static FTYPE x1_of_x0(FTYPE x0 )
{
FTYPE x1,vsq;
FTYPE dv = 1.e-15;
vsq = fabs(vsq_calc(x0)) ; // guaranteed to be positive
return( ( vsq > 1. ) ? (1.0 - dv) : vsq );
}
static FTYPE x1_of_x0(FTYPE x0 )
{
FTYPE x1,vsq;
// FTYPE dv = 1.e-15;
vsq = fabs(vsq_calc(x0)) ; // guaranteed to be positive (>=0)
return( ( vsq > 1. ) ? VSQ_TOO_BIG : vsq );
}
static int Utoprim_new_body(FTYPE U[NPR], FTYPE gcov[NDIM][NDIM],
FTYPE gcon[NDIM][NDIM], FTYPE gdet, FTYPE prim[NPR])
{
FTYPE x_1d[1];
FTYPE QdotB,Bcon[NDIM],Bcov[NDIM],Qcov[NDIM],Qcon[NDIM],ncov[NDIM],ncon[NDIM],Qsq,Qtcon[NDIM];
FTYPE rho0,u,p,w,gammasq,gamma,gtmp,W_last,W,utsq,vsq,tmpdiff ;
FTYPE alpha, ucovt, utsqp1, aco, bco, cco, pevar, agame, the, utt;
int i,j, retval, i_increase ;
double dummy;
// Assume ok initially:
retval = 0;
for(i = BCON1; i <= BCON3; i++) prim[i] = U[i] ;
// Calculate various scalars (Q.B, Q^2, etc) from the conserved variables:
Bcon[0] = 0. ;
for(i=1;i<4;i++) Bcon[i] = U[BCON1+i-1] ;
lower_g(Bcon,gcov,Bcov) ;
for(i=0;i<4;i++) Qcov[i] = U[QCOV0+i] ;
raise_g(Qcov,gcon,Qcon) ;
Bsq = 0. ;
for(i=1;i<4;i++) Bsq += Bcon[i]*Bcov[i] ;
QdotB = 0. ;
for(i=0;i<4;i++) QdotB += Qcov[i]*Bcon[i] ;
QdotBsq = QdotB*QdotB ;
ncov_calc(gcon,ncov) ;
raise_g(ncov,gcon,ncon);
Qdotn = Qcon[0]*ncov[0] ;
Qsq = 0. ;
for(i=0;i<4;i++) Qsq += Qcov[i]*Qcon[i] ;
Qtsq = Qsq + Qdotn*Qdotn ;
D = U[RHO] ;
/* calculate W from last timestep and use for guess */
utsq = 0. ;
for(i=1;i<4;i++)
for(j=1;j<4;j++) utsq += gcov[i][j]*prim[UTCON1+i-1]*prim[UTCON1+j-1] ;
if( (utsq < 0.) && (fabs(utsq) < 1.0e-13) ) {
utsq = fabs(utsq);
}
if(utsq < 0. || utsq > UTSQ_TOO_BIG) {
retval = 2;
return(retval) ;
}
gammasq = 1. + utsq ;
gamma = sqrt(gammasq);
// Always calculate rho from D and gamma so that using D in EOS remains consistent
// i.e. you don't get positive values for dP/d(vsq) .
