_m1 = source_confo.poisson_neumann(bc_conf, 0) ;
539
540 // Re-construction of the conformal factor
541 // ---------------------------------------
542 confo_auto_rs = confo_m1 - 0.5 ;
543 confo_auto_rs.annule_domain(0) ;
544 confo_auto_rs.raccord(1) ;
545
546 confo_auto = confo_auto_rs + confo_auto_bh ;
547 confo_auto.annule_domain(0) ; // confo_auto,_comp->0.5 (r->inf)
548 confo_auto.raccord(1) ; // confo_tot -> 1 (r->inf)
549
550
551 //-----------------------------------------------------------//
552 // Resolution of the Poisson equation for the shift vector //
553 //-----------------------------------------------------------//
554
555 // Source term
556 // -----------
557
558 Vector dlapconf(mp, COV, mp.get_bvect_cart()) ;
559 for (int i=1; i<=3; i++) {
560 dlapconf.set(i) = lapconf_auto_rs.deriv(i)
561 - 7. * lapconf_tot % confo_auto_rs.deriv(i)
562 / confo_tot ;
563 }
564
565 dlapconf.std_spectral_base() ;
566
567 Vector tmps1 = 2. * contract(taij_auto_rs, 1, dlappsi, 0)
568 / pow(confo_tot, 7.)
569 + 2. * contract(taij_comp, 1, dlapconf, 0)
570 * (lapconf_comp+0.5) / lapconf_tot / pow(confo_comp+0.5, 7.) ;
571 tmps1.std_spectral_base() ; // dzpuis = 4
572 tmps1.annule_domain(0) ;
573 for (int i=1; i<=3; i++) {
574 tmps1.set(i).raccord(1) ;
575 }
576
577 Vector tmps2(mp, CON, mp.get_bvect_cart()) ;
578 tmps2.set_etat_qcq() ;
579 for (int i=1; i<=3; i++) {
580 tmps2.set(i) = 2. * psibh_iso
581 * (dlapbh_iso + 0.5*(lapbh_iso - 1.)
582 *(lapbh_iso - 7.*lapconf_tot/confo_tot))
583 * (taij_tot_rs(i,1)%ll(1) + taij_tot_rs(i,2)%ll(2)
584 + taij_tot_rs(i,3)%ll(3)) / pow(confo_tot,7.) / rr ;
585 }
586 tmps2.std_spectral_base() ;
587 tmps2.annule_domain(0) ;
588 for (int i=1; i<=3; i++) {
589 tmps2.set(i).raccord(1) ;
590 }
591 for (int i=1; i<=3; i++) {
592 (tmps2.set(i)).inc_dzpuis(2) ; // dzpuis : 2 -> 4
593 }
594
595 Vector tmps3(mp, CON, mp.get_bvect_cart()) ;
596 tmps3.set_etat_qcq() ;
597 for (int i=1; i<=3; i++) {
598 tmps3.set(i) = 2. * cc * mass * mass * lapbh_iso
599 * (dlappsi(i) - 3.*ll(i)*(ll(1)%dlappsi(1)
600 + ll(2)%dlappsi(2)
601 + ll(3)%dlappsi(3)))
602 / lapconf_tot / pow(r_are*rr,3.) ;
603 }
604 tmps3.std_spectral_base() ;
605 tmps3.annule_domain(0) ;
606 for (int i=1; i<=3; i++) {
607 tmps3.set(i).raccord(1) ;
608 }
609 for (int i=1; i<=3; i++) {
610 (tmps3.set(i)).inc_dzpuis(2) ; // dzpuis : 2 -> 4
611 }
612
613 Vector tmps4 = 4. * cc * mass * mass
614 * (dlapbh_iso * (1. - psibh_iso*lapbh_iso/lapconf_tot)
615 + 0.5 * lapbh_iso * (lapbh_iso - 1.)
616 * (6.*(psibh_iso/confo_tot - 1.)
617 + psibh_iso*(1./confo_tot - lapbh_iso/lapconf_tot)))
618 * ll / rr / pow(r_are*rr,3.) ;
619 tmps4.std_spectral_base() ;
620 tmps4.annule_domain(0) ;
621 for (int i=1; i<=3; i++) {
622 tmps4.set(i).raccord(1) ;
623 }
624 for (int i=1; i<=3; i++) {
625 (tmps4.set(i)).inc_dzpuis(4) ; // dzpuis : 0 -> 4
626 }
627
628 Vector dlappsi_comp(mp, COV, mp.get_bvect_cart()) ;
629 for (int i=1; i<=3; i++) {
630 dlappsi_comp.set(i) = ((lapconf_comp+0.5)/lapconf_tot - 1.)
