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magn.c
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magn.c
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/*! \file magn.c
\brief Magnetic field related routines
*/
#include "ko.h"
//***********************************************************************
/* calculate both magnetic field four-vectors and bsq knowing gas four-velocity ucov */
//***********************************************************************
void calc_bcon_bcov_bsq_from_4vel(ldouble *pp, ldouble *ucon, ldouble *ucov, void* ggg,
ldouble *bcon, ldouble *bcov, ldouble *bsq)
{
int j;
struct geometry *geom
= (struct geometry *) ggg;
// First calculate bcon0
bcon[0] = pp[B1]*ucov[1] + pp[B2] * ucov[2] + pp[B3] * ucov[3] ;
// Then spatial components of bcon
#ifdef NONRELMHD
for(j = 1; j < 4; j++)
bcon[j] = pp[B1-1+j]; //b^i=B^i
#else // relativistic case
ldouble u0inv = 1. / ucon[0];
for(j=1;j<4;j++)
bcon[j] = (pp[B1-1+j] + bcon[0] * ucon[j]) * u0inv ;
#endif //NONRELMHD
// Convert to bcov and calculate bsq
indices_21(bcon, bcov, geom->gg);
*bsq = dotB(bcon, bcov);
return ;
}
//***********************************************************************
/* calculate magnetic field four-vector knowing gas four-velocity ucov */
//***********************************************************************
void calc_bcon_4vel(double *pp, double *ucon, double *ucov, double *bcon)
{
int j;
bcon[0] = pp[B1]*ucov[1] + pp[B2]*ucov[2] + pp[B3]*ucov[3] ;
#ifdef NONRELMHD
for(j=1;j<4;j++)
bcon[j] = pp[B1-1+j]; //b^i=B^i
#else // relativistic case
ldouble u0inv = 1. / ucon[0];
for(j=1;j<4;j++)
bcon[j] = (pp[B1-1+j] + bcon[0]*ucon[j]) * u0inv ;
#endif //NONRELMHD
return ;
}
//***********************************************************************
/* calculate B^i from bcon and gas four-velocity ucon */
//***********************************************************************
// ANDREW only used once
void calc_Bcon_4vel(double *pp, double *ucon, double *bcon, double *Bcon)
{
int j;
Bcon[0]=0.;
#ifdef NONRELMHD
for(j=1;j<4;j++)
{
Bcon[j] = bcon[j];
}
#else
for(j=1;j<4;j++)
{
Bcon[j] = bcon[j]*ucon[0] - bcon[0]*ucon[j];
}
#endif //NONRELMHD
return ;
}
//***********************************************************************
/* calculate magnetic field four-vector from primitives */
//***********************************************************************
void calc_bcon_prim(double *pp, double *bcon, void* ggg)
{
int j;
struct geometry *geom
= (struct geometry *) ggg;
ldouble ucon[4],ucov[4];
calc_ucon_ucov_from_prims(pp, geom, ucon, ucov);
calc_bcon_4vel(pp,ucon,ucov,bcon);
return;
}
//***********************************************************************
/* calculate B^i from bcon and primitives */
//***********************************************************************
void calc_Bcon_prim(double *pp, double *bcon, double *Bcon, void* ggg)
{
int j;
struct geometry *geom
= (struct geometry *) ggg;
ldouble ucon[4],ucov[4];
calc_ucon_ucov_from_prims(pp, geom, ucon, ucov);
Bcon[0]=0.;
#ifdef NONRELMHD
for(j=1;j<4;j++)
Bcon[j] = bcon[j];
#else
for(j=1;j<4;j++)
{
Bcon[j] = bcon[j]*ucon[0] - bcon[0]*ucon[j];
}
#endif //NONRELMHD
return;
}
/***********************************************************************************************/
/* wrappers for missing cells / dimensions */
/***********************************************************************************************/
int fl_x(int i)
{
if(NX==1) return 0;
return i;
}
int fl_y(int i)
{
if(NY==1) return 0;
return i;
}
int fl_z(int i)
{
if(NZ==1) return 0;
return i;
}
int flx_x(int i)
{
return i;
}
int flx_y(int i)
{
return fl_y(i);
}
int flx_z(int i)
{
return fl_z(i);
}
int fly_x(int i)
{
return fl_x(i);
}
int fly_y(int i)
{
return i;
}
int fly_z(int i)
{
return fl_z(i);
}
int flz_x(int i)
{
return fl_x(i);
}
int flz_y(int i)
{
return fl_y(i);
}
int flz_z(int i)
{
return i;
}
/***********************************************************************************************/
/* flux constrained transport */
/***********************************************************************************************/
// B^i = \dF^{it}
// E_i = - [ijk] v^j B^k , such that (\detg B^i),t = - (\detg(B^i v^j - B^j v^i)),j
// = - (\detg [ijk] E_k),j = ([ijk] emf[k]),j
// -> E_1 = v^3 B^2 - v^2 B^3
// -> E_2 = v^1 B^3 - v^3 B^1
// -> E_3 = v^2 B^1 - v^1 B^2
// emf[i] = - \detg E_i
// And notice that Fj[Bi] = \dF^{ij} = B^i v^j - B^j v^i , where j=dir
// so:
// emf_1 = B^3 v^2 - B^2 v^3 = F2[B3] or -F3[B2]
// emf_2 = B^1 v^3 - B^3 v^1 = F3[B1] or -F1[B3]
// emf_3 = B^2 v^1 - B^1 v^2 = F1[B2] or -F2[B1]
// Notice only 6 independent ways. The diagonal terms vanish (e.g. Fi[Bi]=0).
