static void func_1d_gnr(FTYPE x[], FTYPE dx[], FTYPE resid[],
FTYPE jac[][NEWT_DIM], FTYPE *f, FTYPE *df, int n)
{
FTYPE vsq,W,W0,dpdW,Wsq,W3,p_tmp,dWdvsq , dpdvsq, fact_tmp ;
int retval, iters;
static void func_1d_gnr2(FTYPE x[], FTYPE dx[], FTYPE resid[],
FTYPE jac[][NEWT_DIM], FTYPE *f, FTYPE *df, int n);
static int gnr2( FTYPE x[], int n,
void (*funcd) (FTYPE [], FTYPE [], FTYPE [],
FTYPE [][NEWT_DIM], FTYPE *, FTYPE *, int) );
static FTYPE dpdvsq_calc(FTYPE W, FTYPE vsq);
vsq = x[0];
// Calculate best value for W given current guess for vsq:
vsq_for_gnr2 = vsq;
W0 = W_for_gnr;
retval = 1 ;
iters = 0;
while ( (retval != 0) && (++iters < 6) ) {
x[0] = W0;
retval = gnr2( x, 1, func_1d_gnr2 ) ;
W0 *= 10.;
}
W = W_for_gnr = x[0];
Wsq = W*W;
W3 = W*Wsq;
x[0] = vsq;
dpdW = dpdW_calc_vsq( W, vsq );
dpdvsq = dpdvsq_calc( W, vsq );
dWdvsq = ( dpdvsq - 0.5*Bsq ) / ( 1. - dpdW + QdotBsq/W3 ) ;
fact_tmp = (Bsq + W) ;
resid[0] = Qtsq - vsq * fact_tmp * fact_tmp + QdotBsq * ( Bsq + 2.*W ) / Wsq ;
jac[0][0] = -fact_tmp * ( fact_tmp + 2. * dWdvsq * ( vsq + QdotBsq/W3 ) ) ;
dx[0] = -resid[0]/jac[0][0];
*f = 0.5*resid[0]*resid[0];
*df = -2. * (*f);
}
//isentropic version: eq. (27)
static void func_1d_orig1(FTYPE x[], FTYPE dx[], FTYPE resid[],
FTYPE jac[][NEWT_DIM], FTYPE *f, FTYPE *df, int n)
{
int retval, ntries;
FTYPE Dc, t1, t10, t2 , t21, t23, t26, t29, t3 , t30;
FTYPE t32, t33, t34, t38, t5 , t51, t67, t8, W, x_rho[1], rho, rho_g ;
W = x[0];
W_for_gnr2_old = W_for_gnr2;
W_for_gnr2 = W;
// get rho from NR:
rho_g = x_rho[0] = rho_for_gnr2;
ntries = 0;
while ( (retval = gnr2( x_rho, 1, func_gnr2_rho)) && ( ntries++ < 10 ) ) {
rho_g *= 10.;
x_rho[0] = rho_g;
}
#if(LTRACE)
if( x_rho[0] <= 0. ) {
fprintf(stderr,"gnr2 neg rho = %d ,rho_n,rho,rho_o,W,W_o = %26.20e %26.20e %26.20e %26.20e %26.20e \n", retval, x_rho[0], rho_for_gnr2, rho_for_gnr2_old, x[0], W_for_gnr2_old);
fflush(stderr);
}
if( retval ) {
fprintf(stderr,"gnr2 retval = %d ,rho_n,rho,rho_o,W,W_o = %26.20e %26.20e %26.20e %26.20e %26.20e \n", retval, x_rho[0], rho_for_gnr2, rho_for_gnr2_old, x[0], W_for_gnr2_old);
fflush(stderr);
}
#endif
rho_for_gnr2_old = rho_for_gnr2;
rho = rho_for_gnr2 = x_rho[0];
Dc = D;
t1 = Dc*Dc;
t2 = QdotBsq*t1;
t3 = t2*Bsq;
t5 = Bsq*Bsq;
t8 = t1*Bsq;
t10 = t1*W;
t21 = W*W;
t23 = rho*rho;
t26 = 1/t1;
resid[0] = (t3+(2.0*t2+((Qtsq-t5)*t1
+(-2.0*t8-t10)*W)*W)*W+(t5+(2.0*Bsq+W)*W)*t21*t23)*t26/t21;
t29 = t1*t1;
t30 = QdotBsq*t29;
t32 = GAMMA*K_atm;
t33 = pow(rho,1.0*GAMMA);
t34 = t32*t33;
t38 = t23 * t33;
t51 = GAMMA*t1*K_atm*t33;
t67 = t21*W;
jac[0][0] = -2.0*(t30*Bsq*t34+(t30*t34
+((-t38*Bsq*t32+Bsq*GAMMA*t1*K_atm*t33)*t1
+(-t38*GAMMA*K_atm+t51)*t1*W)*t21)*W
+((-t3+(-t2+(-t8-t10)*t21)*W)*W+(-t5-Bsq*W)*t67*t23)*t23)*t26/(t51-W*t23)/t67;
dx[0] = -resid[0]/jac[0][0];
*f = 0.5*resid[0]*resid[0];
*df = -2. * (*f);
return;
}
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) ;
}
