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Merge pull request #778 from CoolProp/mixture_derivs

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Mixture derivs
This commit is contained in:
Ian Bell
2015-08-16 17:44:42 -06:00
parent ba7d5a9c97 30c5abc35c
commit 381f613164
5 changed files with 945 additions and 162 deletions
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162
doc/notebooks/Check critical point derivative matrices.ipynb Normal file
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@@ -0,0 +1,162 @@
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import *\n",
"from IPython.display import display, Math, Latex\n",
"from IPython.core.display import display_html\n",
"init_session(quiet=True, use_latex='mathjax')\n",
"init_printing()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"IPython console for SymPy 0.7.6 (Python 2.7.6-32-bit) (ground types: python)\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x1,x2,tau,delta = symbols('x1,x2,tau,delta')\n",
"L11 = symbols('L11', cls=Function)(x1,x2,tau,delta)\n",
"L12 = symbols('L12', cls=Function)(x1,x2,tau,delta)\n",
"L21 = symbols('L21', cls=Function)(x1,x2,tau,delta)\n",
"L22 = symbols('L22', cls=Function)(x1,x2,tau,delta)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Lstar = Matrix([[L11,L12],[L21,L22]])\n",
"L1star = Lstar.det()\n",
"deriv1 = L1star.diff(t)\n",
"deriv2 = (Lstar.adjugate()*Lstar.diff(t)).trace()\n",
"\n",
"Mstar = Matrix([[L11,L12],[Lstar.det().diff(x1),Lstar.det().diff(x2)]])\n",
"\n",
"deriv1 = Mstar.det().diff(tau)\n",
"deriv2 = (Mstar.adjugate()*Mstar.diff(tau)).trace()\n",
"simplify(deriv1-deriv2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$0$$"
],
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOBAMAAADkjZCYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJdjLNVN0iZu+7\nq0QgoRR7AAAAVklEQVQIHWNgEDJRZWBgSGeQmMDAtYGBOYGB5wID+0cG/gsMfN8Z5BUY+L4wzDdg\nYP0MJeUNQCL8Cgzs3xk4DjBwfWRg2cDAlMDA0M4gHcDAIOxylQEA9FISlFfRJtkAAAAASUVORK5C\nYII=\n",
"prompt_number": 3,
"text": [
"0"
]
}
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"prompt_number": 3
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"cell_type": "code",
"collapsed": false,
"input": [
"Mstar = Matrix([[0.00112865, 8.76232e-006],[9.57021e-007, 7.42578e-009]])\n",
"dMstar_dTau = Matrix([[-0.000245724,-0.00118232],[3.20921e-006, -7.171e-008]])\n",
"adjM = Matrix([[7.42578e-009,-9.57021e-007],[-8.76232e-006, 0.00112865]])\n",
"(adjM*dMstar_dTau).trace()\n",
"print Mstar.adjugate()\n",
"print adjM"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Matrix([[7.42578000000000e-9, -8.76232000000000e-6], [-9.57021000000000e-7, 0.00112865000000000]])\n",
"Matrix([[7.42578000000000e-9, -9.57021000000000e-7], [-8.76232000000000e-6, 0.00112865000000000]])\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a,b,c,d = symbols('a,b,c,d')\n",
"M = Matrix([[a,b],[c,d]])\n",
"display(M)\n",
"M.adjugate()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$\\left[\\begin{matrix}a & b\\\\c & d\\end{matrix}\\right]$$"
],
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAyBAMAAAAKOF7GAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhAiq3bdRLtm\nmc0lg57xAAABSUlEQVQ4Ee3UPUsDMRwG8OdSr9DT1oIuouANDgoO9w0qWPdzFrlu7rp0cOhQEARB\nEHHVT2D9AIqjo4Pgpi7iVBGlDlI4E/LSZ7hmdjDLJfnxz11yD8Fi/omiJvK8jpnmRpEhbK7XMVtI\nanKiGLfmPIg3H355MBp4UBwTlne7p2poW619lLivvWhNflhQz+wV3xbDBVR7jI0U8tj0PqsDVDqM\nTwgdBj1ka4x9RHIzujKL0UBKOoRczGKCm1KL8AebtxZrnakzQYZ9XMuhXjZsL+0cMm4fyEKDPE99\nXUkT3P1HeRpjDyG6uh+PmE48eJl6cMXzTvRHKJa7/LNkyF3AUD7BO6MMuQsYghh7hCrkL27ZZ84l\nVC4rscN5KpPdQIb83KLKPjcTcnN8Q6BEmumQG3xE+EBoQm5QrN6RwYTcIMuo/xfRe6X6LuNfjWlM\nFpMM9N8AAAAASUVORK5CYII=\n",
"text": [
"\u23a1a b\u23a4\n",
"\u23a2 \u23a5\n",
"\u23a3c d\u23a6"
]
},
{
"latex": [
"$$\\left[\\begin{matrix}d & - b\\\\- c & a\\end{matrix}\\right]$$"
],
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAFMAAAAyBAMAAADSNPrMAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
"prompt_number": 11,
"text": [
"\u23a1d -b\u23a4\n",
"\u23a2 \u23a5\n",
"\u23a3-c a \u23a6"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}

