static int region1_df(const gsl_vector *x, void *user_data, gsl_matrix *J){
#define D ((Solver2Data *)user_data)
double p = gsl_vector_get(x,0);
double T = gsl_vector_get(x,1);
SteamState S = freesteam_region1_set_pT(p,T);
gsl_matrix_set(J, 0, 0, freesteam_region1_dAdpT(D->A,S));
gsl_matrix_set(J, 0, 1, freesteam_region1_dAdTp(D->A,S));
gsl_matrix_set(J, 1, 0, freesteam_region1_dAdpT(D->B,S));
gsl_matrix_set(J, 1, 1, freesteam_region1_dAdTp(D->B,S));
return GSL_SUCCESS;
#undef D
}
SteamState freesteam_set_pu(double p, double u){
double lb, ub, tol, sol, err;
SolvePUData D = {p, u, 0.};
SteamState S;
int region = freesteam_region_pu(p,u);
switch(region){
case 1:
lb = IAPWS97_TMIN;
ub = REGION1_TMAX;
tol = 1e-9; /* ??? */
zeroin_solve(&pu_region1_fn, &D, lb, ub, tol, &sol, &err);
S = freesteam_region1_set_pT(p,sol);
break;
case 2:
lb = IAPWS97_TMIN;
ub = REGION2_TMAX;
tol = 1e-9; /* ??? */
zeroin_solve(&pu_region2_fn, &D, lb, ub, tol, &sol, &err);
S = freesteam_region2_set_pT(p,sol);
break;
case 4:
lb = 0.;
ub = 1.;
tol = 1e-9; /* ??? */
D.T = freesteam_region4_Tsat_p(p);
//fprintf(stderr,"%s: (%s:%d): p = %g\n",__func__,__FILE__,__LINE__,D.p);
zeroin_solve(&pu_region4_fn, &D, lb, ub, tol, &sol, &err);
S = freesteam_region4_set_Tx(D.T,sol);
break;
case 3:
/* FIXME looks like a problem with the derivative routines here? */
{
int status;
SteamState guess = freesteam_region3_set_rhoT(IAPWS97_RHOCRIT,IAPWS97_TCRIT);
S = freesteam_solver2_region3('p','u', p, u, guess, &status);
if(status){
fprintf(stderr,"%s (%s:%d): Failed solve in region 3 for (p = %g MPa, u = %g kJ/kg\n"
,__func__,__FILE__,__LINE__,p/1e6,u/1e3);
//exit(1);
}
}
break;
default:
fprintf(stderr,"%s (%s:%d): Region '%d' not implemented\n",__func__,__FILE__,__LINE__,region);
exit(1);
}
return S;
}
double freesteam_drhofdT_T(double T){
double dpsatdT = freesteam_region4_dpsatdT_T(T);
if(T < REGION1_TMAX){
double psat = freesteam_region4_psat_T(T);
SteamState Sf = freesteam_region1_set_pT(psat,T);
double vf = freesteam_v(Sf);
return -1./SQ(vf) * (PT1('v',Sf) * dpsatdT + TP1('v',Sf));
}else{
/* FIXME: add iterative refinement of value of rhof */
double rhof = freesteam_region4_rhof_T(T);
SteamState Sf = freesteam_region3_set_rhoT(rhof,T);
double dpdT = TV3('p',Sf);
double dpdrho = -1./SQ(rhof) * VT3('p',Sf);
return (dpsatdT - dpdT)/dpdrho;
}
}
/*
⎰ ∂z ⎱ = ⎰∂z_f⎱ (1 - x) + ⎰∂z_f⎱ x
⎱ ∂T ⎰x ⎱ ∂T ⎰ ⎱ ∂T ⎰
*/
double freesteam_region4_dAdTx(FREESTEAM_CHAR z, SteamState S){
double res;
#define T S.R4.T
switch(z){
case 'p': res = freesteam_region4_dpsatdT_T(T); return res;
case 'T': res = 1; return res;
case 'x': res = 0; return res;
}
//fprintf(stderr,"%s: T = %g\n",__func__,T);
assert(!isnan(T));
double dzfdT, dzgdT;
if(T < REGION1_TMAX){
//fprintf(stderr,"%s: below REGION1_TMAX\n",__func__);
double psat = freesteam_region4_psat_T(T);
SteamState Sf = freesteam_region1_set_pT(psat,T);
SteamState Sg = freesteam_region2_set_pT(psat,T);
double dpsatdT = freesteam_region4_dpsatdT_T(T);
dzfdT = PT1(z,Sf)*dpsatdT + TP1(z,Sf);
dzgdT = PT2(z,Sg)*dpsatdT + TP2(z,Sg);
}else{
double rhof = freesteam_region4_rhof_T(T);
double rhog = freesteam_region4_rhog_T(T);
assert(rhof!=0);
assert(rhog!=0);
SteamState Sf = freesteam_region3_set_rhoT(rhof,T);
SteamState Sg = freesteam_region3_set_rhoT(rhog,T);
double dvfdT = -1./SQ(rhof) * freesteam_drhofdT_T(T);
assert(!isnan(dvfdT));
double dvgdT = -1./SQ(rhog) * freesteam_drhogdT_T(T);
assert(!isnan(dvgdT));
dzfdT = VT3(z,Sf)*dvfdT + TV3(z,Sf);
dzgdT = VT3(z,Sg)*dvgdT + TV3(z,Sg);
}
assert(!isnan(dzfdT));
assert(!isnan(dzgdT));
#define x S.R4.x
res = dzfdT*(1-x) + dzgdT*x;
//fprintf(stderr,"(∂%c/∂T)x = %g\n",z,res);
return res;
#undef T
#undef x
}
SteamState freesteam_solver2_region1(FREESTEAM_CHAR A, FREESTEAM_CHAR B, double atarget, double btarget, SteamState guess, int *retstatus){
const gsl_multiroot_fdfsolver_type *T;
gsl_multiroot_fdfsolver *s;
int status;
size_t iter = 0;
const size_t n = 2;
//fprintf(stderr,"region 1 solver...\n");
Solver2Data D = {A,B,solver2_region1_propfn(A), solver2_region1_propfn(B), atarget,btarget};
gsl_multiroot_function_fdf f = {®ion1_f, ®ion1_df, ®ion1_fdf, n, &D};
gsl_vector *x = gsl_vector_alloc(n);
gsl_vector_set(x, 0, freesteam_rho(guess));
gsl_vector_set(x, 1, freesteam_T(guess));
T = gsl_multiroot_fdfsolver_gnewton;
s = gsl_multiroot_fdfsolver_alloc(T, n);
gsl_multiroot_fdfsolver_set(s, &f, x);
//region1_print_state(iter, s);
do{
iter++;
status = gsl_multiroot_fdfsolver_iterate(s);
//region1_print_state(iter, s);
if(status){
/* check if solver is stuck */
break;
}
status = gsl_multiroot_test_residual(s->f, 1e-6);
} while(status == GSL_CONTINUE && iter < 20);
SteamState S = freesteam_region1_set_pT(gsl_vector_get(s->x,0), gsl_vector_get(s->x,1));
gsl_multiroot_fdfsolver_free(s);
gsl_vector_free(x);
*retstatus = status;
if(status){
fprintf(stderr,"%s (%s:%d): %s: ",__func__,__FILE__,__LINE__,gsl_strerror(status));
freesteam_fprint(stderr,S);
}
return S;
}