rho0 = D / gamma ;
p = pressure_of_rho( rho0 );
u = u_of_p(p);
w = rho0 + u + p ;
#if(LTRACE)
if( rho0 <= 0. ) {
fprintf(stderr,"beg neg rho fix1, rho,D,gamma = %26.20e %26.20e %26.20e \n", rho0, D, gamma); fflush(stderr);
rho0 = fabs(rho0);
}
#endif
W_last = w*gammasq ;
// Make sure that W is large enough so that v^2 < 1 :
i_increase = 0;
while( (( W_last*W_last*W_last * ( W_last + 2.*Bsq )
- QdotBsq*(2.*W_last + Bsq) ) <= W_last*W_last*(Qtsq-Bsq*Bsq))
&& (i_increase < 10) ) {
W_last *= 10.;
i_increase++;
}
W_for_gnr2 = W_for_gnr2_old = W_last;
rho_for_gnr2 = rho_for_gnr2_old = rho0;
// Calculate W:
x_1d[0] = W_last;
#if( USE_ISENTROPIC )
retval = general_newton_raphson( x_1d, 1, func_1d_orig1);
#else
retval = general_newton_raphson( x_1d, 1, func_1d_orig2);
#endif
W = x_1d[0];
/* Problem with solver, so return denoting error before doing anything further */
if( (retval != 0) || (W == FAIL_VAL) ) {
retval = retval*100+1;
#if(LTRACE)
fprintf(stderr,"fix1: retval, W, rho = %d %26.20e %26.20e \n", retval,W, rho_for_gnr2);fflush(stderr);
#endif
return(retval);
}
else{
if(W <= 0. || W > W_TOO_BIG) {
retval = 3;
#if(LTRACE)
fprintf(stderr,"fix1: retval, W, rho = %d %26.20e %26.20e \n", retval,W, rho_for_gnr2);fflush(stderr);
#endif
return(retval) ;
}
}
// Calculate v^2 :
vsq = vsq_calc(W) ;
if( vsq >= 1. ) {
retval = 4;
#if(LTRACE)
fprintf(stderr,"fix1: retval, W, rho,vsq = %d %26.20e %26.20e %26.20e \n", retval,W, rho_for_gnr2,vsq);fflush(stderr);
#endif
return(retval) ;
}
// Recover the primitive variables from the scalars and conserved variables:
gtmp = sqrt(1. - vsq);
gamma = 1./gtmp ;
rho0 = D * gtmp;
w = W * (1. - vsq) ;
p = pressure_of_rho( rho0 );
u = u_of_p(p);
// User may want to handle this case differently, e.g. do NOT return upon
// a negative rho/u, calculate v^i so that rho/u can be floored by other routine:
if( (rho0 <= 0.) || (u <= 0.) ) {
retval = 5;
#if(LTRACE)
fprintf(stderr,"fix1: retval, W, rho,vsq,u = %d %26.20e %26.20e %26.20e %26.20e \n", retval,W, rho0,vsq,u);fflush(stderr);
#endif
return(retval) ;
}
prim[RHO] = rho0 ;
prim[UU] = u ;
for(i=1;i<4;i++) Qtcon[i] = Qcon[i] + ncon[i] * Qdotn;
for(i=1;i<4;i++) prim[UTCON1+i-1] = gamma/(W+Bsq) * ( Qtcon[i] + QdotB*Bcon[i]/W ) ;
/* set field components */
for(i = BCON1; i <= BCON3; i++) prim[i] = U[i] ;
/* done! */
return(retval) ;
}
static int Utoprim_new_body(FTYPE U[NPR], struct of_geom *ptrgeom, FTYPE prim[NPR])
{
FTYPE Wtest;
FTYPE x_1d[1];
FTYPE QdotB,Bcon[4],Bcov[4],Qcov[4],Qcon[4],ncov[4],ncon[4],Qsq,Qtcon[4];
FTYPE rho0,u,p,w,gammasq,gamma,gtmp,W_last,W,utsq,vsq,tmpdiff ;
int i,j, retval, retval2, i_increase ;
static void raise_g(FTYPE vcov[], FTYPE gcon[][4], FTYPE vcon[]);
static void lower_g(FTYPE vcon[], FTYPE gcov[][4], FTYPE vcov[]);
