void CPengRobinson::SetTDState_hs (su2double h, su2double s ) {
su2double T, fv, sqrt2=sqrt(2.0), A;
su2double f, v, atanh;
su2double x1, x2, xmid, dx, fx1, fx2, fmid, rtb;
su2double toll = 1e-9, FACTOR=0.2;
su2double cons_s, cons_h;
unsigned short countrtb=0, NTRY=10, ITMAX=100;
A = Gas_Constant / Gamma_Minus_One;
T = h*Gamma_Minus_One/Gas_Constant/Gamma;
v = exp(-1/Gamma_Minus_One*log(T) + s/Gas_Constant);
if (Zed<0.9999) {
x1 = Zed*v;
x2 = v;
} else{
x1 = 0.2*v;
x2 = v;
}
T = T_v_h(x1, h);
atanh = (log(1.0+( b*sqrt2 / (x1 + b))) - log(1.0-( b*sqrt2 / (x1 + b))))/2.0;
fv = atanh;
fx1 = A*log(T) + Gas_Constant*log(x1 - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
T = T_v_h(x2, h);
atanh = (log(1.0+( b*sqrt2 / (x2 + b))) - log(1.0-( b*sqrt2 / (x2 + b))))/2.0;
fv = atanh;
fx2 = A*log(T) + Gas_Constant*log(x2 - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
// zbrac algorithm NR
for (int j=1; j<=NTRY; j++) {
if (fx1*fx2 > 0.0) {
if (fabs(fx1) < fabs(fx2)) {
x1 += FACTOR*(x1-x2);
T = T_v_h(x1, h);
atanh = (log(1.0+( b*sqrt2/(x1 + b))) - log(1.0-( b*sqrt2/(x1 + b))))/2.0;
fv = atanh;
fx1 = A*log(T) + Gas_Constant*log(x1 - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
} else{
x2 += FACTOR*(x2-x1);
T = T_v_h(x2, h);
atanh = (log(1.0+( b*sqrt2/(x2 + b))) - log(1.0-( b*sqrt2/(x2 + b))))/2.0;
fv = atanh;
fx2 = A*log(T) + Gas_Constant*log(x2 - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
}
}
}
// rtbis algorithm NR
f=fx1;
fmid=fx2;
if (f*fmid >= 0.0) {
cout<< "Root must be bracketed for bisection in rtbis"<< endl;
SetTDState_rhoT(Density, Temperature);
}
rtb = f < 0.0 ? (dx=x2-x1,x1) : (dx=x1-x2,x2);
do{
xmid=rtb+(dx *= 0.5);
T = T_v_h(xmid, h);
atanh = (log(1.0+( b* sqrt2/(xmid + b))) - log(1.0-( b* sqrt2/(xmid + b))))/2.0;
fv = atanh;
fmid= A*log(T) + Gas_Constant*log(xmid - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
if (fmid <= 0.0) rtb=xmid;
countrtb++;
}while(abs(fmid) > toll && countrtb<ITMAX);
v = xmid;
if (countrtb==ITMAX) {
cout <<"Too many bisections in rtbis" << endl;
// do{
// atanh = (log(1.0+( b/v* sqrt2/(1 + b/v))) - log(1.0-( b/v* sqrt2/(1 + b/v))))/2.0;
// fv = atanh;
// T=T_v_h(v, h);
// f = A*log(T) + Gas_Constant*log(v - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
// f1= Gas_Constant/(v-b)+ a*sqrt(alpha2(T)) *k/(sqrt(T*TstarCrit)*(v*v - b*b - 2*v*b));
// dv= f/f1;
// v-= dv;
// countnw++;
// }while(abs(f/x2) > toll && countnw<ITMAXNW);
//
// } else{
}
if (v!=v) {
cout <<"not physical solution found, h and s input " << h << " "<< s << endl;
