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Analytic derivatives for M1_star implemented

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Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
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Ian Bell
2015-06-03 21:32:20 -06:00
parent 179cb2ff9d
commit 94bda21420
1 changed files with 37 additions and 7 deletions
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44
src/Backends/Helmholtz/MixtureDerivatives.h
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@@ -14,6 +14,7 @@
#ifndef MIXTURE_DERIVATIVES_H
#define MIXTURE_DERIVATIVES_H
#include <Eigen/Core>
#include "HelmholtzEOSMixtureBackend.h"
namespace CoolProp{
@@ -177,18 +178,47 @@ class MixtureDerivatives{
// Fill in the symmetric elements
for (std::size_t i = 0; i < N; ++i){
for (std::size_t j = 0; j < i; ++j){
L(i, j) = nAij(HEOS, i, j, xN_flag);
L(i, j) = L(j, i);
}
}
return L.determinant();
}
static CoolPropDbl M1_star(HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag){
Eigen::Matrix2d M1;
M1(0, 0) = nAij(HEOS, 0, 0, xN_flag);
M1(0, 1) = nAij(HEOS, 0, 1, xN_flag);
M1(1, 0) = nAij(HEOS, 0, 0, xN_flag)*n2Aijk(HEOS, 0, 1, 1, xN_flag) + nAij(HEOS, 1, 1, xN_flag)*n2Aijk(HEOS, 0, 0, 0, xN_flag) - 2*nAij(HEOS, 0, 1, xN_flag)*n2Aijk(HEOS, 0, 0, 1, xN_flag);;
M1(1, 1) = nAij(HEOS, 0, 0, xN_flag)*n2Aijk(HEOS, 1, 1, 1, xN_flag) + nAij(HEOS, 1, 1, xN_flag)*n2Aijk(HEOS, 0, 0, 1, xN_flag) - 2*nAij(HEOS, 0, 1, xN_flag)*n2Aijk(HEOS, 0, 1, 1, xN_flag);
return M1.determinant();
std::size_t N = HEOS.mole_fractions.size();
Eigen::MatrixXd L;
L.resize(N, N);
for (std::size_t i = 0; i < N; ++i){
for (std::size_t j = i; j < N; ++j){
L(i, j) = nAij(HEOS, i, j, xN_flag);
}
}
// Fill in the symmetric elements
for (std::size_t i = 0; i < N; ++i){
for (std::size_t j = 0; j < i; ++j){
L(i, j) = L(j, i);
}
}
Eigen::MatrixXd M = L;
// Last row
for (std::size_t i = 0; i < N; ++i){
Eigen::MatrixXd n2dLdni(N, N);
for (std::size_t j = 0; j < N; ++j){
for (std::size_t k = j; k < N; ++k){
n2dLdni(j, k) = n2Aijk(HEOS, j, k, i, xN_flag);
}
}
// Fill in the symmetric elements
for (std::size_t j = 0; j < N; ++j){
for (std::size_t k = 0; k < j; ++k){
n2dLdni(j, k) = n2dLdni(k, j);
}
}
M(N-1, i) = (adjugate(L, N)*n2dLdni).trace();
}
return M.determinant();
}
/** \brief Table B4, Kunz, JCED, 2012 for the original term and the subsequent substitutions