static void ncov_calc(FTYPE gcon[][4],FTYPE ncov[]) ;
static FTYPE pressure_rho0_u(FTYPE rho0, FTYPE u);
static FTYPE pressure_rho0_w(FTYPE rho0, FTYPE w);
static int find_root_2D_gen(FTYPE x0, FTYPE *xnew) ;
const int ltrace = 0;
const int ltrace2 = 0;
/* TEMPORARY */
/*
primtoU_g(prim,gcov,gcon,U) ;
*/
#if(!OPTIMIZED)
if( ltrace ) {
for(i=0;i<8;i++) dualfprintf(fail_file,"%d %21.15g %21.15g\n",i,prim[i],U[i]) ;
}
#endif
// Assume ok initially:
pflag[ptrgeom->i][ptrgeom->j][FLAGUTOPRIMFAIL]= UTOPRIMNOFAIL;
for(i = BCON1; i <= BCON3; i++) prim[i] = U[i] ;
Bcon[0] = 0. ;
for(i=1;i<4;i++) Bcon[i] = U[BCON1+i-1] ;
lower_g(Bcon,ptrgeom->gcov,Bcov) ;
for(i=0;i<4;i++) Qcov[i] = U[QCOV0+i] ;
raise_g(Qcov,ptrgeom->gcon,Qcon) ;
Bsq = 0. ;
for(i=1;i<4;i++) Bsq += Bcon[i]*Bcov[i] ;
QdotB = 0. ;
for(i=0;i<4;i++) QdotB += Qcov[i]*Bcon[i] ;
QdotBsq = QdotB*QdotB ;
ncov_calc(ptrgeom->gcon,ncov) ;
raise_g(ncov,ptrgeom->gcon,ncon);
Qdotn = Qcon[0]*ncov[0] ;
Qsq = 0. ;
for(i=0;i<4;i++) Qsq += Qcov[i]*Qcon[i] ;
Qtsq = Qsq + Qdotn*Qdotn ;
D = U[RHO] ;
/* calculate W from last timestep and use
for guess */
utsq = 0. ;
for(i=1;i<4;i++)
for(j=1;j<4;j++) utsq += ptrgeom->gcov[i][j]*prim[UTCON1+i-1]*prim[UTCON1+j-1] ;
if( (utsq < 0.) && (fabs(utsq) < MAXNEGUTSQ) ) {
utsq = 0.0;
}
if(utsq < 0. || utsq > UTSQ_TOO_BIG) {
if( debugfail>=2 ) dualfprintf(fail_file,"Utoprim_new(): utsq < 0 in utoprim_1d attempt, utsq = %21.15g \n", utsq) ;
pflag[ptrgeom->i][ptrgeom->j][FLAGUTOPRIMFAIL]= UTOPRIMFAILCONVUTSQ;
return(1) ;
}
gammasq = 1. + utsq ;
gamma = sqrt(gammasq);
// Always calculate rho from D and gamma so that using D in EOS remains consistent
// i.e. you don't get positive values for dP/d(vsq) .
rho0 = D / gamma ;
u = prim[UU] ;
p = pressure_rho0_u(rho0,u) ;
w = rho0 + u + p ;
W_last = w*gammasq ;
// Make sure that W is large enough so that v^2 < 1 :
i_increase = 0;
while( (( W_last*W_last*W_last * ( W_last + 2.*Bsq ) - QdotBsq*(2.*W_last + Bsq) ) <= W_last*W_last*(Qtsq-Bsq*Bsq))
&& (i_increase < 10) ) {
W_last *= 10.;
i_increase++;
#if(!OPTIMIZED)
dualfprintf(fail_file,"badval : W = %21.15g, i_increase = %d \n", W_last, i_increase);
#endif
}
#if(!OPTIMIZED)
if( i_increase >= 10 ) {
dualfprintf(fail_file,"i_increase is too large, i_increase = %d , W = %21.15g \n", i_increase, W_last);
}
#endif
#if(!OPTIMIZED)
if( ltrace ) {
dualfprintf(fail_file,"u = %21.15g, p = %21.15g, Bsq = %21.15g, Qsq = %21.15g \n",u,p,Bsq,Qsq);
dualfprintf(fail_file,"Bcon[0-3] = %21.15g %21.15g %21.15g %21.15g \n", Bcon[0],Bcon[1],Bcon[2],Bcon[3]);
dualfprintf(fail_file,"Bcov[0-3] = %21.15g %21.15g %21.15g %21.15g \n", Bcov[0],Bcov[1],Bcov[2],Bcov[3]);
dualfprintf(fail_file,"Qcon[0-3] = %21.15g %21.15g %21.15g %21.15g \n", Qcon[0],Qcon[1],Qcon[2],Qcon[3]);