631 * d_lapconf_comp(i)
632 - 7. * (lapconf_comp+0.5) * ((confo_comp+0.5)/confo_tot - 1.)
633 * d_confo_comp(i) / (confo_comp+0.5) ;
634 }
635
636 dlappsi_comp.std_spectral_base() ;
637
638 Vector tmps5 = 2. * contract(taij_comp, 1, dlappsi_comp, 0)
639 / pow(confo_comp+0.5, 7.) ;
640 tmps5.std_spectral_base() ;
641 tmps5.annule_domain(0) ;
642 for (int i=1; i<=3; i++) {
643 tmps5.set(i).raccord(1) ;
644 }
645
646 source_shift = tmps1 + tmps2 + tmps3 + tmps4 + tmps5 ;
647 source_shift.std_spectral_base() ;
648 source_shift.annule_domain(0) ;
649
650 for (int i=1; i<=3; i++) {
651 source_shift.set(i).raccord(1) ;
652 }
653
654 if (filter_r_s != 0) {
655 for (int i=1; i<=3; i++) {
656 if (source_shift(i).get_etat() != ETATZERO)
657 source_shift.set(i).filtre(filter_r_s) ;
658 }
659 }
660
661 if (filter_p_s != 0) {
662 for (int i=1; i<=3; i++) {
663 if (source_shift(i).get_etat() != ETATZERO) {
664 source_shift.set(i).filtre_phi(filter_p_s, nz-1) ;
665 /*
666 for (int l=1; l<nz; l++) {
667 source_shift.set(i).filtre_phi(filter_p_s, l) ;
668 }
669 */
670 }
671 }
672 }
673
674 /*
675 for (int i=1; i<=3; i++) {
676 if (source_shift(i).dz_nonzero()) {
677 assert( source_shift(i).get_dzpuis() == 4 ) ;
678 }
679 else {
680 (source_shift.set(i)).set_dzpuis(4) ;
681 }
682 }
683 */
684
685 Tenseur source_p(mp, 1, CON, mp.get_bvect_cart()) ;
686 source_p.set_etat_qcq() ;
687 for (int i=0; i<3; i++) {
688 source_p.set(i) = Cmp(source_shift(i+1)) ;
689 }
690
691 Tenseur resu_p(mp, 1, CON, mp.get_bvect_cart()) ;
692 resu_p.set_etat_qcq() ;
693
694 for (int i=0; i<3; i++) {
695 resu_p.set(i) = Cmp(shift_auto_rs(i+1)) ;
696 }
697
698 // Boundary condition
699 bc_shif_x = bc_shift_x(omega_orb, y_rot) ;
700 bc_shif_y = bc_shift_y(omega_orb, x_rot) ;
701 bc_shif_z = bc_shift_z() ;
702
703 poisson_vect_frontiere(1./3., source_p, resu_p,
704 bc_shif_x, bc_shif_y, bc_shif_z,
705 0, precis, 7) ;
706
707 for (int i=1; i<=3; i++) {
708 shift_auto_rs.set(i) = resu_p(i-1) ;
709 }
710
711 shift_auto_rs.std_spectral_base() ;
712 shift_auto_rs.annule_domain(0) ;
713 for (int i=1; i<=3; i++) {
714 shift_auto_rs.set(i).raccord(1) ;
715 }
716
717 shift_auto = shift_auto_rs + shift_auto_bh ;
718 shift_auto.std_spectral_base() ;
719 shift_auto.annule_domain(0) ;
720 for (int i=1; i<=3; i++) {
721 shift_auto.set(i).raccord(1) ;
722 }
723
724 } // End of isotropic
725
726 //------------------------------------------------//
727 // Relative difference in the metric quantities //
728 //------------------------------------------------//
729
730 // Difference is calculated only outside the inner boundary.