/***********************************************************************************************/
int
flux_ct()
{
#ifdef MAGNFIELD
//requires GDETIN = 1
if(GDETIN==0)
{
my_err("MAGNFIELD requires GDETIN==1\n");
exit(0);
}
//TOTH algorithm from HARM's fluxct.c
ldouble coefemf[4];
if((NY>1)&&(NZ>1)) coefemf[1]=0.25;
else coefemf[1]=0.5;
if((NX>1)&&(NZ>1)) coefemf[2]=0.25;
else coefemf[2]=0.5;
if((NX>1)&&(NY>1)) coefemf[3]=0.25;
else coefemf[3]=0.5;
int ix,iy,iz,iv,ii;
#pragma omp parallel for private(ix,iy,iz,iv) schedule (static)
//calculating EMF at corners
for(ii=0;ii<Nloop_4;ii++)
{
ix=loop_4[ii][0];
iy=loop_4[ii][1];
iz=loop_4[ii][2];
////////////////////
// EMF1
////////////////////
#if((NY>1)||(NZ>1))
set_emf(1,ix,iy,iz,
coefemf[1] * (
#if(NY>1)
+ get_ub(flby,B3,fly_x(ix),fly_y(iy),fly_z(iz),1)
+ get_ub(flby,B3,fly_x(ix),fly_y(iy),fly_z(iz-1),1)
#endif
#if(NZ>1)
- get_ub(flbz,B2,flz_x(ix),flz_y(iy),flz_z(iz),2)
- get_ub(flbz,B2,flz_x(ix),flz_y(iy-1),flz_z(iz),2)
#endif
));
#else
set_emf(1,ix,iy,iz,0.); // not really 0, but differences in emf will be 0
#endif
////////////////////
// EMF2
////////////////////
#if((NX>1)||(NZ>1))
set_emf(2,ix,iy,iz,
coefemf[2] * (
#if(NZ>1)
+ get_ub(flbz,B1,flz_x(ix),flz_y(iy),flz_z(iz),2)
+ get_ub(flbz,B1,flz_x(ix-1),flz_y(iy),flz_z(iz),2)
#endif
#if(NX>1)
- get_ub(flbx,B3,flx_x(ix),flx_y(iy),flx_z(iz),0)
- get_ub(flbx,B3,flx_x(ix),flx_y(iy),flx_z(iz-1),0)
#endif
));
#else
set_emf(2,ix,iy,iz,0.);
#endif
////////////////////
// EMF3
////////////////////
#if((NX>1)||(NY>1))
set_emf(3,ix,iy,iz,
coefemf[3] * (
#if(NX>1)
+ get_ub(flbx,B2,flx_x(ix),flx_y(iy),flx_z(iz),0)
+ get_ub(flbx,B2,flx_x(ix),flx_y(iy-1),flx_z(iz),0)
#endif
#if(NY>1)
- get_ub(flby,B1,fly_x(ix),fly_y(iy),fly_z(iz),1)
- get_ub(flby,B1,fly_x(ix-1),fly_y(iy),fly_z(iz),1)
#endif
));
#else
set_emf(3,ix,iy,iz,0.);
#endif
}
//reset certain emfs at the boundaries to ensure stationarity
adjust_fluxcttoth_emfs();
#pragma omp parallel for private(ix,iy,iz,iv) schedule (static)
for(ii=0;ii<Nloop_4;ii++) // 0...NX
{
ix=loop_4[ii][0];
iy=loop_4[ii][1];
iz=loop_4[ii][2];
/////////////////////////////////////
// F1
////////////////////////////////////
#if(NX>1)
if(iy<NY && iz<NZ) //no need to fill x-face fluxes for iy=NY etc.,
{
set_ubx(flbx,B1,ix,iy,iz,0.);
set_ubx(flbx,B2,ix,iy,iz,0.5 * (get_emf(3,ix,iy,iz) + get_emf(3,ix,iy+1,iz)));
set_ubx(flbx,B3,ix,iy,iz,-0.5 * (get_emf(2,ix,iy,iz) + get_emf(2,ix,iy,iz+1)));
}
#endif
/////////////////////////////////////
// F2
////////////////////////////////////
#if(NY>1)
if(ix<NX && iz<NZ)
{
set_uby(flby,B1,ix,iy,iz,-0.5 * (get_emf(3,ix,iy,iz) + get_emf(3,ix+1,iy,iz)));
set_uby(flby,B2,ix,iy,iz,0.);
set_uby(flby,B3,ix,iy,iz,0.5 * (get_emf(1,ix,iy,iz) + get_emf(1,ix,iy,iz+1)));
}
#endif
/////////////////////////////////////
// F3
////////////////////////////////////
#if(NZ>1)
if(ix<NX && iy<NY)
{
set_ubz(flbz,B1,ix,iy,iz,0.5 * (get_emf(2,ix,iy,iz) + get_emf(2,ix+1,iy,iz)));
set_ubz(flbz,B2,ix,iy,iz,-0.5 * (get_emf(1,ix,iy,iz) + get_emf(1,ix,iy+1,iz)));
set_ubz(flbz,B3,ix,iy,iz,0.);
}
#endif
}
#endif //MAGNFIELD
return 0;
}
/***********************************************************************************************/
// resets emf's near the boundaries where corresponding velocities are zero
/***********************************************************************************************/
int adjust_fluxcttoth_emfs()
{
int ix,iz;
#ifdef CORRECT_POLARAXIS
#ifndef TRANSMITTING_YBC // Brandon - only sets both Er, Ephi to 0 if using reflecting pole
#ifdef MPI
if(TJ==0) //upper axis
#endif
{
//over all corners at the polar edge
for(ix=0;ix<=NX;ix++)
for(iz=0;iz<=NZ;iz++)
{
set_emf(1,ix,0,iz,0.);
set_emf(3,ix,0,iz,0.);
}
}
#ifdef MPI
if(TJ==NTY-1) //lower axis
#endif
{
//over all corners at the polar edge
for(ix=0;ix<=NX;ix++)
for(iz=0;iz<=NZ;iz++)
{
set_emf(1,ix,NY,iz,0.);
set_emf(3,ix,NY,iz,0.);
}
}
#endif //ifndef TRANSMITTING_YBC
#endif //CORRECTPOLARAXIS
#ifdef TRANSMITTING_YBC //set E_phi = 0 and average E_r in phi (this is done above by the 0.5)?