dualfprintf(fail_file,"Qcov[0-3] = %21.15g %21.15g %21.15g %21.15g \n", Qcov[0],Qcov[1],Qcov[2],Qcov[3]);
dualfprintf(fail_file,"call find_root\n") ;
}
#endif
// METHOD specific:
wglobal=w; // used to validate normalized version of W
retval = find_root_2D_gen(W_last, &W) ;
/* Problem with solver, so return denoting error before doing anything further */
if( (retval != 0) || (W == FAIL_VAL) ) {
if( debugfail>=2 ) {
dualfprintf(fail_file, "Failed to find a prim. var. solution!! %21.15g %21.15g %21.15g %21.15g %21.15g %21.15g \n",W_last,Bsq,QdotBsq,Qdotn,D,Qtsq);
dualfprintf(fail_file, "Utoprim_new_body(): bad newt failure, t,i,j, p[0-7], U[0-7] = %21.15g %d %d ", t, ptrgeom->i, ptrgeom->j );
for( i = 0 ; i < NPR; i++ ) {
dualfprintf(fail_file, "%21.15g ", prim[i]);
}
for( i = 0 ; i < NPR; i++ ) {
dualfprintf(fail_file, "%21.15g ", U[i]);
}
dualfprintf(fail_file, "\n");
}
pflag[ptrgeom->i][ptrgeom->j][FLAGUTOPRIMFAIL]= retval*100+1;// related to UTOPRIMFAILCONVRET
return(retval);
}
else{
Wtest=W/wglobal; // normalize to old densities
if(Wtest <= 0. || Wtest > GAMMASQ_TOO_BIG) {
//if(Wtest <= 0.) {
if( debugfail>=2 ) {
dualfprintf(fail_file,"Wtest failure %21.15g \n",Wtest) ;
dualfprintf(fail_file, "Utoprim_new_body(): Wtest<0 or Wtest=toobig failure, t,i,j, p[0-7], U[0-7] = %21.15g %d %d ", t, ptrgeom->i, ptrgeom->j );
for( i = 0 ; i < NPR; i++ ) {
dualfprintf(fail_file, "%21.15g ", prim[i]);
}
for( i = 0 ; i < NPR; i++ ) {
dualfprintf(fail_file, "%21.15g ", U[i]);
}
dualfprintf(fail_file, "\n");
}
pflag[ptrgeom->i][ptrgeom->j][FLAGUTOPRIMFAIL]= UTOPRIMFAILCONVW;
return(retval) ;
}
}
#if(!OPTIMIZED)
if( ltrace ) {
dualfprintf(fail_file,"(W,W_last,Bsq,Qtsq,QdotB,gammasq,Qdotn) %21.15g %21.15g %21.15g %21.15g %21.15g %21.15g %21.15g\n",
W,W_last,
Bsq,Qtsq,QdotB,gammasq,Qdotn) ;
dualfprintf(fail_file,"done find_root\n") ;
}
if( ltrace2 ) {
dualfprintf(fail_file, "\n <--------- %21.15g %21.15g %21.15g %21.15g %21.15g \n", Bsq,QdotBsq,Qdotn,D,Qtsq);
}
#endif
/*
if( nstep == 3 ) {
if( ((ptrgeom->i==89) && (ptrgeom->j==88||ptrgeom->j==111)) || (ptrgeom->i==92&&(ptrgeom->j==86||ptrgeom->j==113))
|| (ptrgeom->i==92&&(ptrgeom->j==86||ptrgeom->j==113) ) || (ptrgeom->i==94&&(ptrgeom->j==84||ptrgeom->j==115) )
|| (ptrgeom->i==105&&(ptrgeom->j==84||ptrgeom->j==115) ) || (ptrgeom->i==107&&(ptrgeom->j==86||ptrgeom->j==113) )
|| (ptrgeom->i==110&&(ptrgeom->j==88||ptrgeom->j==111) ) ) {
dualfprintf(fail_file, "\n <--------- %21.15g %21.15g %21.15g %21.15g %21.15g \n", Bsq,QdotBsq,Qdotn,D,Qtsq);
}
}
*/
// Calculate vsq
vsq = vsq_calc(W) ;
if( (vsq < 0.) && (fabs(vsq) < MAXNEGVSQ) ) {
vsq = 0.0;
}
// no check for vsq>1 since looking for failure to fix that's not just simple like above
