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Yes!! Composition derivatives working almost entirely.

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This commit is contained in:
Ian Bell
2014-08-28 21:52:25 +02:00
parent e7aa3df917
commit d539f5cde8
9 changed files with 400 additions and 184 deletions
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228
src/Backends/Helmholtz/ReducingFunctions.cpp
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@@ -146,12 +146,28 @@ ReducingFunction *ReducingFunction::factory(const std::vector<CoolPropFluid*> &c
long double ReducingFunction::d_ndTrdni_dxj__constxi(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
long double s = 0;
for (std::size_t k = 0; k < N; k++)
{
s += x[k]*d2Trdxidxj(x,j,k, xN_flag);
}
return d2Trdxidxj(x,i,j, xN_flag)-dTrdxi__constxj(x,j, xN_flag)-s;
if (xN_flag == XN_INDEPENDENT){
long double s = 0;
for (std::size_t k = 0; k < N; k++)
{
s += x[k]*d2Trdxidxj(x,j,k, xN_flag);
}
return d2Trdxidxj(x,i,j, xN_flag)-dTrdxi__constxj(x,j, xN_flag)-s;
}
else if (xN_flag == XN_DEPENDENT){
if (j == N-1){ return 0;}
long double s = 0;
for (std::size_t k = 0; k < N-1; k++)
{
s += x[k]*d2Trdxidxj(x,j,k, xN_flag);
}
long double val = d2Trdxidxj(x,i,j, xN_flag)-dTrdxi__constxj(x,j, xN_flag)-s;
return val;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
long double ReducingFunction::d_ndrhorbardni_dxj__constxi(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
@@ -217,6 +233,14 @@ long double GERG2008ReducingFunction::dTrdxi__constxj(const std::vector<long dou
{
return dYrdxi__constxj(x, i, beta_T, gamma_T, T_c, Yc_T, xN_flag);
}
long double GERG2008ReducingFunction::d2Trdxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return d2Yrdxi2__constxj(x, i, beta_T, gamma_T, T_c, Yc_T, xN_flag);
}
long double GERG2008ReducingFunction::d2Trdxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
return d2Yrdxidxj__constxj(x, i, j, beta_T, gamma_T, T_c, Yc_T, xN_flag);
}
long double GERG2008ReducingFunction::rhormolar(const std::vector<long double> &x)
{
return 1/Yr(x, beta_v, gamma_v, v_c, Yc_v);
@@ -229,6 +253,14 @@ long double GERG2008ReducingFunction::dvrmolardxi__constxj(const std::vector<lon
{
return dYrdxi__constxj(x, i, beta_v, gamma_v, v_c, Yc_v, xN_flag);
}
long double GERG2008ReducingFunction::d2vrmolardxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
return d2Yrdxi2__constxj(x, i, beta_v, gamma_v, v_c, Yc_v, xN_flag);
}
long double GERG2008ReducingFunction::d2vrmolardxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
return d2Yrdxidxj__constxj(x, i, j, beta_v, gamma_v, v_c, Yc_v, xN_flag);
}
long double GERG2008ReducingFunction::d2rhormolardxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
long double rhor = this->rhormolar(x);
@@ -243,105 +275,22 @@ long double GERG2008ReducingFunction::d2rhormolardxidxj(const std::vector<long d
return 2*pow(rhor,(std::size_t)3)*dvrbardxi*dvrbardxj-pow(rhor,(std::size_t)2)*this->d2vrmolardxidxj(x,i,j, xN_flag);
}
long double GERG2008ReducingFunction::d2Trdxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
// See Table B9 from Kunz Wagner 2012 (GERG 2008)
long double d2Tr_dxi2 = 2*pFluids[i]->pEOS->reduce.T;
for (std::size_t k = 0; k < i; k++)
{
d2Tr_dxi2 += c_Y_ij(k,i,beta_T,gamma_T,T_c)*d2fYkidxi2__constxk(x,k,i,beta_T);
}
for (std::size_t k = i+1; k < N; k++)