#ifdef MPI
if(TJ==0) //upper axis
#endif
{
//over all corners at the polar edge
for(ix=0;ix<=NX;ix++)
for(iz=0;iz<=NZ;iz++)
{
set_emf(1,ix,0,iz,get_emf(1,ix,0,iz));
set_emf(3,ix,0,iz,0.);
}
}
#ifdef MPI
if(TJ==NTY-1) //lower axis
#endif
{
//over all corners at the polar edge
for(ix=0;ix<=NX;ix++)
for(iz=0;iz<=NZ;iz++)
{
set_emf(1,ix,NY,iz,get_emf(1,ix,NY,iz));
set_emf(3,ix,NY,iz,0.);
}
}
#endif //TRANSMITTING_YBC
return 0;
}
/***********************************************************************************************/
//calculates magnetic field from vector potential given in pinput[B1..B3]
/***********************************************************************************************/
int
calc_BfromA(ldouble* pinput, int ifoverwrite)
{
#ifdef MAGNFIELD
int ix,iy,iz,iv,ii;
//ANDERW loop_4 seems to be the same as loop_0?
#pragma omp parallel for private(ix,iy,iz,iv) schedule (static)
for(ii=0;ii<Nloop_4;ii++) //all corners of the inner domain
{
ix=loop_4[ii][0];
iy=loop_4[ii][1];
iz=loop_4[ii][2];
if(NZ==1 && iz>0) continue;
if(NY==1 && iy>0) continue;
//calculating A_i on corners by averaging neighbouring cell centers
ldouble A[3];
for(iv=0;iv<3;iv++)
{
#if defined(MONOPOLE_FIELD_CORNERS) // explicit monopole B field solution
ldouble xxvec[4],xxvecBL[4],r,th;
if (iv==2)
{
xxvec[0] = global_time;
xxvec[1] = get_xb(ix,0);
xxvec[2] = get_xb(iy,1);
xxvec[3] = get_xb(iz,2);
coco_N(xxvec,xxvecBL,MYCOORDS,BLCOORDS);
th=xxvecBL[2];
A[iv] = 1.-cos(th);
}
else A[iv]=0.;
#elif defined(INIT_MAGN_CORNERS) // define the vecpot on the corners in the init.c
A[iv]=get_u(pinput,B1+iv,ix,iy,iz);
#else // linear interpolation to corners
if(NY==1 && NZ==1)
A[iv]=1./2.*(get_u(pinput,B1+iv,ix,iy,iz) + get_u(pinput,B1+iv,ix-1,iy,iz));
if(NY>1 && NZ==1)
A[iv]=1./4.*(get_u(pinput,B1+iv,ix,iy,iz) + get_u(pinput,B1+iv,ix,iy-1,iz) +
get_u(pinput,B1+iv,ix-1,iy,iz) + get_u(pinput,B1+iv,ix-1,iy-1,iz));
if(NZ>1 && NY==1)
A[iv]=1./4.*(get_u(pinput,B1+iv,ix,iy,iz) + get_u(pinput,B1+iv,ix,iy,iz-1) +
get_u(pinput,B1+iv,ix-1,iy,iz) + get_u(pinput,B1+iv,ix-1,iy,iz-1));
if(NZ>1 && NY>1)
A[iv]=1./8.*(get_u(pinput,B1+iv,ix,iy,iz) + get_u(pinput,B1+iv,ix,iy-1,iz) +
get_u(pinput,B1+iv,ix-1,iy,iz) + get_u(pinput,B1+iv,ix-1,iy-1,iz)
+get_u(pinput,B1+iv,ix,iy,iz-1) + get_u(pinput,B1+iv,ix,iy-1,iz-1)
+get_u(pinput,B1+iv,ix-1,iy,iz-1) + get_u(pinput,B1+iv,ix-1,iy-1,iz-1));
#endif
//saving to pvecpot
set_u(pvecpot,B1+iv,ix,iy,iz,A[iv]);
}
} //cell loop
//calculating curl to get B
//new components of B^i in pvecpot[1...3]
calc_BfromA_core();
//overwriting vector potential with magnetic fields (e.g., at init)
if(ifoverwrite)
{
for(ix=0-NGCX;ix<NX+NGCX;ix++)
for(iy=0-NGCY;iy<NY+NGCY;iy++)
for(iz=0-NGCZ;iz<NZ+NGCZ;iz++)
{
struct geometry geom;
fill_geometry(ix,iy,iz,&geom);
ldouble pp[NV],uu[NV];
PLOOP(iv)
pp[iv]=get_u(p,iv,ix,iy,iz);
pp[B1]=get_u(pvecpot,1,ix,iy,iz);
pp[B2]=get_u(pvecpot,2,ix,iy,iz);
pp[B3]=get_u(pvecpot,3,ix,iy,iz);
p2u(pp,uu,&geom);
set_u(p,B1,ix,iy,iz,pp[B1]);
set_u(p,B2,ix,iy,iz,pp[B2]);
set_u(p,B3,ix,iy,iz,pp[B3]);