//else if(vsq>=1.0){
// if(vsq<1.0+MAXNEGVSQ) vsq=VSQ_TOO_BIG;
// }
if( (vsq > VSQ_TOO_BIG)||(vsq<0.0) ) {
if( debugfail>=2 ) {
dualfprintf(fail_file,"vsq failure: vsq = %21.15g , W = %21.15g \n",vsq, W) ;
dualfprintf(fail_file, "Utoprim_new_body(): utsq==bad failure, t,i,j, p[0-7], U[0-7] = %21.15g %d %d ", t, ptrgeom->i, ptrgeom->j );
for( i = 0 ; i < NPR; i++ ) {
dualfprintf(fail_file, "%21.15g ", prim[i]);
}
for( i = 0 ; i < NPR; i++ ) {
dualfprintf(fail_file, "%21.15g ", U[i]);
}
dualfprintf(fail_file, "\n");
}
pflag[ptrgeom->i][ptrgeom->j][FLAGUTOPRIMFAIL]= UTOPRIMFAILCONVUTSQ2;
return(retval) ;
}
gtmp = sqrt(1. - vsq);
gamma = 1./gtmp ;
rho0 = D * gtmp;
w = W * (1. - vsq) ;
p = pressure_rho0_w(rho0,w) ;
u = w - (rho0 + p) ;
if( (rho0 <= 0.) || (u < 0.) ) {
if( debugfail>=2 ) {
tmpdiff = w - rho0;
dualfprintf(fail_file,
"rho or uu < 0 failure: rho,w,(w-rho),p,u = %21.15g %21.15g %21.15g %21.15g %21.15g \n",
rho0,w,tmpdiff,p,u) ;
dualfprintf(fail_file,
"rho or uu < 0 failure: gamma,utsq = %21.15g %21.15g \n", gamma, utsq) ;
}
if((rho0<=0.)&&(u>=0.)) pflag[ptrgeom->i][ptrgeom->j][FLAGUTOPRIMFAIL]= UTOPRIMFAILRHONEG;
if((rho0>0.)&&(u<0.)) pflag[ptrgeom->i][ptrgeom->j][FLAGUTOPRIMFAIL]= UTOPRIMFAILUNEG;
if((rho0<=0.)&&(u<0.)) pflag[ptrgeom->i][ptrgeom->j][FLAGUTOPRIMFAIL]= UTOPRIMFAILRHOUNEG;
if(UTOPRIMFAILRETURNTYPE==UTOPRIMRETURNNOTADJUSTED) return(retval) ; // else let assign -- used to check how bad failure is.
}
prim[RHO] = rho0 ;
prim[UU] = u ;
for(i=1;i<4;i++) Qtcon[i] = Qcon[i] + ncon[i] * Qdotn;
for(i=1;i<4;i++) prim[UTCON1+i-1] = gamma/(W+Bsq) * ( Qtcon[i] + QdotB*Bcon[i]/W ) ;
/* set field components */
for(i = BCON1; i <= BCON3; i++) prim[i] = U[i] ;
#if(!OPTIMIZED)
if( ltrace ) {
dualfprintf(fail_file," rho final = %21.15g , u final = %21.15g \n", rho0, u);
}
#endif
/* done! */
return(retval) ;
}
static int Utoprim_new_body(FTYPE U[NPR], FTYPE gcov[NDIM][NDIM],
FTYPE gcon[NDIM][NDIM], FTYPE gdet, FTYPE prim[NPR])
{
static void func_1d_gnr(FTYPE x[], FTYPE dx[], FTYPE resid[],
FTYPE jac[][NEWT_DIM], FTYPE *f, FTYPE *df, int n);
static void func_1d_gnr2(FTYPE x[], FTYPE dx[], FTYPE resid[],
FTYPE jac[][NEWT_DIM], FTYPE *f, FTYPE *df, int n);
static int general_newton_raphson( FTYPE x[], int n,
void (*funcd) (FTYPE [], FTYPE [], FTYPE [],
FTYPE [][NEWT_DIM], FTYPE *,
FTYPE *, int) );
static int gnr2( FTYPE x[], int n,
void (*funcd) (FTYPE [], FTYPE [], FTYPE [],
FTYPE [][NEWT_DIM], FTYPE *, FTYPE *, int) );
FTYPE x_1d[1];
FTYPE QdotB,Bcon[NDIM],Bcov[NDIM],Qcov[NDIM],Qcon[NDIM],ncov[NDIM],ncon[NDIM],Qsq,Qtcon[NDIM];
FTYPE rho0,u,p,w,gammasq,gamma,gtmp,W_last,W,utsq,vsq,tmpdiff ;
int i,j, retval, retval2, i_increase ;
// Assume ok initially:
retval = 0 ;
for(i = BCON1; i <= BCON3; i++) prim[i] = U[i] ;