{
d2Tr_dxi2 += c_Y_ij(i,k,beta_T,gamma_T,T_c)*d2fYikdxi2__constxk(x,i,k,beta_T);
}
return d2Tr_dxi2;
}
long double GERG2008ReducingFunction::d2Trdxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
if (i == j)
{
return d2Trdxi2__constxj(x, i, xN_flag);
}
else
{
// See Table B9 from Kunz Wagner 2012 (GERG 2008)
return c_Y_ij(i, j, beta_T, gamma_T, T_c)*d2fYijdxidxj(x, i, j, beta_T);
}
}
long double GERG2008ReducingFunction::d2vrmolardxidxj(const std::vector<long double> &x, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
{
if (i == j)
{
return d2vrmolardxi2__constxj(x, i, xN_flag);
}
else
{
return c_Y_ij(i, j, beta_v, gamma_v, v_c)*d2fYijdxidxj(x, i, j, beta_v);
}
}
long double GERG2008ReducingFunction::d2vrmolardxi2__constxj(const std::vector<long double> &x, std::size_t i, x_N_dependency_flag xN_flag)
{
// See Table B9 from Kunz Wagner 2012 (GERG 2008)
double d2vrbardxi2 = 2/pFluids[i]->pEOS->reduce.rhomolar;
for (std::size_t k = 0; k < i; k++)
{
d2vrbardxi2 += c_Y_ij(k, i, beta_v, gamma_v, v_c)*d2fYkidxi2__constxk(x, k, i, beta_v);
}
for (std::size_t k = i+1; k < N; k++)
{
d2vrbardxi2 += c_Y_ij(i, k, beta_v, gamma_v, v_c)*d2fYikdxi2__constxk(x, i, k, beta_v);
}
return d2vrbardxi2;
}
long double GERG2008ReducingFunction::Yr(const std::vector<long double> &x, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc)
{
long double Yr = 0;
// if (xN_flag == XN_INDEPENDENT)
// {
for (std::size_t i = 0; i < N; i++)
{
double xi = x[i];
Yr += xi*xi*Yc[i];
// The last term is only used for the pure component, as it is sum_{i=1}^{N-1}sum_{j=1}^{N}
if (i==N-1){ break; }
for (std::size_t i = 0; i < N; i++)
{
double xi = x[i];
Yr += xi*xi*Yc[i];
// The last term is only used for the pure component, as it is sum_{i=1}^{N-1}sum_{j=1}^{N}
if (i==N-1){ break; }
for (std::size_t j = i+1; j < N; j++)
{
Yr += c_Y_ij(i, j, beta, gamma, Y_c_ij)*f_Y_ij(x, i, j, beta);
}
for (std::size_t j = i+1; j < N; j++)
{
Yr += c_Y_ij(i, j, beta, gamma, Y_c_ij)*f_Y_ij(x, i, j, beta);
}
// }
// else if (xN_flag == XN_DEPENDENT){
//
// // A.43 from Gernert, 2014, supplemental information
// for (std::size_t k = 0; k < N-1; ++k)
// {
// double xk = x[k];
// Yr += xk*xk*Yc[k];
// }
// for (std::size_t k = 0; k < N-2; ++k)
// {
// for (std::size_t m = k+1; m < N-1; ++m)
// {
// Yr += c_Y_ij(k, m, beta, gamma, Y_c_ij)*f_Y_ij(x, k, m, beta);
// }
// }
// for (std::size_t k = 0; k < N-1; ++k)
// {
// Yr += c_Y_ij(k, N-1, beta, gamma, Y_c_ij)*f_Y_ij(x, k, N-1, beta);
// }
// double xN = x[N-1];
// Yr += xN*xN*Yc[N-1];
// }
// else{
// throw ValueError(format("xN dependency flag invalid"));
// }
}
return Yr;
}
long double GERG2008ReducingFunction::dYrdxi__constxj(const std::vector<long double> &x, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag)
@@ -362,6 +311,7 @@ long double GERG2008ReducingFunction::dYrdxi__constxj(const std::vector<long dou
}
else if (xN_flag == XN_DEPENDENT){
// Table S1 from Gernert, 2014, supplemental information
if (i == N-1){return 0.0;}
long double dYr_dxi = 2*x[i]*Yc[i] - 2*x[N-1]*Yc[N-1];
for (std::size_t k = 0; k < i; k++)
{
@@ -384,6 +334,84 @@ long double GERG2008ReducingFunction::dYrdxi__constxj(const std::vector<long dou
throw ValueError(format("xN dependency flag invalid"));
}
}
long double GERG2008ReducingFunction::d2Yrdxi2__constxj(const std::vector<long double> &x, std::size_t i, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag)
