LORENE
etoile_eqsph_falloff.C
1 /*
2  * Method of class Etoile to compute a static spherical configuration
3  * with the outer boundary condition at a finite radius
4  *
5  * (see file etoile.h for documentation).
6  *
7  */
8 
9 /*
10  * Copyright (c) 2004 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 as published by
16  * the Free Software Foundation; either version 2 of the License, or
17  * (at your option) any later version.
18  *
19  * LORENE is distributed in the hope that it will be useful,
20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22  * GNU General Public License for more details.
23  *
24  * You should have received a copy of the GNU General Public License
25  * along with LORENE; if not, write to the Free Software
26  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
27  *
28  */
29 
30 
31 char etoile_eqsph_falloff_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/etoile_eqsph_falloff.C,v 1.2 2014/10/13 08:52:58 j_novak Exp $" ;
32 
33 /*
34  * $Id: etoile_eqsph_falloff.C,v 1.2 2014/10/13 08:52:58 j_novak Exp $
35  * $Log: etoile_eqsph_falloff.C,v $
36  * Revision 1.2 2014/10/13 08:52:58 j_novak
37  * Lorene classes and functions now belong to the namespace Lorene.
38  *
39  * Revision 1.1 2004/11/30 20:52:24 k_taniguchi
40  * *** empty log message ***
41  *
42  *
43  *
44  * $Header: /cvsroot/Lorene/C++/Source/Etoile/etoile_eqsph_falloff.C,v 1.2 2014/10/13 08:52:58 j_novak Exp $
45  *
46  */
47 
48 // Headers C
49 #include "math.h"
50 
51 // Headers Lorene
52 #include "etoile.h"
53 #include "param.h"
54 #include "unites.h"
55 
56 namespace Lorene {
57 void Etoile::equil_spher_falloff(double ent_c, double precis) {
58 
59  // Fundamental constants and units
60  // -------------------------------
61  using namespace Unites ;
62 
63  // Initializations
64  // ---------------
65 
66  const Mg3d* mg = mp.get_mg() ;
67  int nz = mg->get_nzone() ; // total number of domains
68 
69  // Index of the point at phi=0, theta=pi/2 at the surface of the star:
70  int l_b = nzet - 1 ;
71  int i_b = mg->get_nr(l_b) - 1 ;
72  int j_b = mg->get_nt(l_b) - 1 ;
73  int k_b = 0 ;
74 
75  // Value of the enthalpy defining the surface of the star
76  double ent_b = 0 ;
77 
78  // Initialization of the enthalpy field to the constant value ent_c :
79 
80  ent = ent_c ;
81  ent.annule(nzet, nz-1) ;
82 
83 
84  // Corresponding profiles of baryon density, energy density and pressure
85 
87 
88  // Initial metric
89  a_car = 1 ; // this value will remain unchanged in the Newtonian case
90  beta_auto = 0 ; // this value will remain unchanged in the Newtonian case
91 
92 
93  // Auxiliary quantities
94  // --------------------
95 
96  // Affine mapping for solving the Poisson equations
97  Map_af mpaff(mp);
98 
99  Param par_nul ; // Param (null) for Map_af::poisson.
100 
101  Tenseur ent_jm1(mp) ; // Enthalpy at previous step
102  ent_jm1 = 0 ;
103 
104  Tenseur source(mp) ;
105  Tenseur logn(mp) ;
106  Tenseur logn_quad(mp) ;
107  logn = 0 ;
108  logn_quad = 0 ;
109 
110  Cmp dlogn(mp) ;
111  Cmp dbeta(mp) ;
112 
113  double diff_ent = 1 ;
114  int mermax = 200 ; // Max number of iterations
115 
116  double alpha_r = 1 ;
117  int k_falloff = 1 ;
118 
119  //=========================================================================
120  // Start of iteration
121  //=========================================================================
122 
123  for(int mer=0 ; (diff_ent > precis) && (mer<mermax) ; mer++ ) {
124 
125  cout << "-----------------------------------------------" << endl ;
126  cout << "step: " << mer << endl ;
127  cout << "alpha_r: " << alpha_r << endl ;
128  cout << "diff_ent = " << diff_ent << endl ;
129 
130  //-----------------------------------------------------
131  // Resolution of Poisson equation for ln(N)
132  //-----------------------------------------------------
133 
134  // Matter part of ln(N)
135  // --------------------
136  if (relativistic) {
137  source = a_car * (ener + 3*press) ;
138  }
139  else {
140  source = nbar ;
141  }
142 
143  (source.set()).set_dzpuis(4) ;
144 
145  source.set_std_base() ; // Sets the standard spectral bases.