731
732 Tbl tdiff_lapconf = diffrel(lapconf_auto_rs, lapconf_jm1) ;
733 tdiff_lapconf.set(0) = 0. ;
734 cout << "Relative difference in the lapconf function : " << endl ;
735 for (int l=0; l<nz; l++) {
736 cout << tdiff_lapconf(l) << " " ;
737 }
738 cout << endl ;
739
740 diff_lapconf = tdiff_lapconf(1) ;
741 for (int l=2; l<nz; l++) {
742 diff_lapconf += tdiff_lapconf(l) ;
743 }
744 diff_lapconf /= nz ;
745
746 Tbl tdiff_confo = diffrel(confo_auto_rs, confo_jm1) ;
747 tdiff_confo.set(0) = 0. ;
748 cout << "Relative difference in the conformal factor : " << endl ;
749 for (int l=0; l<nz; l++) {
750 cout << tdiff_confo(l) << " " ;
751 }
752 cout << endl ;
753
754 diff_confo = tdiff_confo(1) ;
755 for (int l=2; l<nz; l++) {
756 diff_confo += tdiff_confo(l) ;
757 }
758 diff_confo /= nz ;
759
760 Tbl tdiff_shift_x = diffrel(shift_auto_rs(1), shift_jm1(1)) ;
761 tdiff_shift_x.set(0) = 0. ;
762 cout << "Relative difference in the shift vector (x) : " << endl ;
763 for (int l=0; l<nz; l++) {
764 cout << tdiff_shift_x(l) << " " ;
765 }
766 cout << endl ;
767
768 diff_shift_x = tdiff_shift_x(1) ;
769 for (int l=2; l<nz; l++) {
770 diff_shift_x += tdiff_shift_x(l) ;
771 }
772 diff_shift_x /= nz ;
773
774 Tbl tdiff_shift_y = diffrel(shift_auto_rs(2), shift_jm1(2)) ;
775 tdiff_shift_y.set(0) = 0. ;
776 cout << "Relative difference in the shift vector (y) : " << endl ;
777 for (int l=0; l<nz; l++) {
778 cout << tdiff_shift_y(l) << " " ;
779 }
780 cout << endl ;
781
782 diff_shift_y = tdiff_shift_y(1) ;
783 for (int l=2; l<nz; l++) {
784 diff_shift_y += tdiff_shift_y(l) ;
785 }
786 diff_shift_y /= nz ;
787
788 Tbl tdiff_shift_z = diffrel(shift_auto_rs(3), shift_jm1(3)) ;
789 tdiff_shift_z.set(0) = 0. ;
790 cout << "Relative difference in the shift vector (z) : " << endl ;
791 for (int l=0; l<nz; l++) {
792 cout << tdiff_shift_z(l) << " " ;
793 }
794 cout << endl ;
795
796 diff_shift_z = tdiff_shift_z(1) ;
797 for (int l=2; l<nz; l++) {
798 diff_shift_z += tdiff_shift_z(l) ;
799 }
800 diff_shift_z /= nz ;
801
802 /*
803 des_profile( lapconf_auto_rs, 0., 10.,
804 M_PI/2., 0., "Residual lapconf function of BH",
805 "Lapconf (theta=pi/2, phi=0)" ) ;
806
807 des_profile( lapconf_auto_bh, 0., 10.,
808 M_PI/2., 0., "Analytic lapconf function of BH",
809 "Lapconf (theta=pi/2, phi=0)" ) ;
810
811 des_profile( lapconf_auto, 0., 10.,
812 M_PI/2., 0., "Self lapconf function of BH",
813 "Lapconf (theta=pi/2, phi=0)" ) ;
814
815 des_profile( lapconf_tot, 0., 10.,
816 M_PI/2., 0., "Total lapconf function of BH",
817 "Lapconf (theta=pi/2, phi=0)" ) ;
818
819 des_profile( confo_auto_rs, 0., 10.,
820 M_PI/2., 0., "Residual conformal factor of BH",
821 "Confo (theta=pi/2, phi=0)" ) ;
822
823 des_profile( confo_auto_bh, 0., 10.,
824 M_PI/2., 0., "Analytic conformal factor of BH",
825 "Confo (theta=pi/2, phi=0)" ) ;
826
827 des_profile( confo_auto, 0., 10.,
828 M_PI/2., 0., "Self conformal factor of BH",
829 "Confo (theta=pi/2, phi=0)" ) ;
830
831 des_profile( confo_tot, 0., 10.,
832 M_PI/2., 0., "Total conformal factor of BH",
833 "Confo (theta=pi/2, phi=0)" ) ;
834
835 des_coupe_vect_z( shift_auto_rs, 0., -3., 0.5, 3,
836 "Residual shift vector of NS") ;
837
838 des_coupe_vect_z( shift_auto_bh, 0., -3., 0.5, 3,
839 "Analytic shift vector of NS") ;
840
841 des_coupe_vect_z( shift_auto, 0., -3., 0.5, 3,
842 "Self shift vector of NS") ;
843
844 des_coupe_vect_z( shift_tot, 0., -3., 0.5, 3,
845 "Total Shift vector seen by NS") ;
846 */
847 } // End of main loop
848
849 //====================================//
850 // End of iteration //
851 //====================================//
852
853}
854}
Lorene::Black_hole::r_coord
const Scalar r_coord(bool neumann, bool first) const
Expresses the areal radial coordinate by that in spatially isotropic coordinates.