set_u(u,B1,ix,iy,iz,uu[B1]);
set_u(u,B2,ix,iy,iz,uu[B2]);
set_u(u,B3,ix,iy,iz,uu[B3]);
}
}
#endif //MAGNFIELD
return 0;
}
/***********************************************************************************************/
//calculates B-field from A given on corners in B1-B3 primitives of pvecpot
//new components of B^i in pvecpot[1...3]
/***********************************************************************************************/
int
calc_BfromA_core()
{
#ifdef MAGNFIELD
int ix,iy,iz,iv,ii;
if(NY==1 && NZ==1)
{
my_err("1D calc_BfromA_core() not implemented.\n"); exit(-1);
}
if(NY>1 && NZ>1)
if(PROCID==0) printf("calc_BfromA_core(): warning: assumes d/dz A_i = 0. \n");
#pragma omp parallel for private(ix,iy,iz,iv) schedule (static)
for(ii=0;ii<Nloop_0;ii++) //domain, need vecpot defined on domain + 1 layer
{
ix=loop_0[ii][0];
iy=loop_0[ii][1];
iz=loop_0[ii][2];
struct geometry geom;
fill_geometry(ix,iy,iz,&geom);
ldouble B[4];
ldouble dA[4][4];
dA[1][1]=dA[2][2]=dA[3][3]=0.;
if(TNZ==1) /* flux-ct-compatible, axisymmetric! */
{
dA[1][2] = -(get_u(pvecpot,B1,ix,iy,iz) - get_u(pvecpot,B1,ix,iy+1,iz)
+ get_u(pvecpot,B1,ix+1,iy,iz) - get_u(pvecpot,B1,ix+1,iy+1,iz))/(2.*get_size_x(iy,1)) ;
dA[1][1] = -(get_u(pvecpot,B1,ix,iy,iz) + get_u(pvecpot,B1,ix,iy+1,iz)
- get_u(pvecpot,B1,ix+1,iy,iz) - get_u(pvecpot,B1,ix+1,iy+1,iz))/(2.*get_size_x(ix,0)) ;
dA[1][3] = 0.;
dA[2][2] = -(get_u(pvecpot,B2,ix,iy,iz) - get_u(pvecpot,B2,ix,iy+1,iz)
+ get_u(pvecpot,B2,ix+1,iy,iz) - get_u(pvecpot,B2,ix+1,iy+1,iz))/(2.*get_size_x(iy,1)) ;
dA[2][1] = -(get_u(pvecpot,B2,ix,iy,iz) + get_u(pvecpot,B2,ix,iy+1,iz)
- get_u(pvecpot,B2,ix+1,iy,iz) - get_u(pvecpot,B2,ix+1,iy+1,iz))/(2.*get_size_x(ix,0)) ;
dA[2][3] = 0.;
dA[3][2] = -(get_u(pvecpot,B3,ix,iy,iz) - get_u(pvecpot,B3,ix,iy+1,iz)
+ get_u(pvecpot,B3,ix+1,iy,iz) - get_u(pvecpot,B3,ix+1,iy+1,iz))/(2.*get_size_x(iy,1)) ;
dA[3][1] = -(get_u(pvecpot,B3,ix,iy,iz) + get_u(pvecpot,B3,ix,iy+1,iz)
- get_u(pvecpot,B3,ix+1,iy,iz) - get_u(pvecpot,B3,ix+1,iy+1,iz))/(2.*get_size_x(ix,0)) ;
dA[3][3] = 0.;
}
else //generalized to three dimensions
{
dA[1][1] = (get_u(pvecpot,B1,ix+1,iy,iz) - get_u(pvecpot,B1,ix,iy,iz) +
get_u(pvecpot,B1,ix+1,iy+1,iz) - get_u(pvecpot,B1,ix,iy+1,iz) +
get_u(pvecpot,B1,ix+1,iy,iz+1) - get_u(pvecpot,B1,ix,iy,iz+1) +
get_u(pvecpot,B1,ix+1,iy+1,iz+1) - get_u(pvecpot,B1,ix,iy+1,iz+1) )/(4.*get_size_x(ix,0)) ;
dA[1][2] = (get_u(pvecpot,B1,ix,iy+1,iz) - get_u(pvecpot,B1,ix,iy,iz) +
get_u(pvecpot,B1,ix+1,iy+1,iz) - get_u(pvecpot,B1,ix+1,iy,iz) +
get_u(pvecpot,B1,ix,iy+1,iz+1) - get_u(pvecpot,B1,ix,iy,iz+1) +
get_u(pvecpot,B1,ix+1,iy+1,iz+1) - get_u(pvecpot,B1,ix+1,iy,iz+1))/(4.*get_size_x(iy,1)) ;
dA[1][3] = (get_u(pvecpot,B1,ix,iy,iz+1) - get_u(pvecpot,B1,ix,iy,iz) +
get_u(pvecpot,B1,ix+1,iy,iz+1) - get_u(pvecpot,B1,ix+1,iy,iz) +
get_u(pvecpot,B1,ix,iy+1,iz+1) - get_u(pvecpot,B1,ix,iy+1,iz) +
get_u(pvecpot,B1,ix+1,iy+1,iz+1) - get_u(pvecpot,B1,ix+1,iy+1,iz))/(4.*get_size_x(iz,2)) ;
dA[2][1] = (get_u(pvecpot,B2,ix+1,iy,iz) - get_u(pvecpot,B2,ix,iy,iz) +