SetTDState_rhoT(Density, Temperature);
}
T=T_v_h(v, h);
SetTDState_rhoT(1/v, T);
// consistency check
cons_h= abs(((StaticEnergy + Pressure/Density) - h)/h);
cons_s= abs((Entropy-s)/s);
if (cons_h >1e-4 || cons_s >1e-4) {
cout<< "TD consistency not verified in hs call"<< endl;
//cout <<"Before "<< h <<" "<< s << endl;
//cout <<"After "<< StaticEnergy + Pressure/Density <<" "<< Entropy << fmid <<" "<< f<< " "<< countrtb<<" "<< countnw<< endl;
//getchar();
}
}
void CPengRobinson::SetTDState_Ps (su2double P, su2double s){
su2double T, rho, v, cons_P, cons_s, fv, A, atanh;
su2double x1,x2, fx1, fx2,f, fmid, rtb, dx, xmid, sqrt2=sqrt(2.0);
su2double toll = 1e-5, FACTOR=0.2;
unsigned short count=0, NTRY=10, ITMAX=100;
A = Gas_Constant / Gamma_Minus_One;
T = exp(Gamma_Minus_One/Gamma* (s/Gas_Constant +log(P) -log(Gas_Constant)) );
v = (T*Gas_Constant)/P;
if(Zed<0.9999){
x1 = Zed*v;
x2 = v;
}else{
x1 = 0.2*v;
x2 = v;
}
T = T_P_rho(P,1.0/x1);
atanh = (log(1.0 + ( b*sqrt2 / (x1 + b) )) - log(1.0-( b*sqrt2 / (x1 + b) )))/2.0;
fv = atanh;
fx1 = A*log(T) + Gas_Constant*log(x1 - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
T = T_P_rho(P,1.0/x2);
atanh = (log(1.0 + ( b*sqrt2 / (x2 + b) )) - log(1.0-( b*sqrt2 / (x2 + b) )))/2.0;
fv = atanh;
fx2 = A*log(T) + Gas_Constant*log(x2 - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
// zbrac algorithm NR
for (int j=1;j<=NTRY;j++) {
if (fx1*fx2 > 0.0){
if (fabs(fx1) < fabs(fx2)){
x1 += FACTOR*(x1-x2);
T = T_P_rho(P,1.0/x1);
atanh = (log(1.0 + ( b*sqrt2 / (x1 + b) )) - log(1.0-( b*sqrt2 / (x1 + b) )))/2.0;
fv = atanh;
fx1 = A*log(T) + Gas_Constant*log(x1 - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
}else{
T = T_P_rho(P,1.0/x2);
atanh = (log(1.0 + ( b*sqrt2 / (x2 + b) )) - log(1.0-( b*sqrt2 / (x2 + b) )))/2.0;
fv = atanh;
fx2 = A*log(T) + Gas_Constant*log(x2 - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
}
}
}
// rtbis algorithm NR
f=fx1;
fmid=fx2;
if (f*fmid >= 0.0){
cout<< "Root must be bracketed for bisection in rtbis"<< endl;
SetTDState_rhoT(Density, Temperature);
}
rtb = f < 0.0 ? (dx=x2-x1,x1) : (dx=x1-x2,x2);
do{
xmid=rtb+(dx *= 0.5);
T = T_P_rho(P,1.0/xmid);
atanh = (log(1.0 + ( b*sqrt2 / (xmid + b) )) - log(1.0-( b*sqrt2 / (xmid + b) )))/2.0;
fv = atanh;
fmid = A*log(T) + Gas_Constant*log(xmid - b) - a*sqrt(alpha2(T)) *k*fv/(b*sqrt2*sqrt(T*TstarCrit)) - s;
if (fmid <= 0.0) rtb=xmid;
count++;
}while(abs(fmid) > toll && count<ITMAX);
if(count==ITMAX){
cout <<"Too many bisections in rtbis" << endl;
}
rho = 1.0/xmid;