Definition blackhole_r_coord.C:69
Lorene::Black_hole::mp
Map & mp
Mapping associated with the black hole.
Definition blackhole.h:80
Lorene::Black_hole::kerrschild
bool kerrschild
true for a Kerr-Schild background, false for a conformally flat background
Definition blackhole.h:85
Lorene::Black_hole::mass_bh
double mass_bh
Gravitational mass of BH.
Definition blackhole.h:88
Lorene::Cmp::Cmp
Cmp(const Map &map)
Constructor from mapping.
Definition cmp.C:211
Lorene::Hole_bhns::confo_auto
Scalar confo_auto
Conformal factor generated by the black hole.
Definition hole_bhns.h:163
Lorene::Hole_bhns::lapconf_auto
Scalar lapconf_auto
Lapconf function generated by the black hole.
Definition hole_bhns.h:95
Lorene::Hole_bhns::taij_comp
Sym_tensor taij_comp
Part of the extrinsic curvature tensor generated by the companion star.
Definition hole_bhns.h:221
Lorene::Hole_bhns::equilibrium_bhns
void equilibrium_bhns(int mer, int mermax_bh, int filter_r, int filter_r_s, int filter_p_s, double x_rot, double y_rot, double precis, double omega_orb, double resize_bh, const Tbl &fact_resize, Tbl &diff)
Computes a black-hole part in a black hole-neutron star binary by giving boundary conditions on the a...
Definition hole_bhns_equilibrium.C:72
Lorene::Hole_bhns::confo_auto_bh
Scalar confo_auto_bh
Part of the conformal factor from the analytic background.
Definition hole_bhns.h:160
Lorene::Hole_bhns::bc_lapconf
const Valeur bc_lapconf() const
Boundary condition on the apparent horizon of the black hole for the lapconf function: 2-D Valeur.
Definition hole_bhns_bc.C:71
Lorene::Hole_bhns::taij_tot_rs
Sym_tensor taij_tot_rs
Part of the extrinsic curvature tensor from the numerical computation.
Definition hole_bhns.h:190
Lorene::Hole_bhns::taij_quad_auto
Scalar taij_quad_auto
Part of the scalar from the black hole.
Definition hole_bhns.h:238
Lorene::Hole_bhns::bc_shift_x
const Valeur bc_shift_x(double ome_orb, double y_rot) const
Boundary condition on the apparent horizon of the black hole for the shift vector of the \fx\f direct...
Definition hole_bhns_bc.C:186
Lorene::Hole_bhns::shift_auto_rs
Vector shift_auto_rs
Part of the shift vector from the numerical computation.
Definition hole_bhns.h:126
Lorene::Hole_bhns::bc_shift_y
const Valeur bc_shift_y(double ome_orb, double x_rot) const
Boundary condition on the apparent horizon of the black hole for the shift vector of the \fy\f direct...
Definition hole_bhns_bc.C:296
Lorene::Hole_bhns::bc_lapconf_fs
bool bc_lapconf_fs
true for the first type BC for the lapconf function, false for the second type BH
Definition hole_bhns.h:78
Lorene::Hole_bhns::confo_auto_rs
Scalar confo_auto_rs
Part of the conformal factor from the numerical computation.
Definition hole_bhns.h:157
Lorene::Hole_bhns::bc_shift_z
const Valeur bc_shift_z() const
Boundary condition on the apparent horizon of the black hole for the shift vector of the \fz\f direct...
Definition hole_bhns_bc.C:406
Lorene::Hole_bhns::d_lapconf_comp
Vector d_lapconf_comp
Derivative of the lapconf function generated by the companion star.
Definition hole_bhns.h:123
Lorene::Hole_bhns::bc_confo
const Valeur bc_confo(double ome_orb, double x_rot, double y_rot) const
Boundary condition on the apparent horizon of the black hole for the conformal factor: 2-D Valeur.
Definition hole_bhns_bc.C:506
Lorene::Hole_bhns::shift_auto_bh
Vector shift_auto_bh
Part of the shift vector from the analytic background.
Definition hole_bhns.h:129
Lorene::Hole_bhns::confo_comp
Scalar confo_comp
Conformal factor generated by the companion star.
Definition hole_bhns.h:166
Lorene::Hole_bhns::lapconf_comp
Scalar lapconf_comp
Lapconf function generated by the companion star.
Definition hole_bhns.h:98
Lorene::Hole_bhns::lapconf_auto_bh
Scalar lapconf_auto_bh
Part of the lapconf function from the analytic background.
