static int find_root_2D_gen(FTYPE *x0)
{
FTYPE x[2], x_orig[2];
int ntries = 0;
int n = 2;
int ret;
const int ltrace = 0;
// extern void func_gamma( FTYPE x[2], FTYPE dx[2], FTYPE *f, FTYPE *df, int n);
// extern void func_vsq( FTYPE x[2], FTYPE dx[2], FTYPE *f, FTYPE *df, int n);
// extern void func_utsq( FTYPE x[2], FTYPE dx[2], FTYPE *f, FTYPE *df, int n);
/* Set presets: */
x_orig[0] = x[0] = fabs(*x0) ;
x_orig[1] = x[1] = x1_of_x0( *x0, 3 ) ;
if( ltrace ) {
fprintf(stdout, "find_root_2D_gen(): x[0] = %21.15g , x[1] = %21.15g \n", x[0], x[1]);
fflush(stdout);
}
ret = general_newton_raphson( x, n, func_vsq );
while( (ret != 0) && (ntries < MAX_NEWT_RETRIES ) ) {
x[0] = x_orig[0] * (1. + 0.2*(1.*rand())/(1.*RAND_MAX) );
x[1] = x1_of_x0( x[0], 3 ) ;
ntries++;
}
if( (ntries >= MAX_NEWT_RETRIES) && (MAX_NEWT_RETRIES > 0) ) {
fprintf(stderr, "find_root_2D_gen(): Bad exit value from general_newton_raphson() !! \n");
fprintf(stderr, "find_root_2D_gen(): ntries = %d , x[0] = %21.15g , x[1] = %21.15g \n", ntries, x[0], x[1]); fflush(stderr);
}
if( ret != 0 ) {
*x0 = FAIL_VAL;
return( ret );
}
*x0 = x[0];
return(0);
}
static int Utoprim_new_body(FTYPE U[NPR], FTYPE gcov[NDIM][NDIM],
FTYPE gcon[NDIM][NDIM], FTYPE gdet, FTYPE prim[NPR])
{
FTYPE x_2d[NEWT_DIM];
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;
int i,j, n, retval, i_increase ;
double dummy;
n = NEWT_DIM ;
// 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) ;
// fprintf(stderr,"failure, utsq_too_big at %d %d\n", i,j);
}
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++;
}
// Calculate W and vsq:
x_2d[0] = fabs( W_last );
x_2d[1] = x1_of_x0( W_last ) ;
retval = general_newton_raphson( x_2d, n, func_vsq ) ;
W = x_2d[0];
vsq = x_2d[1];
/* Problem with solver, so return denoting error before doing anything further */
if( (retval != 0) || (W == FAIL_VAL) ) {
// fprintf(stderr,"failure, in solver at %d %d\n", i,j);
retval = retval*100+1;
return(retval);
}
else{
if(W <= 0. || W > W_TOO_BIG) {
// fprintf(stderr,"failure, W_too_big at %d %d\n", i,j);
retval = 3;
return(retval) ;
}
}
// Calculate v^2:
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) ;
}
static int find_root_2D_gen(FTYPE x0, FTYPE *xnew)
{
FTYPE x[2], x_orig[2];
int ntries = 0;
int retval, n = 2;
int it;
static void func_vsq( FTYPE [], FTYPE [], FTYPE [], FTYPE [][NEWT_DIM], FTYPE *f, FTYPE *df, int n);
static void func_vsq2( FTYPE [], FTYPE [], FTYPE [], FTYPE [][NEWT_DIM], FTYPE *f, FTYPE *df, int n);
static FTYPE res_sq_vsq( FTYPE [] );
static FTYPE res_sq_vsq2( FTYPE [] );
static FTYPE x1_of_x0(FTYPE x0 ) ;
static int general_newton_raphson( FTYPE x[], int n, int do_line_search,
void (*funcd) (FTYPE [], FTYPE [], FTYPE [], FTYPE [][NEWT_DIM],
FTYPE *, FTYPE *, int),
FTYPE (*res_func) (FTYPE []) );
const int ltrace = 0;
/* Set presets: */
x_orig[0] = x[0] = fabs(x0) ;
x_orig[1] = x[1] = x1_of_x0( x0 ) ;
#if(!OPTIMIZED)
if( ltrace ) {
dualfprintf(fail_file, "find_root_2D_gen(): x[0] = %21.15g , x[1] = %21.15g \n", x[0], x[1]);
}
#endif
retval = general_newton_raphson( x, n, USE_LINE_SEARCH, func_vsq2, res_sq_vsq2 ) ;
ntries++;
while( (retval==1) && (ntries <= MAX_NEWT_RETRIES ) ) {
// x[0] = x_orig[0] * (1. + ( (1.*rand())/(1.*RAND_MAX) - 0.5 ) );
x[0] = x_orig[0];
for( it=0; it<ntries; it++) x[0] *= 10.0;
x[1] = x1_of_x0( x[0] ) ;
// retval = general_newton_raphson( x, n, USE_LINE_SEARCH, func_vsq, res_sq_vsq ) ;
retval = general_newton_raphson( x, n, USE_LINE_SEARCH, func_vsq2, res_sq_vsq2 ) ;
#if(!OPTIMIZED)
if( ltrace ) {
dualfprintf(fail_file, "find_root_2D_gen(): ntries, x[0,1] = %4i %21.15g %21.15g \n", ntries, x[0], x[1]);
}
#endif
ntries++;
}
#if( MAX_NEWT_RETRIES > 0 )
if( (ntries > MAX_NEWT_RETRIES) && (retval==1) ) {
if( debugfail >= 2 ) {
dualfprintf(fail_file, "find_root_2D_gen(): Bad exit value from general_newton_raphson() !! \n");
dualfprintf(fail_file, "find_root_2D_gen(): ntries = %d , x[0] = %21.15g , x[1] = %21.15g \n", ntries, x[0], x[1]);
}
}
#endif
*xnew = x[0];
return(retval);
}