LORENE
star_bhns_hydro.C
1 /*
2  * Method of class Star_bhns to compute hydro quantities
3  *
4  * (see file star_bhns.h for documentation).
5  *
6  */
7 
8 /*
9  * Copyright (c) 2005 Keisuke Taniguchi
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 version 2
15  * as published by the Free Software Foundation.
16  *
17  * LORENE is distributed in the hope that it will be useful,
18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20  * GNU General Public License for more details.
21  *
22  * You should have received a copy of the GNU General Public License
23  * along with LORENE; if not, write to the Free Software
24  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25  *
26  */
27 
28 char star_bhns_hydro_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star_bhns/star_bhns_hydro.C,v 1.3 2014/10/13 08:53:41 j_novak Exp $" ;
29 
30 /*
31  * $Id: star_bhns_hydro.C,v 1.3 2014/10/13 08:53:41 j_novak Exp $
32  * $Log: star_bhns_hydro.C,v $
33  * Revision 1.3 2014/10/13 08:53:41 j_novak
34  * Lorene classes and functions now belong to the namespace Lorene.
35  *
36  * Revision 1.2 2014/10/06 15:13:16 j_novak
37  * Modified #include directives to use c++ syntax.
38  *
39  * Revision 1.1 2007/06/22 01:31:42 k_taniguchi
40  * *** empty log message ***
41  *
42  *
43  * $Header: /cvsroot/Lorene/C++/Source/Star_bhns/star_bhns_hydro.C,v 1.3 2014/10/13 08:53:41 j_novak Exp $
44  *
45  */
46 
47 // C++ headers
48 //#include <>
49 
50 // C headers
51 #include <cmath>
52 
53 // Lorene headers
54 #include "star_bhns.h"
55 #include "utilitaires.h"
56 #include "unites.h"
57 
58 namespace Lorene {
59 void Star_bhns::hydro_euler_bhns(bool kerrschild, const double& mass_bh,
60  const double& sepa) {
61 
62  // Fundamental constants and units
63  // -------------------------------
64  using namespace Unites ;
65 
66  int nz = mp.get_mg()->get_nzone() ;
67  int nzm1 = nz - 1 ;
68 
69  //--------------------------------
70  // Specific relativistic enthalpy ---> hhh
71  //--------------------------------
72 
73  Scalar hhh = exp(ent) ; // = 1 at the Newtonian limit
74  hhh.std_spectral_base() ;
75 
76  if (kerrschild) {
77 
78  double mass = ggrav * mass_bh ;
79 
80  Scalar xx(mp) ;
81  xx = mp.x ;
82  xx.std_spectral_base() ;
83  Scalar yy(mp) ;
84  yy = mp.y ;
85  yy.std_spectral_base() ;
86  Scalar zz(mp) ;
87  zz = mp.z ;
88  zz.std_spectral_base() ;
89 
90  double yns = mp.get_ori_y() ;
91 
92  Scalar rbh(mp) ;
93  rbh = sqrt( (xx+sepa)*(xx+sepa) + (yy+yns)*(yy+yns) + zz*zz ) ;
94  rbh.std_spectral_base() ;
95 
96  Vector ll(mp, CON, mp.get_bvect_cart()) ;
97  ll.set_etat_qcq() ;
98  ll.set(1) = (xx+sepa) / rbh ;
99  ll.set(2) = (yy+yns) / rbh ;
100  ll.set(3) = zz / rbh ;
101  ll.std_spectral_base() ;
102 
103  Scalar msr(mp) ;
104  msr = mass / rbh ;
105  msr.std_spectral_base() ;
106 
107  //--------------------------------------------
108  // Lorentz factor and 3-velocity of the fluid
109  // with respect to the Eulerian observer
110  //--------------------------------------------
111 
112  if (irrotational) {
113 
115 
116  Scalar dpsi2(mp) ;
117  dpsi2 = d_psi(1)%d_psi(1) + d_psi(2)%d_psi(2)
118  + d_psi(3)%d_psi(3) ;
119  dpsi2.std_spectral_base() ;
120 
121  Scalar lldpsi(mp) ;
122  lldpsi = ll(1)%d_psi(1) + ll(2)%d_psi(2) + ll(3)%d_psi(3) ;
123  lldpsi.std_spectral_base() ;
124 
125  Scalar lap_bh2(mp) ;
126  lap_bh2 = 1. / (1.+2.*msr) ;
127  lap_bh2.std_spectral_base() ;
128 
129  Scalar tmp1(mp) ;
130  tmp1 = 2. * msr % lap_bh2 % lldpsi % lldpsi ;
131  tmp1.std_spectral_base() ;
132 
133  gam_euler = sqrt( 1.+(dpsi2-tmp1)/(hhh%hhh)/psi4 ) ;
135 
137  assert( u_euler.get_triad() == bsn.get_triad() ) ;
138 
139  for (int i=1; i<=3; i++)
140  u_euler.set(i) = (d_psi(i)-2.*msr%lap_bh2%lldpsi%ll(i))
141  / (hhh % gam_euler) / psi4 ;
142 
144 
145  }
146  else {
147 
148  // Rigid rotation
149  // --------------
150 
151  gam_euler = gam0 ;
153  u_euler = bsn ;
154 
155  }
156 
157  //--------------------------------------------------------
158  // Energy density E with respect to the Eulerian observer
159  // See Eq (53) from Gourgoulhon et al. (2001)
160  //--------------------------------------------------------
161 
164 
165  //---------------------------------------------------
166  // Trace of the stress-energy tensor with respect to