Definition hole_bhns.h:92
Lorene::Hole_bhns::shift_auto
Vector shift_auto
Shift vector generated by the black hole.
Definition hole_bhns.h:132
Lorene::Hole_bhns::lapconf_auto_rs
Scalar lapconf_auto_rs
Part of the lapconf function from the numerical computation.
Definition hole_bhns.h:89
Lorene::Hole_bhns::d_confo_comp
Vector d_confo_comp
Derivative of the conformal factor generated by the companion star.
Definition hole_bhns.h:185
Lorene::Hole_bhns::taij_quad_comp
Scalar taij_quad_comp
Part of the scalar from the companion star.
Definition hole_bhns.h:241
Lorene::Hole_bhns::bc_lapconf_nd
bool bc_lapconf_nd
true for the Neumann type BC for the lapconf function, false for the Dirichlet type BH
Definition hole_bhns.h:73
Lorene::Hole_bhns::lapconf_tot
Scalar lapconf_tot
Total lapconf function.
Definition hole_bhns.h:101
Lorene::Hole_bhns::confo_tot
Scalar confo_tot
Total conformal factor.
Definition hole_bhns.h:169
Lorene::Hole_bhns::taij_auto_rs
Sym_tensor taij_auto_rs
Part of the extrinsic curvature tensor numericalty computed for the black hole.
Definition hole_bhns.h:211
Lorene::Mg3d
Multi-domain grid.
Definition grilles.h:279
Lorene::Mg3d::get_angu
const Mg3d * get_angu() const
Returns the pointer on the associated angular grid.
Definition mg3d.C:604
Lorene::Mg3d::get_nzone
int get_nzone() const
Returns the number of domains.
Definition grilles.h:465
Lorene::Scalar
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:393
Lorene::Scalar::poisson_neumann
Scalar poisson_neumann(const Valeur &, int) const
Idem as Scalar::poisson_dirichlet , the boundary condition being on the radial derivative of the solu...
Definition scalar_pde_frontiere.C:101
Lorene::Scalar::raccord
void raccord(int n)
Performs the matching of the nucleus with respect to the first shell.
Definition scalar_raccord.C:65
Lorene::Scalar::deriv
const Scalar & deriv(int i) const
Returns of *this , where .
Definition scalar_deriv.C:359
Lorene::Scalar::filtre
void filtre(int n)
Sets the n lasts coefficients in r to 0 in the external domain.
Definition scalar_manip.C:157
Lorene::Scalar::set_etat_qcq
virtual void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition scalar.C:359
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:790
Lorene::Scalar::inc_dzpuis
virtual void inc_dzpuis(int inc=1)
Increases by inc units the value of dzpuis and changes accordingly the values of the Scalar in the co...
Definition scalar_r_manip.C:473
Lorene::Scalar::get_etat
int get_etat() const
Returns the logical state ETATNONDEF (undefined), ETATZERO (null) or ETATQCQ (ordinary).
Definition scalar.h:560
Lorene::Scalar::filtre_phi
void filtre_phi(int n, int zone)
Sets the n lasts coefficients in to 0 in the domain zone .
Definition scalar_manip.C:255
Lorene::Scalar::poisson_dirichlet
Scalar poisson_dirichlet(const Valeur &limite, int num) const
Is identicall to Scalar::poisson() .
Definition scalar_pde_frontiere.C:67
Lorene::Tbl
Basic array class.
Definition tbl.h:161
Lorene::Tbl::set
double & set(int i)
Read/write of a particular element (index i) (1D case).
Definition tbl.h:281
Lorene::Tenseur
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:304
Lorene::Tenseur::set
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:830
Lorene::Tenseur::set_etat_qcq
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tenseur.C:642
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition valeur.h:297
Lorene::Vector
Tensor field of valence 1.
Definition vector.h:188
Lorene::Vector::std_spectral_base
virtual void std_spectral_base()
Sets the standard spectal bases of decomposition for each component.
Definition vector.C:319
Lorene::Vector::set
Scalar & set(int)
Read/write access to a component.
Definition vector.C:299
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:223
Lorene::diffrel
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition cmp_math.C:507
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:351
Lorene::Tensor::annule_domain
void annule_domain(int l)
Sets the Tensor to zero in a given domain.
Definition tensor.C:675
Lorene::Tensor::set_etat_qcq
virtual void set_etat_qcq()
Sets the logical state of all components to ETATQCQ (ordinary state).
Definition tensor.C:490
Lorene::contract
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Definition tenseur_operateur.C:282
Lorene
Lorene prototypes.
Definition app_hor.h:67
Unites
Standard units of space, time and mass.