T = T_P_rho(P, rho);
SetTDState_rhoT(rho, T);
// cout << xmid << " "<< T<< " "<< Pressure<< " "<< P << " "<< Entropy << " "<< s <<endl;
cons_P= abs((Pressure -P)/P);
cons_s= abs((Entropy-s)/s);
if(cons_P >1e-3 || cons_s >1e-3){
cout<< "TD consistency not verified in hs call"<< endl;
}
}
void CVanDerWaalsGas::SetTDState_hs (double h, double s ) {
double v, T, rho, f, fmid, rtb;
double x1,x2,xmid, dx, fx1, fx2;
double toll = 1e-5, FACTOR=0.2;
unsigned short count=0, NTRY=10, ITMAX=100;
double cons_s, cons_h;
// cout <<"Before "<< h <<" "<< s << endl;
T = 1.0*h*Gamma_Minus_One/Gas_Constant/Gamma;
v =exp(-1/Gamma_Minus_One*log(T) + s/Gas_Constant);
if (Zed<0.9999) {
x1 = Zed*v;
x2 = v;
} else{
x1 = 0.5*v;
x2 = v;
}
fx1 = log(x1-b) - s/Gas_Constant + log((h+ 2*a/x1)/Gas_Constant/(1/Gamma_Minus_One+ x1/(x1-b)))/Gamma_Minus_One;
fx2 = log(x2-b) - s/Gas_Constant + log((h+ 2*a/x2)/Gas_Constant/(1/Gamma_Minus_One+ x2/(x2-b)))/Gamma_Minus_One;
// zbrac algorithm NR
for (int j=1; j<=NTRY; j++) {
if (fx1*fx2 > 0.0) {
if (fabs(fx1) < fabs(fx2)) {
x1 += FACTOR*(x1-x2);
fx1 = log(x1-b) - s/Gas_Constant + log((h+ 2*a/x1)/Gas_Constant/(1/Gamma_Minus_One+ x1/(x1-b)))/Gamma_Minus_One;
} else{
x2 += FACTOR*(x2-x1);
fx2 = log(x2-b) - s/Gas_Constant + log((h+ 2*a/x2)/Gas_Constant/(1/Gamma_Minus_One+ x2/(x2-b)))/Gamma_Minus_One;
}
}
}
// rtbis algorithm NR
f=fx1;
fmid=fx2;
if (f*fmid >= 0.0) {
cout<< "Root must be bracketed for bisection in rtbis"<< endl;
SetTDState_rhoT(Density, Temperature);
}
rtb = f < 0.0 ? (dx=x2-x1,x1) : (dx=x1-x2,x2);
do{
xmid=rtb+(dx *= 0.5);
fmid= log(xmid-b) - s/Gas_Constant + log((h+ 2*a/xmid)/Gas_Constant/(1/Gamma_Minus_One+ xmid/(xmid-b)))/Gamma_Minus_One;
if (fmid <= 0.0) rtb=xmid;
count++;
}while(abs(fmid) > toll && count<ITMAX);
v = xmid;
if (count==ITMAX) {
cout <<"Too many bisections in rtbis" << endl;
}
rho = 1/v;
T= (h+ 2*a/v)/Gas_Constant/(1/Gamma_Minus_One+ v/(v-b));
SetTDState_rhoT(rho, T);
cons_h= abs(((StaticEnergy + Pressure/Density) - h)/h);
cons_s= abs((Entropy-s)/s);
if (cons_h >1e-3 or cons_s >1e-3) {
cout<< "TD consistency not verified in hs call"<< endl;
}
// cout <<"After "<< StaticEnergy + Pressure/Density <<" "<< Entropy<<" "<< fmid <<" "<< f<< " "<< count<< endl;
// T= (h+ 2*a/v)/Gas_Constant/(1/Gamma_Minus_One+ v/(v-b));
// do{
// f= log(v-b) - s/Gas_Constant + log(T)/Gamma_Minus_One;
// f1= 1.0/(v-b);
// dv= f/f1;
// v-= 1.0*dv;
// T= (h+ 2*a/v)/Gas_Constant/(1/Gamma_Minus_One+ v/(v-b));
// count++;
// }while(abs(dv/v) > toll && count < nmax);
}