167  // the Eulerian observer
168  // See Eq (54) from Gourgoulhon et al. (2001)
169  //---------------------------------------------------
170 
171  Scalar ueuler2(mp) ;
172  ueuler2 = u_euler(1)%u_euler(1) + u_euler(2)%u_euler(2)
173  + u_euler(3)%u_euler(3) ;
174  ueuler2.std_spectral_base() ;
175 
176  Scalar llueuler(mp) ;
177  llueuler = ll(1)%u_euler(1) + ll(2)%u_euler(2) + ll(3)%u_euler(3) ;
178  llueuler.std_spectral_base() ;
179 
180  s_euler = 3. * press + (ener_euler + press) * psi4
181  * (ueuler2 + 2.*msr%llueuler%llueuler) ;
183 
184  //--------------------------------------------
185  // Lorentz factor between the fluid and ---> gam
186  // co-orbiting observers
187  // See Eq (58) from Gourgoulhon et al. (2001)
188  //--------------------------------------------
189 
190  if (irrotational) {
191 
192  Scalar bsnueuler(mp) ;
193  bsnueuler = bsn(1)%u_euler(1) + bsn(2)%u_euler(2)
194  + bsn(3)%u_euler(3) ;
195  bsnueuler.std_spectral_base() ;
196 
197  Scalar llbsn(mp) ;
198  llbsn = ll(1)%bsn(1) + ll(2)%bsn(2) + ll(3)%bsn(3) ;
199  llbsn.std_spectral_base() ;
200 
201  Scalar tmp2(mp) ;
202  tmp2 = 1. - psi4 * (bsnueuler + 2.*msr%llueuler%llbsn) ;
203  tmp2.std_spectral_base() ;
204 
205  gam = gam0 % gam_euler % tmp2 ;
207 
208  //--------------------------------------------
209  // Spetial projection of the fluid 3-velocity
210  // with respect to the co-orbiting observer
211  //--------------------------------------------
212 
213  wit_w = gam_euler / gam * u_euler - gam0 * bsn ;
215  wit_w.annule_domain(nzm1) ;
216 
217  //-----------------------------------------
218  // Logarithm of the Lorentz factor between
219  // the fluid and co-orbiting observer
220  //-----------------------------------------
221 
222  loggam = log( gam ) ;
224 
225  //-------------------------------------------------
226  // Velocity fields set to zero in external domains
227  //-------------------------------------------------
228 
229  loggam.annule_domain(nzm1) ;
230  wit_w.annule_domain(nzm1) ;
231  u_euler.annule_domain(nzm1) ;
232 
233  loggam.set_dzpuis(0) ;
234 
235  }
236  else { // Rigid rotation
237 
238  gam = 1. ;
240  loggam = 0. ;
241  wit_w.set_etat_zero() ;
242 
243  }
244 
245  } // End of Kerr-Schild
246  else { // Isotropic coordinates with the maximal slicing
247 
248  //--------------------------------------------
249  // Lorentz factor and 3-velocity of the fluid
250  // with respect to the Eulerian observer
251  //--------------------------------------------
252 
253  if (irrotational) {
254 
256 
257  Scalar dpsi2(mp) ;
258  dpsi2 = d_psi(1)%d_psi(1) + d_psi(2)%d_psi(2)
259  + d_psi(3)%d_psi(3) ;
260  dpsi2.std_spectral_base() ;
261 
262  gam_euler = sqrt( 1. + dpsi2/(hhh%hhh)/psi4 ) ;
264 
266  for (int i=1; i<=3; i++)
267  u_euler.set(i) = d_psi(i)/(hhh%gam_euler)/psi4 ;
268 
270 
271  }
272  else {
273 
274  // Rigid rotation
275  // --------------
276 
277  gam_euler = gam0 ;
279  u_euler = bsn ;
280 
281  }
282 
283  //--------------------------------------------------------
284  // Energy density E with respect to the Eulerian observer
285  // See Eq (53) from Gourgoulhon et al. (2001)
286  //--------------------------------------------------------
287 
290 
291  //---------------------------------------------------
292  // Trace of the stress-energy tensor with respect to
293  // the Eulerian observer
294  // See Eq (54) from Gourgoulhon et al. (2001)
295  //---------------------------------------------------
296 
297  Scalar ueuler2(mp) ;
298  ueuler2 = u_euler(1)%u_euler(1) + u_euler(2)%u_euler(2)
299  + u_euler(3)%u_euler(3) ;
300  ueuler2.std_spectral_base() ;
301 
302  s_euler = 3.*press + (ener_euler+press)*psi4*ueuler2 ;
304 
305 
306  //--------------------------------------------
307  // Lorentz factor between the fluid and ---> gam
308  // co-orbiting observers
309  // See Eq (58) from Gourgoulhon et al. (2001)
310  //--------------------------------------------
311 
312  if (irrotational) {
313 
314  Scalar bsnueuler(mp) ;
315  bsnueuler = bsn(1)%u_euler(1) + bsn(2)%u_euler(2)
316  + bsn(3)%u_euler(3) ;
317  bsnueuler.std_spectral_base() ;
318 
319  Scalar tmp3(mp) ;
320  tmp3 = 1. - psi4 % bsnueuler ;
321  tmp3.std_spectral_base() ;
322 
323  gam = gam0 % gam_euler % tmp3 ;
325 
326  //--------------------------------------------