get_u(pvecpot,B2,ix+1,iy+1,iz) - get_u(pvecpot,B2,ix,iy+1,iz) +
get_u(pvecpot,B2,ix+1,iy,iz+1) - get_u(pvecpot,B2,ix,iy,iz+1) +
get_u(pvecpot,B2,ix+1,iy+1,iz+1) - get_u(pvecpot,B2,ix,iy+1,iz+1) )/(4.*get_size_x(ix,0)) ;
dA[2][2] = (get_u(pvecpot,B2,ix,iy+1,iz) - get_u(pvecpot,B2,ix,iy,iz) +
get_u(pvecpot,B2,ix+1,iy+1,iz) - get_u(pvecpot,B2,ix+1,iy,iz) +
get_u(pvecpot,B2,ix,iy+1,iz+1) - get_u(pvecpot,B2,ix,iy,iz+1) +
get_u(pvecpot,B2,ix+1,iy+1,iz+1) - get_u(pvecpot,B2,ix+1,iy,iz+1))/(4.*get_size_x(iy,1)) ;
dA[2][3] = (get_u(pvecpot,B2,ix,iy,iz+1) - get_u(pvecpot,B2,ix,iy,iz) +
get_u(pvecpot,B2,ix+1,iy,iz+1) - get_u(pvecpot,B2,ix+1,iy,iz) +
get_u(pvecpot,B2,ix,iy+1,iz+1) - get_u(pvecpot,B2,ix,iy+1,iz) +
get_u(pvecpot,B2,ix+1,iy+1,iz+1) - get_u(pvecpot,B2,ix+1,iy+1,iz))/(4.*get_size_x(iz,2)) ;
dA[3][1] = (get_u(pvecpot,B3,ix+1,iy,iz) - get_u(pvecpot,B3,ix,iy,iz) +
get_u(pvecpot,B3,ix+1,iy+1,iz) - get_u(pvecpot,B3,ix,iy+1,iz) +
get_u(pvecpot,B3,ix+1,iy,iz+1) - get_u(pvecpot,B3,ix,iy,iz+1) +
get_u(pvecpot,B3,ix+1,iy+1,iz+1) - get_u(pvecpot,B3,ix,iy+1,iz+1) )/(4.*get_size_x(ix,0)) ;
dA[3][2] = (get_u(pvecpot,B3,ix,iy+1,iz) - get_u(pvecpot,B3,ix,iy,iz) +
get_u(pvecpot,B3,ix+1,iy+1,iz) - get_u(pvecpot,B3,ix+1,iy,iz) +
get_u(pvecpot,B3,ix,iy+1,iz+1) - get_u(pvecpot,B3,ix,iy,iz+1) +
get_u(pvecpot,B3,ix+1,iy+1,iz+1) - get_u(pvecpot,B3,ix+1,iy,iz+1))/(4.*get_size_x(iy,1)) ;
dA[3][3] = (get_u(pvecpot,B3,ix,iy,iz+1) - get_u(pvecpot,B3,ix,iy,iz) +
get_u(pvecpot,B3,ix+1,iy,iz+1) - get_u(pvecpot,B3,ix+1,iy,iz) +
get_u(pvecpot,B3,ix,iy+1,iz+1) - get_u(pvecpot,B3,ix,iy+1,iz) +
get_u(pvecpot,B3,ix+1,iy+1,iz+1) - get_u(pvecpot,B3,ix+1,iy+1,iz))/(4.*get_size_x(iz,2)) ;
}
B[1]=(dA[2][3] - dA[3][2])/geom.gdet;
B[2]=(dA[3][1] - dA[1][3])/geom.gdet;
B[3]=(dA[1][2] - dA[2][1])/geom.gdet;
#if PROBLEM==132 && defined(SPLIT_MONOPOLE)
ldouble xxBL[4];
get_xx_arb(ix,iy,iz,xxBL,BLCOORDS);
if(xxBL[2]>0.5*M_PI)
{
B[1]*=-1;
B[2]*=-2;
B[3]*=-3;
}
#endif
set_u(pvecpot,1,ix,iy,iz,B[1]);
set_u(pvecpot,2,ix,iy,iz,B[2]);
set_u(pvecpot,3,ix,iy,iz,B[3]);
} //cell loop
#endif //MAGNFIELD
return 0;
}
/***********************************************************************************************/
/** calculates div B for given cell *****************************************************/
/***********************************************************************************************/
ldouble
calc_divB(int ix,int iy,int iz)
{
if(!if_indomain(ix,iy,iz)) return 0.; //do not calculate in ghost cells
ldouble divB;
if(NZ==1)
{
//this is corner based, but uses cell centered values
divB = (pick_gdet(ix,iy,iz)*get_u(p,B1,ix,iy,iz) + pick_gdet(ix,iy-1,iz)*get_u(p,B1,ix,iy-1,iz)
- pick_gdet(ix-1,iy,iz)*get_u(p,B1,ix-1,iy,iz) - pick_gdet(ix-1,iy-1,iz)*get_u(p,B1,ix-1,iy-1,iz))/(2.*(get_x(ix+1,0)-get_x(ix,0)))
+ (pick_gdet(ix,iy,iz)*get_u(p,B2,ix,iy,iz) + pick_gdet(ix-1,iy,iz)*get_u(p,B2,ix-1,iy,iz)
- pick_gdet(ix,iy-1,iz)*get_u(p,B2,ix,iy-1,iz) - pick_gdet(ix-1,iy-1,iz)*get_u(p,B2,ix-1,iy-1,iz))/(2.*(get_x(iy+1,1)-get_x(iy,1)));