146 
148 
149  mpaff.poisson_falloff(source(), par_nul, logn_auto.set(), k_falloff) ;
150 
151  // NB: at this stage logn_auto is in machine units, not in c^2
152 
153  // Quadratic part of ln(N)
154  // -----------------------
155 
156  if (relativistic) {
157 
158  mpaff.dsdr(logn(), dlogn) ;
159  mpaff.dsdr(beta_auto(), dbeta) ;
160 
161  source = - dlogn * dbeta ;
162 
163  logn_quad.set_etat_qcq() ;
164 
165  mpaff.poisson_falloff(source(), par_nul, logn_quad.set(),
166  k_falloff) ;
167 
168  }
169 
170  //-----------------------------------------------------
171  // Computation of the new radial scale
172  //-----------------------------------------------------
173 
174  // alpha_r (r = alpha_r r') is determined so that the enthalpy
175  // takes the requested value ent_b at the stellar surface
176 
177  double nu_mat0_b = logn_auto()(l_b, k_b, j_b, i_b) ;
178  double nu_mat0_c = logn_auto()(0, 0, 0, 0) ;
179 
180  double nu_quad0_b = logn_quad()(l_b, k_b, j_b, i_b) ;
181  double nu_quad0_c = logn_quad()(0, 0, 0, 0) ;
182 
183  double alpha_r2 = ( ent_c - ent_b - nu_quad0_b + nu_quad0_c )
184  / ( qpig*(nu_mat0_b - nu_mat0_c) ) ;
185 
186  alpha_r = sqrt(alpha_r2) ;
187 
188  // New radial scale
189  mpaff.homothetie( alpha_r ) ;
190 
191  //--------------------
192  // First integral
193  //--------------------
194 
195  // Gravitation potential in units c^2 :
196  logn_auto = alpha_r2*qpig * logn_auto ;
197  logn = logn_auto + logn_quad ;
198 
199  // Enthalpy in all space
200  double logn_c = logn()(0, 0, 0, 0) ;
201  ent = ent_c - logn() + logn_c ;
202 
203  //---------------------
204  // Equation of state
205  //---------------------
206 
207  equation_of_state() ;
208 
209  if (relativistic) {
210 
211  //----------------------------
212  // Equation for beta = ln(AN)
213  //----------------------------
214 
215  mpaff.dsdr(logn(), dlogn) ;
216  mpaff.dsdr(beta_auto(), dbeta) ;
217 
218  source = 3 * qpig * a_car * press ;
219 
220  source = source()
221  - 0.5 * ( dlogn * dlogn + dbeta * dbeta ) ;
222 
223  source.set_std_base() ; // Sets the standard spectral bases.
224 
226 
227  mpaff.poisson_falloff(source(), par_nul, beta_auto.set(),
228  k_falloff) ;
229 
230 
231  // Metric coefficient A^2 update
232 
233  a_car = exp(2*(beta_auto - logn)) ;
234 
235  }
236 
237  // Relative difference with enthalpy at the previous step
238  // ------------------------------------------------------
239 
240  diff_ent = norme( diffrel(ent(), ent_jm1()) ) / nzet ;
241 
242  // Next step
243  // ---------
244 
245  ent_jm1 = ent ;
246 
247 
248  } // End of iteration loop
249 
250  //=========================================================================
251  // End of iteration
252  //=========================================================================
253 
254 
255  // The mapping is transfered to that of the star:
256  // ----------------------------------------------
257  mp = mpaff ;
258 
259 
260  // Sets value to all the Tenseur's of the star
261  // -------------------------------------------
262 
263  // ... hydro
264  ent.annule(nzet, nz-1) ; // enthalpy set to zero at the exterior of
265  // the star
266  ener_euler = ener ;
267  s_euler = 3 * press ;
268  gam_euler = 1 ;
269  u_euler = 0 ;
270 
271  // ... metric
272  nnn = exp( unsurc2 * logn ) ;
273  nnn.set_std_base() ;
274  shift = 0 ;
275  a_car.set_std_base() ;
276 
277  // Info printing
278  // -------------
279 
280  cout << endl
281  << "Characteristics of the star obtained by Etoile::equil_spher_falloff : "
282  << endl
283  << "-------------------------------------------------------------------"
284  << endl ;
285 
286  double ray = mp.val_r(l_b, 1., M_PI/2., 0) ;
287  cout << "Coordinate radius : " << ray / km << " km" << endl ;
288 
289  double rcirc = ray * sqrt( a_car()(l_b, k_b, j_b, i_b) ) ;
290 
291  double compact = qpig/(4.*M_PI) * mass_g() / rcirc ;
292 
293  cout << "Circumferential radius R : " << rcirc/km << " km" << endl ;
294  cout << "Baryon mass : " << mass_b()/msol << " Mo" << endl ;
295  cout << "Gravitational mass M : " << mass_g()/msol << " Mo" << endl ;
296  cout << "Compacity parameter GM/(c^2 R) : " << compact << endl ;
297 
298 
299  //-----------------
300  // Virial theorem
301  //-----------------
302 
303  //... Pressure term