// Calculate various scalars (Q.B, Q^2, etc) from the conserved variables:
Bcon[0] = 0. ;
for(i=1;i<4;i++) Bcon[i] = U[BCON1+i-1] ;
lower_g(Bcon,gcov,Bcov) ;
for(i=0;i<4;i++) Qcov[i] = U[QCOV0+i] ;
raise_g(Qcov,gcon,Qcon) ;
Bsq = 0. ;
for(i=1;i<4;i++) Bsq += Bcon[i]*Bcov[i] ;
QdotB = 0. ;
for(i=0;i<4;i++) QdotB += Qcov[i]*Bcon[i] ;
QdotBsq = QdotB*QdotB ;
ncov_calc(gcon,ncov) ;
raise_g(ncov,gcon,ncon);
Qdotn = Qcon[0]*ncov[0] ;
Qsq = 0. ;
for(i=0;i<4;i++) Qsq += Qcov[i]*Qcon[i] ;
Qtsq = Qsq + Qdotn*Qdotn ;
D = U[RHO] ;
/* calculate W from last timestep and use for guess */
utsq = 0. ;
for(i=1;i<4;i++)
for(j=1;j<4;j++) utsq += gcov[i][j]*prim[UTCON1+i-1]*prim[UTCON1+j-1] ;
if( (utsq < 0.) && (fabs(utsq) < 1.0e-13) ) {
utsq = fabs(utsq);
}
if(utsq < 0. || utsq > UTSQ_TOO_BIG) {
retval = 2;
return(retval) ;
}
gammasq = 1. + utsq ;
gamma = sqrt(gammasq);
// Always calculate rho from D and gamma so that using D in EOS remains consistent
// i.e. you don't get positive values for dP/d(vsq) .
rho0 = D / gamma ;
u = prim[UU] ;
p = pressure_rho0_u(rho0,u) ;
w = rho0 + u + p ;
W_last = w*gammasq ;
// Make sure that W is large enough so that v^2 < 1 :
i_increase = 0;
while( (( W_last*W_last*W_last * ( W_last + 2.*Bsq )
- QdotBsq*(2.*W_last + Bsq) ) <= W_last*W_last*(Qtsq-Bsq*Bsq))
&& (i_increase < 10) ) {
W_last *= 10.;
i_increase++;
}
// Initialize independent variables for Newton-Raphson:
W_for_gnr = W_last;
x_1d[0] = vsq_for_gnr2 = 1. - 1. / gammasq ;
// Find vsq via Newton-Raphson:
retval = general_newton_raphson( x_1d, 1, func_1d_gnr) ;
// Find W from this vsq:
vsq_for_gnr2 = x_1d[0] ;
x_1d[0] = W_for_gnr;
retval2 = gnr2( x_1d, 1, func_1d_gnr2 ) ;
W = x_1d[0];
retval += retval2 ;
/* Problem with solver, so return denoting error before doing anything further */
if( (retval != 0) || (W == FAIL_VAL) ) {
retval = retval*100+1;
return(retval);
}
else{
if(W <= 0. || W > W_TOO_BIG) {
retval = 3;
return(retval) ;
}
}
// Calculate v^2 :
vsq = vsq_calc(W) ;
if( vsq >= 1. ) {
retval = 4;
return(retval) ;
}
// Recover the primitive variables from the scalars and conserved variables:
gtmp = sqrt(1. - vsq);
gamma = 1./gtmp ;
rho0 = D * gtmp;
w = W * (1. - vsq) ;
p = pressure_rho0_w(rho0,w) ;
u = w - (rho0 + p) ;
// User may want to handle this case differently, e.g. do NOT return upon
// a negative rho/u, calculate v^i so that rho/u can be floored by other routine:
if( (rho0 <= 0.) || (u <= 0.) ) {
retval = 5;
return(retval) ;
}
prim[RHO] = rho0 ;
prim[UU] = u ;
for(i=1;i<4;i++) Qtcon[i] = Qcon[i] + ncon[i] * Qdotn;
for(i=1;i<4;i++) prim[UTCON1+i-1] = gamma/(W+Bsq) * ( Qtcon[i] + QdotB*Bcon[i]/W ) ;
/* set field components */
for(i = BCON1; i <= BCON3; i++) prim[i] = U[i] ;
/* done! */
return(retval) ;
}