}
if(NZ>1)
{
divB = (pick_gdet(ix,iy,iz)*get_u(p,B1,ix,iy,iz) + pick_gdet(ix,iy-1,iz)*get_u(p,B1,ix,iy-1,iz)
- pick_gdet(ix-1,iy,iz)*get_u(p,B1,ix-1,iy,iz) - pick_gdet(ix-1,iy-1,iz)*get_u(p,B1,ix-1,iy-1,iz)
+ pick_gdet(ix,iy,iz-1)*get_u(p,B1,ix,iy,iz-1) + pick_gdet(ix,iy-1,iz-1)*get_u(p,B1,ix,iy-1,iz-1)
- pick_gdet(ix-1,iy,iz-1)*get_u(p,B1,ix-1,iy,iz-1) - pick_gdet(ix-1,iy-1,iz-1)*get_u(p,B1,ix-1,iy-1,iz-1))
/(4.*(get_x(ix,0)-get_x(ix-1,0)))
+(pick_gdet(ix,iy,iz)*get_u(p,B2,ix,iy,iz) + pick_gdet(ix-1,iy,iz)*get_u(p,B2,ix-1,iy,iz)
- pick_gdet(ix,iy-1,iz)*get_u(p,B2,ix,iy-1,iz) - pick_gdet(ix-1,iy-1,iz)*get_u(p,B2,ix-1,iy-1,iz)
+pick_gdet(ix,iy,iz-1)*get_u(p,B2,ix,iy,iz-1) + pick_gdet(ix-1,iy,iz-1)*get_u(p,B2,ix-1,iy,iz-1)
- pick_gdet(ix,iy-1,iz-1)*get_u(p,B2,ix,iy-1,iz-1) - pick_gdet(ix-1,iy-1,iz-1)*get_u(p,B2,ix-1,iy-1,iz-1))
/(4.*(get_x(iy,1)-get_x(iy-1,1)))
+(pick_gdet(ix,iy,iz)*get_u(p,B3,ix,iy,iz) + pick_gdet(ix-1,iy,iz)*get_u(p,B3,ix-1,iy,iz)
- pick_gdet(ix,iy,iz-1)*get_u(p,B3,ix,iy,iz-1) - pick_gdet(ix-1,iy,iz-1)*get_u(p,B3,ix-1,iy,iz-1)
+pick_gdet(ix,iy-1,iz)*get_u(p,B3,ix,iy-1,iz) + pick_gdet(ix-1,iy-1,iz)*get_u(p,B3,ix-1,iy-1,iz)
- pick_gdet(ix,iy-1,iz-1)*get_u(p,B3,ix,iy-1,iz-1) - pick_gdet(ix-1,iy-1,iz-1)*get_u(p,B3,ix-1,iy-1,iz-1))
/(4.*(get_x(iz,2)-get_x(iz-1,2)));
}
divB/=pick_gdet(ix,iy,iz);
return divB;
}
/***********************************************************************************************/
//calculate Q_theta MRI parameter
/***********************************************************************************************/
int
calc_Qthetaphi(int ix, int iy, int iz,ldouble *Qtheta,ldouble *Qphi)
{
if(!doingavg)
{
struct geometry geom;
fill_geometry(ix,iy,iz,&geom);
ldouble rho=get_u(p,RHO,ix,iy,iz);
ldouble bcon[4];
calc_bcon_prim(&get_u(p,0,ix,iy,iz),bcon,&geom);
ldouble ucon[4];
ucon[1]=get_u(p,VX,ix,iy,iz);
ucon[2]=get_u(p,VY,ix,iy,iz);
ucon[3]=get_u(p,VZ,ix,iy,iz);
conv_vels(ucon,ucon,VELPRIM,VEL4,geom.gg,geom.GG);
ldouble Omega = ucon[3]/ucon[0];
if(Omega==0.) Omega=BIG;
ldouble dxth=get_xb(iy+1,1)-get_xb(iy,1);
ldouble dxph=get_xb(iz+1,2)-get_xb(iz,2);
*Qtheta = 2.*M_PI/fabs(Omega)/dxth*fabs(bcon[2])/sqrt(rho);
*Qphi = 2.*M_PI/fabs(Omega)/dxph*fabs(bcon[3])/sqrt(rho);
}
else //doingavg, in BL
{
struct geometry geomBL;
fill_geometry_arb(ix,iy,iz,&geomBL,BLCOORDS);
ldouble bcon2 = get_uavg(pavg,AVGBCON(2),ix,iy,iz);
ldouble bcon3 = get_uavg(pavg,AVGBCON(3),ix,iy,iz);
ldouble Omega = get_uavg(pavg,AVGUCON(3),ix,iy,iz)/get_uavg(pavg,AVGUCON(0),ix,iy,iz);
ldouble rho = get_uavg(pavg,RHO,ix,iy,iz);
ldouble dxth,dxph;
ldouble xx1[4],xx2[4],dx[3];
if(OUTCOORDS==BLCOORDS)
{
get_cellsize_out(ix, iy, iz, dx);
dxth = dx[1];
dxph = dx[2];
}
else
{
xx1[0]=0.;xx1[1]=get_x(ix,0);xx1[2]=get_xb(iy,1);xx1[3]=get_x(iz,2);
xx2[0]=0.;xx2[1]=get_x(ix,0);xx2[2]=get_xb(iy+1,1);xx2[3]=get_x(iz,2);
coco_N(xx1,xx1,MYCOORDS,BLCOORDS);
coco_N(xx2,xx2,MYCOORDS,BLCOORDS);
dxth=fabs(xx2[2]-xx1[2]);
xx1[0]=0.;xx1[1]=get_x(ix,0);xx1[2]=get_x(iy,1);xx1[3]=get_xb(iz,2);
