bhns_set_evo_fields_generic.math

# add and set evolution fields into ELLIPTICA grid. the convention chosen as 
# the BAM code. hence, if you want another definition for these field you need to
# replace 'evo' with another name, say gra for GR-Athena++, and redefine
# them as you like.


# Manifold or grid Dimension
Dimension = 3;

# point on manifold shown by:
Point = ijk;

C_macro  = reav_v_if_exists(name);
C_macro2 = REALLOC_v_WRITE_v(name);
C_macro3 = DECLARE_AND_EMPTY_FIELD(name);
C_macro4 = add_alloc_get_field(name);
C_macro5 = add_alloc_field(name);

# main function:
`#include "bhns_header.h"`
``
``
`#define add_alloc_get_field(name) ADD_FIELD(name) REALLOC_v_WRITE_v(name)`
``
``
`#define add_alloc_field(name) ADD_AND_ALLOC_FIELD(name) `
``
``
`#define reav_v_if_exists(name) const double *name = 0; \`
` if (_Ind(#name) >= 0) name = patch->fields[Ind(#name)]->v;`
``
``
`void bhns_set_evo_fields_generic(Grid_T *const grid);`
`void bhns_set_evo_fields_generic(Grid_T *const grid)`
`{`
`  Uint p;`
`  const Uint np = grid->np;`
``
`  OpenMP_Patch_Pragma(omp parallel for)`
`  for (p = 0; p < np; ++p)`
`  {`
`  Patch_T *patch = grid->patch[p];`
``
Declare = 
{
 # add: evo_grhd_v^i
 (obj = Field,name = evo_grhd_v, rank = U, C_macro4);

 # add: evo_grhd_rho
 (obj = Field,name = evo_grhd_rho, rank = 0, C_macro4);

 # add: evo_grhd_p
 (obj = Field,name = evo_grhd_p, rank = 0, C_macro4);

 # add: evo_grhd_epsl
 (obj = Field,name = evo_grhd_epsl, rank = 0, C_macro4);

 # add: evo_alpha
 (obj = Field,name = evo_alpha, rank = 0, C_macro4);

 # add: evo_beta^i
 (obj = Field,name = evo_beta, rank = U, C_macro4);

 # add: evo_adm_g_ij
 (obj = Field,name = evo_adm_g, rank = DD, C_macro4);

 # add: evo_adm_K_ij
 (obj = Field,name = evo_adm_Kij, rank = DD, C_macro4);

 # conformal metric 
 (obj = Field,name = gConf, rank = DD, C_macro);

 # conformal metric inverse
 (obj = Field,name = igConf, rank = UU, C_macro);

 # K_{ij}
 (obj = Field,name = adm_Kij, rank = DD, C_macro);

 # add: evo_chi = psi^-4
 #(obj = Field,name = evo_chi, rank = 0, C_macro4);
 
 # shift
 (obj = Field,name = beta, rank = U, C_macro);

 # psi
 (obj = Field,name = psi, rank = 0, C_macro);

 # alphaPsi
 (obj = Field,name = alphaPsi, rank = 0, C_macro);

 # B1 in beta = B0+B1
 #(obj = Field,name = B1, rank = U, C_macro);
 
 # trKij
 #(obj = Field,name = K, rank = 0, C_macro);

 # enthalpy
 (obj = Field,name = enthalpy, rank = 0, C_macro);

 # spin part of fluid
 (obj = Field,name = W, rank = U, C_macro);

 # d(phi)/d? for irrotional part of fluid
 (obj = Field,name = dphi, rank = D, C_macro);

 # u0
 (obj = Field,name = u0, rank = 0, C_macro);

}

# symmetries:
Symm[adm_Kij(i,j)     = adm_Kij(j,i)];
Symm[evo_adm_Kij(i,j) = evo_adm_Kij(j,i)];
Symm[evo_adm_g(i,j)   = evo_adm_g(j,i)];
Symm[gConf(i,j)     = gConf(j,i)];
Symm[igConf(i,j)    = igConf(j,i)];

## set metric fields in all patches:
`  FOR_ALL_ijk`
`  {`
   psi4   = psi**4;

# alpha:
`   evo_alpha[ijk] = alphaPsi[ijk]/psi[ijk];`

# beta:
`   evo_beta_U0[ijk] = beta_U0[ijk];`
`   evo_beta_U1[ijk] = beta_U1[ijk];`
`   evo_beta_U2[ijk] = beta_U2[ijk];`

# g_ij:
   adm_g(-i,-j) = psi4*gConf(i,j);
   Symm[adm_g(i,j) = adm_g(j,i)];
   Cpopulate[evo_adm_g = adm_g];

# K_ij:
   Kdd(-i,-j) = adm_Kij(i,j);
   Symm[Kdd(i,j) = Kdd(j,i)];
   Cpopulate[evo_adm_Kij = Kdd];

# evo_chi (for test purposes)
#`   evo_chi[ijk] = 1/psi4;`

`  }`# FOR_ALL_ijk

## set matter fields if needed
`  if (IsItCovering(patch,"NS"))`
`  {`
`  Physics_T *ns = init_physics(0,NS);`
`  EoS_T *eos    = init_EoS(ns);`

`  FOR_ALL_ijk`
`  {`

   # grhd_v^i:
   psim4     = psi**(-4);
   grhd_v(i) = (psim4*igConf(i,j)*dphi(-j)+W(i))/(evo_alpha*enthalpy*u0);
   Cpopulate[evo_grhd_v = grhd_v];

   # total_energy_density = grhd_rho(1+grhd_epsl)
`  eos->h = enthalpy[ijk];`
`  if(!isfinite(eos->h) || LSSEQL(eos->h,1.))`
`  {`
`    evo_grhd_rho[ijk]  = 0;`
`    evo_grhd_p[ijk]    = 0;`
`    evo_grhd_epsl[ijk] = 0;`
`  }`
`  else`
`  {`
`   evo_grhd_rho[ijk]  = eos->rest_mass_density(eos);`
`   evo_grhd_p[ijk]    = eos->pressure(eos);`
`   evo_grhd_epsl[ijk] = eos->specific_internal_energy(eos);` 
`  }`

`  }`# FOR_ALL_ijk

`  free_physics(ns);`
`  free_EoS(eos);`
`  }` # if (IsItCovering(patch,"NS"))

`  }`# end of FOR_ALL_PATCHES

`}` # end of function