{
if (xN_flag == XN_INDEPENDENT){
// See Table B9 from Kunz Wagner 2012 (GERG 2008)
long double d2Yr_dxi2 = 2*Yc[i];
for (std::size_t k = 0; k < i; k++)
{
d2Yr_dxi2 += c_Y_ij(k,i,beta,gamma,Y_c_ij)*d2fYkidxi2__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N; k++)
{
d2Yr_dxi2 += c_Y_ij(i,k,beta,gamma,Y_c_ij)*d2fYikdxi2__constxk(x,i,k,beta);
}
return d2Yr_dxi2;
}
else if (xN_flag == XN_DEPENDENT){
// Table S1 from Gernert, 2014, supplemental information
if (i == N-1){return 0.0;}
long double d2Yr_dxi2 = 2*Yc[i] + 2*Yc[N-1];
for (std::size_t k = 0; k < i; k++)
{
d2Yr_dxi2 += c_Y_ji(k, i, beta, gamma, Y_c_ij)*d2fYkidxi2__constxk(x,k,i,beta);
}
for (std::size_t k = i+1; k < N-1; k++)
{
d2Yr_dxi2 += c_Y_ji(i, k, beta, gamma, Y_c_ij)*d2fYkidxi2__constxk(x,i,k,beta);
}
double beta_Y_iN = beta[i][N-1], xN = x[N-1];
d2Yr_dxi2 += 2*c_Y_ji(i, N-1, beta, gamma, Y_c_ij)*(-(x[i]+xN)/(pow(beta_Y_iN,2)*x[i]+xN)+(1-beta_Y_iN*beta_Y_iN)*(xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2)+((1-beta_Y_iN*beta_Y_iN)*x[i]*xN*xN-beta_Y_iN*beta_Y_iN*x[i]*x[i]*xN)/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 3)));
for (std::size_t k = 0; k < N-1; ++k)
{
double beta_Y_kN = beta[k][N-1];
d2Yr_dxi2 += 2*c_Y_ji(k, N-1, beta, gamma, Y_c_ij)*x[k]*x[k]*(1-beta_Y_kN*beta_Y_kN)/pow(pow(beta_Y_kN,2)*x[k]+xN, 2)*(xN/(beta_Y_kN*beta_Y_kN*x[k]+xN)-1);
}
return d2Yr_dxi2;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
long double GERG2008ReducingFunction::d2Yrdxidxj__constxj(const std::vector<long double> &x, std::size_t i, std::size_t j, const STLMatrix &beta, const STLMatrix &gamma, const STLMatrix &Y_c_ij, const std::vector<long double> &Yc, x_N_dependency_flag xN_flag)
{
if (xN_flag == XN_INDEPENDENT){
if (i == j)
{
return d2Yrdxi2__constxj(x, i, beta, gamma, Y_c_ij, Yc, xN_flag);
}
else
{
// See Table B9 from Kunz Wagner 2012 (GERG 2008)
return c_Y_ij(i, j, beta, gamma, Y_c_ij)*d2fYijdxidxj(x, i, j, beta);
}
}
else if (xN_flag == XN_DEPENDENT){
// Table S1 from Gernert, 2014, supplemental information
if (j == N-1 || i == N-1){ return 0.0; }
if (i == j){ return d2Yrdxi2__constxj(x, i, beta, gamma, Y_c_ij, Yc, xN_flag); }
long double xN = x[N-1];
long double d2Yr_dxidxj = 2*Yc[N-1];
d2Yr_dxidxj += c_Y_ji(i, j, beta, gamma, Y_c_ij)*d2fYijdxidxj(x,i,j,beta);
for (std::size_t k = 0; k < N-1; k++)
{
double beta_Y_kN = beta[k][N-1];
d2Yr_dxidxj += 2*c_Y_ji(k, N-1, beta, gamma, Y_c_ij)*x[k]*x[k]*(1-beta_Y_kN*beta_Y_kN)/pow(beta_Y_kN*beta_Y_kN*x[k]+xN,2)*(xN/(beta_Y_kN*beta_Y_kN*x[k]+xN)-1);
}
double beta_Y_iN = beta[i][N-1], beta_Y_jN = beta[j][N-1];
d2Yr_dxidxj += c_Y_ji(i, N-1, beta, gamma, Y_c_ij)*((1-beta_Y_iN*beta_Y_iN)*(2*x[i]*xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 3)-x[i]*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2)) - (x[i]+xN)/(beta_Y_iN*beta_Y_iN*x[i]+xN));
d2Yr_dxidxj += -c_Y_ji(j, N-1, beta, gamma, Y_c_ij)*((1-beta_Y_jN*beta_Y_jN)*(2*x[j]*x[j]*xN*beta_Y_jN*beta_Y_jN/pow(beta_Y_jN*beta_Y_jN*x[j]+xN, 3)-x[j]*xN/pow(beta_Y_jN*beta_Y_jN*x[j]+xN, 2)) - (x[j]+xN)/(beta_Y_jN*beta_Y_jN*x[j]+xN));
return d2Yr_dxidxj;
}
else{
throw ValueError(format("xN dependency flag invalid"));
}
}
long double GERG2008ReducingFunction::dfYkidxi__constxk(const std::vector<long double> &x, std::size_t k, std::size_t i, const STLMatrix &beta)
{