xx2[0]=0.;xx2[1]=get_x(ix,0);xx2[2]=get_x(iy,1);xx2[3]=get_xb(iz,2);
coco_N(xx1,xx1,MYCOORDS,BLCOORDS);
coco_N(xx2,xx2,MYCOORDS,BLCOORDS);
dxph=fabs(xx2[3]-xx1[3]);
}
*Qtheta = 2.*M_PI/fabs(Omega)/dxth*fabs(bcon2)/sqrt(rho);
*Qphi= 2.*M_PI/fabs(Omega)/dxph*fabs(bcon3)/sqrt(rho);
}
return 0;
}
/***********************************************************************************************/
//calculates sqrt(g_rr g_phph) , (b^r b^phi) , and b^2
/***********************************************************************************************/
int
calc_angle_brbphibsq(int ix, int iy, int iz, ldouble *brbphi, ldouble *bsq, ldouble *bcon,ldouble *bcov)
{
int i;
struct geometry geom;
fill_geometry(ix,iy,iz,&geom);
struct geometry geomBL;
fill_geometry_arb(ix,iy,iz,&geomBL,BLCOORDS);
ldouble pp[NV];
if(doingavg)
{
*bsq = get_uavg(pavg,AVGBSQ,ix,iy,iz);
ldouble bcon1bcon3 =
get_uavg(pavg,AVGBCONBCOV(1,0),ix,iy,iz)*geomBL.GG[3][0] +
get_uavg(pavg,AVGBCONBCOV(1,1),ix,iy,iz)*geomBL.GG[3][1] +
get_uavg(pavg,AVGBCONBCOV(1,2),ix,iy,iz)*geomBL.GG[3][2] +
get_uavg(pavg,AVGBCONBCOV(1,3),ix,iy,iz)*geomBL.GG[3][3];
*brbphi = sqrt(geomBL.gg[1][1]*geomBL.gg[3][3])*bcon1bcon3;
}
else
{
PLOOP(i)
pp[i]=get_u(p,i,ix,iy,iz);
//to BL
#ifdef PRECOMPUTE_MY2OUT
trans_pmhd_coco_my2out(pp,pp,&geom,&geomBL);
#else
trans_pmhd_coco(pp,pp,MYCOORDS,BLCOORDS,geom.xxvec,&geom,&geomBL);
#endif
//b^mu
calc_bcon_prim(pp, bcon, &geomBL);
//b_mu
indices_21(bcon,bcov,geomBL.gg);
*bsq = dotB(bcon,bcov);
*brbphi = sqrt(geomBL.gg[1][1]*geomBL.gg[3][3])*bcon[1]*bcon[3];
}
return 0;
}
/***********************************************************************************************/
//calculates (b^p b^phi) and b^2
//here cannot work on averages (bpoloidal bphi is not averaged)
/***********************************************************************************************/
int
calc_angle_bpbphibsq(int ix, int iy, int iz, ldouble *bpbphi, ldouble *bsq, ldouble *bcon, ldouble *bcov)
{
int i;
struct geometry geom;
fill_geometry(ix,iy,iz,&geom);
struct geometry geomBL;
fill_geometry_arb(ix,iy,iz,&geomBL,BLCOORDS);
ldouble pp[NV];
PLOOP(i)
pp[i]=get_u(p,i,ix,iy,iz);
//to BL
#ifdef PRECOMPUTE_MY2OUT
trans_pmhd_coco_my2out(pp, pp, &geom, &geomBL);
#else
trans_pmhd_coco(pp,pp,MYCOORDS,BLCOORDS,geom.xxvec,&geom,&geomBL);
#endif
//b^mu
calc_bcon_prim(pp, bcon, &geomBL);
//b_mu
indices_21(bcon,bcov,geomBL.gg);
*bsq = dotB(bcon,bcov);
ldouble br = sqrt(geomBL.gg[1][1])*bcon[1];
ldouble bth = sqrt(geomBL.gg[2][2])*bcon[2];
ldouble bp = sqrt(br*br + bth*bth)*my_sign(bcon[1]);
*bpbphi = bp*sqrt(geomBL.gg[3][3])*bcon[3];
return 0;
}
/***********************************************************************************************/
//calculates curl of a 3-vector field from array ptu
//returns to curl[1..4]
/***********************************************************************************************/
int
calc_curl(ldouble *ptu, int ix, int iy, int iz, void* ggg, ldouble *curl)
{
struct geometry *geom
= (struct geometry *) ggg;
ldouble dA[4][4];