304 
305  source = qpig * a_car * sqrt(a_car) * s_euler ;
306  source.set_std_base() ;
307  double vir_mat = source().integrale() ;
308 
309  //... Gravitational term
310 
311  Cmp tmp = beta_auto() - logn() ;
312 
313  source = - ( logn().dsdr() * logn().dsdr()
314  - 0.5 * tmp.dsdr() * tmp.dsdr() )
315  * sqrt(a_car()) ;
316 
317  source.set_std_base() ;
318 
319  double vir_grav = source().integrale() ;
320 
321  //... Relative error on the virial identity GRV3
322 
323  double grv3 = ( vir_mat + vir_grav ) / vir_mat ;
324 
325  cout << "Virial theorem GRV3 : " << endl ;
326  cout << " 3P term : " << vir_mat << endl ;
327  cout << " grav. term : " << vir_grav << endl ;
328  cout << " relative error : " << grv3 << endl ;
329 
330 }
331 }
const Cmp & dsdr() const
Returns of *this .
Definition: cmp_deriv.C:84
void annule(int l)
Sets the Tenseur to zero in a given domain.
Definition: tenseur.C:900
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition: cmp.h:443
Cmp exp(const Cmp &)
Exponential.
Definition: cmp_math.C:270
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
virtual void homothetie(double lambda)
Sets a new radial scale.
Definition: map_af.C:537
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition: tenseur.C:1170
virtual double mass_g() const
Gravitational mass.
Lorene prototypes.
Definition: app_hor.h:64
Standard units of space, time and mass.
const Mg3d * get_mg() const
Gives the Mg3d on which the mapping is defined.
Definition: map.h:765
Tenseur nnn
Total lapse function.
Definition: etoile.h:509
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition: etoile.h:468
double unsurc2
: unsurc2=1 for a relativistic star, 0 for a Newtonian one.
Definition: etoile.h:442
Tenseur press
Fluid pressure.
Definition: etoile.h:461
Tenseur shift
Total shift vector.
Definition: etoile.h:512
Tbl diffrel(const Cmp &a, const Cmp &b)
Relative difference between two Cmp (norme version).
Definition: cmp_math.C:504
virtual double val_r(int l, double xi, double theta, double pphi) const =0
Returns the value of the radial coordinate r for a given in a given domain.
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition: tenseur.C:824
Tenseur u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Definition: etoile.h:474
Tbl norme(const Cmp &)
Sums of the absolute values of all the values of the Cmp in each domain.
Definition: cmp_math.C:481
Tenseur nbar
Baryon density in the fluid frame.
Definition: etoile.h:459
Tenseur gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition: etoile.h:471
Parameter storage.
Definition: param.h:125
virtual double mass_b() const
Baryon mass.
Map & mp
Mapping associated with the star.
Definition: etoile.h:429
int get_nzone() const
Returns the number of domains.
Definition: grilles.h:448
virtual void equation_of_state()
Computes the proper baryon and energy density, as well as pressure from the enthalpy.
Definition: etoile.C:566
int nzet
Number of domains of *mp occupied by the star.
Definition: etoile.h:432
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition: grilles.h:452
Tenseur a_car
Total conformal factor .
Definition: etoile.h:515
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one. ...
Definition: etoile.h:437
Multi-domain grid.
Definition: grilles.h:273
Tenseur ener
Total energy density in the fluid frame.
Definition: etoile.h:460
Affine radial mapping.
Definition: map.h:2027
Tenseur logn_auto
Total of the logarithm of the part of the lapse N generated principaly by the star.
Definition: etoile.h:484
Tenseur ent
Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case)
Definition: etoile.h:457
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition: grilles.h:457
virtual void equil_spher_falloff(double ent_c, double precis=1.e-14)
Computes a spherical static configuration with the outer boundary condition at a finite radius...
Tenseur beta_auto
Logarithm of the part of the product AN generated principaly by by the star.
Definition: etoile.h:506
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tenseur.C:636
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition: etoile.h:465
virtual void dsdr(const Cmp &ci, Cmp &resu) const
Computes of a Cmp.
Definition: map_af_deriv.C:279
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition: tenseur.h:298