327  // Spetial projection of the fluid 3-velocity
328  // with respect to the co-orbiting observer
329  //--------------------------------------------
330 
331  wit_w = gam_euler / gam * u_euler - gam0 * bsn ;
333  wit_w.annule_domain(nzm1) ;
334 
335  //-----------------------------------------
336  // Logarithm of the Lorentz factor between
337  // the fluid and co-orbiting observer
338  //-----------------------------------------
339 
340  loggam = log( gam ) ;
342 
343  //-------------------------------------------------
344  // Velocity fields set to zero in external domains
345  //-------------------------------------------------
346 
347  loggam.annule_domain(nzm1) ;
348  wit_w.annule_domain(nzm1) ;
349  u_euler.annule_domain(nzm1) ;
350 
351  loggam.set_dzpuis(0) ;
352 
353  }
354  else { // Rigid rotation
355 
356  gam = 1. ;
358  loggam = 0. ;
359  wit_w.set_etat_zero() ;
360 
361  }
362 
363  } // End of Isotropic coordinates
364 
365  // The derived quantities are obsolete
366  // -----------------------------------
367 
368  del_deriv() ;
369 
370 }
371 }
Coord y
y coordinate centered on the grid
Definition: map.h:727
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:765
double get_ori_y() const
Returns the y coordinate of the origin.
Definition: map.h:770
Coord z
z coordinate centered on the grid
Definition: map.h:728
Coord x
x coordinate centered on the grid
Definition: map.h:726
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
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:448
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:387
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
void set_dzpuis(int)
Modifies the dzpuis flag.
Definition: scalar.C:808
Vector wit_w
Spatial projection of the fluid 3-velocity with respect to the co-orbiting observer.
Definition: star_bhns.h:88
Vector bsn
3-vector shift, divided by N , of the rotating coordinates, .
Definition: star_bhns.h:99
virtual void del_deriv() const
Deletes all the derived quantities.
Definition: star_bhns.C:341
Scalar psi4
Fourth power of the total conformal factor.
Definition: star_bhns.h:176
Vector d_psi
Gradient of (in the irrotational case) (Spherical components with respect to the mapping of the star...
Definition: star_bhns.h:82
Scalar gam0
Lorentz factor between the co-orbiting observer and the Eulerian one.
Definition: star_bhns.h:107
void hydro_euler_bhns(bool kerrschild, const double &mass_bh, const double &sepa)
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid fram...
Scalar gam
Lorentz factor between the fluid and the co-orbiting observer.
Definition: star_bhns.h:102
bool irrotational
true for an irrotational star, false for a corotating one
Definition: star_bhns.h:72
Scalar loggam
Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Definition: star_bhns.h:93
Scalar ener
Total energy density in the fluid frame.
Definition: star.h:193
Scalar ener_euler
Total energy density in the Eulerian frame.
Definition: star.h:198
Scalar gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition: star.h:204
Scalar s_euler
Trace of the stress scalar in the Eulerian frame.
Definition: star.h:201
Scalar press
Fluid pressure.
Definition: star.h:194
Scalar ent
Log-enthalpy.
Definition: star.h:190
Vector u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Definition: star.h:207
Map & mp
Mapping associated with the star.
Definition: star.h:180
Tensor field of valence 1.
Definition: vector.h:188
virtual void std_spectral_base()
Sets the standard spectal bases of decomposition for each component.
Definition: vector.C:316
Scalar & set(int)
Read/write access to a component.
Definition: vector.C:296
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
Cmp exp(const Cmp &)
Exponential.
Definition: cmp_math.C:270
Cmp log(const Cmp &)
Neperian logarithm.
Definition: cmp_math.C:296
void annule_domain(int l)
Sets the Tensor to zero in a given domain.
Definition: tensor.C:666
virtual void set_etat_qcq()
Sets the logical state of all components to ETATQCQ (ordinary state).
Definition: tensor.C:481
virtual void set_etat_zero()
Sets the logical state of all components to ETATZERO (zero state).
Definition: tensor.C:497
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition: tensor.h:866
Lorene prototypes.
Definition: app_hor.h:64
Standard units of space, time and mass.