dA[1][1]=dA[2][2]=dA[3][3]=0.;
//d_1 A_2
if(NX==1)
dA[1][2]=0.;
else
{
if(ix>-NG && ix<NX+NG-1)
dA[1][2]=(get_u(ptu,B2,ix+1,iy,iz)-get_u(ptu,B2,ix-1,iy,iz))/(get_x(ix+1,0)-get_x(ix-1,0));
if(ix==-NG)
dA[1][2]=(-3.*get_u(ptu,B2,ix,iy,iz)+4.*get_u(ptu,B2,ix+1,iy,iz)-get_u(ptu,B2,ix,iy,iz+2))/(get_x(ix+2,0)-get_x(ix,0));
if(ix==NX+NG-1)
dA[1][2]=(3.*get_u(ptu,B2,ix,iy,iz)-4.*get_u(ptu,B2,ix-1,iy,iz)+get_u(ptu,B2,ix-2,iy,iz))/(get_x(ix,0)-get_x(ix-2,0));
}
//d_1 A_3
if(NX==1)
dA[1][3]=0.;
else
{
if(ix>-NG && ix<NX+NG-1)
dA[1][3]=(get_u(ptu,B3,ix+1,iy,iz)-get_u(ptu,B3,ix-1,iy,iz))/(get_x(ix+1,0)-get_x(ix-1,0));
if(ix==-NG)
dA[1][3]=(-3.*get_u(ptu,B3,ix,iy,iz)+4.*get_u(ptu,B3,ix+1,iy,iz)-get_u(ptu,B3,ix,iy,iz+2))/(get_x(ix+2,0)-get_x(ix,0));
if(ix==NX+NG-1)
dA[1][3]=(3.*get_u(ptu,B3,ix,iy,iz)-4.*get_u(ptu,B3,ix-1,iy,iz)+get_u(ptu,B3,ix-2,iy,iz))/(get_x(ix,0)-get_x(ix-2,0));
}
//d_2 A_3
if(NY==1)
dA[2][3]=0.;
else
{
if(iy>-NG && iy<NY+NG-1)
dA[2][3]=(get_u(ptu,B3,ix,iy+1,iz)-get_u(ptu,B3,ix,iy-1,iz))/(get_x(iy+1,1)-get_x(iy-1,1));
if(iy==-NG)
dA[2][3]=(-3.*get_u(ptu,B3,ix,iy,iz)+4.*get_u(ptu,B3,ix,iy+1,iz)-get_u(ptu,B3,ix,iy+2,iz))/(get_x(iy+2,1)-get_x(iy,1));
if(iy==NY+NG-1)
dA[2][3]=(3.*get_u(ptu,B3,ix,iy,iz)-4.*get_u(ptu,B3,ix,iy-1,iz)+get_u(ptu,B3,ix,iy-2,iz))/(get_x(iy,1)-get_x(iy-2,1));
}
//d_2 A_1
if(NY==1)
dA[2][1]=0.;
else
{
if(iy>-NG && iy<NY+NG-1)
dA[2][1]=(get_u(ptu,B1,ix,iy+1,iz)-get_u(ptu,B1,ix,iy-1,iz))/(get_x(iy+1,1)-get_x(iy-1,1));
if(iy==-NG)
dA[2][1]=(-3.*get_u(ptu,B1,ix,iy,iz)+4.*get_u(ptu,B1,ix,iy+1,iz)-get_u(ptu,B1,ix,iy+2,iz))/(get_x(iy+2,1)-get_x(iy,1));
if(iy==NY+NG-1)
dA[2][1]=(3.*get_u(ptu,B1,ix,iy,iz)-4.*get_u(ptu,B1,ix,iy-1,iz)+get_u(ptu,B1,ix,iy-2,iz))/(get_x(iy,1)-get_x(iy-2,1));
}
//d_3 A_2
if(NZ==1)
dA[3][2]=0.;
else
{
if(iz>-NG && iz<NZ+NG-1)
dA[3][2]=(get_u(ptu,B2,ix,iy,iz+1)-get_u(ptu,B2,ix,iy,iz-1))/(get_x(iz+1,2)-get_x(iz-1,2));
if(iz==-NG)
dA[3][2]=(-3.*get_u(ptu,B2,ix,iy,iz)+4.*get_u(ptu,B2,ix,iy,iz+1)-get_u(ptu,B2,ix,iy,iz+2))/(get_x(iz+2,2)-get_x(iz,2));
if(iz==NZ+NG-1)
dA[3][2]=(3.*get_u(ptu,B2,ix,iy,iz)-4.*get_u(ptu,B2,ix,iy,iz-1)+get_u(ptu,B2,ix,iy,iz-2))/(get_x(iz,2)-get_x(iz-2,2));
}
//d_3 A_1
if(NZ==1)
dA[3][1]=0.;
else
{
if(iz>-NG && iz<NZ+NG-1)
dA[3][1]=(get_u(ptu,B1,ix,iy,iz+1)-get_u(ptu,B1,ix,iy,iz-1))/(get_x(iz+1,2)-get_x(iz-1,2));
if(iz==-NG)
dA[3][1]=(-3.*get_u(ptu,B1,ix,iy,iz)+4.*get_u(ptu,B1,ix,iy,iz+1)-get_u(ptu,B1,ix,iy,iz+2))/(get_x(iz+2,2)-get_x(iz,2));
if(iz==NZ+NG-1)
dA[3][1]=(3.*get_u(ptu,B1,ix,iy,iz)-4.*get_u(ptu,B1,ix,iy,iz-1)+get_u(ptu,B1,ix,iy,iz-2))/(get_x(iz,2)-get_x(iz-2,2));
}
//gdet B^i = d_j A_k eps^ijk
curl[1]=(dA[2][3] - dA[3][2])/geom->gdet;
curl[2]=(dA[3][1] - dA[1][3])/geom->gdet;
curl[3]=(dA[1][2] - dA[2][1])/geom->gdet;
return 0;
}
/***********************************************************************************************/
// mimics alpha-dynamo in axisymmetric sims involving MRI ***************/
/***********************************************************************************************/