2
include/MatrixMath.h
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@@ -908,7 +908,7 @@ static Eigen::MatrixXd adjugate(const Eigen::MatrixBase<Derived>& A)
for (std::size_t i = 0; i < N; ++i){
for (std::size_t j = 0; j < N; ++j){
int negative_1_to_the_i_plus_j = ((i+j)%2==0) ? 1 : -1;
Aadj(i, j) = negative_1_to_the_i_plus_j*minor_matrix(A, i, j).determinant();
Aadj(i, j) = negative_1_to_the_i_plus_j*minor_matrix(A, j, i).determinant();
}
}
return Aadj;

45
src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
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@@ -2932,34 +2932,46 @@ void HelmholtzEOSMixtureBackend::calc_critical_point(double rho0, double T0)
};
std::vector<std::vector<double> > Jacobian(const std::vector<double> &x)
{
double epsilon;
std::size_t N = x.size();
std::vector<double> r, xp;
std::vector<std::vector<double> > J(N, std::vector<double>(N, 0));
Eigen::MatrixXd J0(N, N), adjL = adjugate(MixtureDerivatives::Lstar(HEOS, XN_INDEPENDENT)),
dLdTau = MixtureDerivatives::dLstar_dX(HEOS, XN_INDEPENDENT, iTau),
dLdDelta = MixtureDerivatives::dLstar_dX(HEOS, XN_INDEPENDENT, iDelta),
adjM = adjugate(MixtureDerivatives::Mstar(HEOS, XN_INDEPENDENT)),
dMdTau = dLdTau, dMdDelta = dLdDelta;
Eigen::MatrixXd adjL = adjugate(MixtureDerivatives::Lstar(HEOS, XN_INDEPENDENT)),
adjM = adjugate(MixtureDerivatives::Mstar(HEOS, XN_INDEPENDENT)),
dLdTau = MixtureDerivatives::dLstar_dX(HEOS, XN_INDEPENDENT, iTau),
dLdDelta = MixtureDerivatives::dLstar_dX(HEOS, XN_INDEPENDENT, iDelta),
dMdTau = MixtureDerivatives::dMstar_dX(HEOS, XN_INDEPENDENT, iTau),
dMdDelta = MixtureDerivatives::dMstar_dX(HEOS, XN_INDEPENDENT, iDelta);
J0(0,0) = (adjL*dLdTau).trace();
J0(0,1) = (adjL*dLdDelta).trace();
//std::cout << J0 << std::endl;
std::vector<double> r0 = call(x);
J[0][0] = (adjL*dLdTau).trace();
J[0][1] = (adjL*dLdDelta).trace();
J[1][0] = (adjM*dMdTau).trace();
J[1][1] = (adjM*dMdDelta).trace();
return J;
}
/// Not used, for testing purposes
std::vector<std::vector<double> > numerical_Jacobian(const std::vector<double> &x)
{
std::size_t N = x.size();
std::vector<double> rplus, rminus, xp;
std::vector<std::vector<double> > J(N, std::vector<double>(N, 0));
double epsilon = 0.0001;
// Build the Jacobian by column
for (std::size_t i = 0; i < N; ++i)
{
xp = x;
epsilon = 0.00001;
xp[i] += epsilon;
r = call(xp);
rplus = call(xp);
xp[i] -= 2*epsilon;
rminus = call(xp);
for (std::size_t j = 0; j < N; ++j)
{
J[j][i] = (r[j]-r0[j])/epsilon;
J[j][i] = (rplus[j]-rminus[j])/(2*epsilon);
}
}
std::cout << J[0][0] << " " << J[0][1] << std::endl;
std::cout << J[1][0] << " " << J[1][1] << std::endl;
return J;
};
};
@@ -2987,13 +2999,11 @@ public:
return L1;
}
double deriv(double tau){
std::size_t N = HEOS.get_mole_fractions().size();
Eigen::MatrixXd adjL = adjugate(MixtureDerivatives::Lstar(HEOS, XN_INDEPENDENT)),
dLdTau = MixtureDerivatives::dLstar_dX(HEOS, XN_INDEPENDENT, iTau);
return (adjL*dLdTau).trace();
};
double second_deriv(double tau){
std::size_t N = HEOS.get_mole_fractions().size();
Eigen::MatrixXd Lstar = MixtureDerivatives::Lstar(HEOS, XN_INDEPENDENT),
dLstardTau = MixtureDerivatives::dLstar_dX(HEOS, XN_INDEPENDENT, iTau),
d2LstardTau2 = MixtureDerivatives::d2Lstar_dX2(HEOS, XN_INDEPENDENT, iTau, iTau),
@@ -3050,7 +3060,6 @@ public:
@param theta The angle
*/
double deriv(double theta){
std::size_t N = HEOS.get_mole_fractions().size();
double dL1_dtau = (adjLstar*dLstardTau).trace(), dL1_ddelta = (adjLstar*dLstardDelta).trace();
return -R_tau*sin(theta)*dL1_dtau + R_delta*cos(theta)*dL1_ddelta;
};

783
src/Backends/Helmholtz/MixtureDerivatives.cpp
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File diff suppressed because it is too large Load Diff

115
src/Backends/Helmholtz/MixtureDerivatives.h
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@@ -71,7 +71,6 @@ class MixtureDerivatives{
static CoolPropDbl d4alphar_dxi_dxj_dDelta2(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d4alphar_dxi_dxj_dDelta_dTau(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d4alphar_dxi_dxj_dTau2(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d4alphardxidxjdxk(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
/** \brief GERG 2004 Monograph equation 7.63
@@ -162,9 +161,14 @@ class MixtureDerivatives{
static CoolPropDbl ndln_fugacity_i_dnj__constT_V_xi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d_ndln_fugacity_i_dnj_dtau__constdelta_x(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_ndln_fugacity_i_dnj_dtau2__constdelta_x(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_ndln_fugacity_i_dnj_ddelta_dtau__constx(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_ndln_fugacity_i_dnj_ddelta2__consttau_x(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d_ndln_fugacity_i_dnj_ddelta__consttau_x(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d_ndln_fugacity_i_dnj_ddxk__consttau_delta(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_ndln_fugacity_i_dnj_dxk_dTau__constdelta(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_ndln_fugacity_i_dnj_dxk_dDelta__consttau(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
static CoolPropDbl nd_ndln_fugacity_i_dnj_dnk__constT_V_xi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
static CoolPropDbl nAij(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag){
@@ -175,6 +179,51 @@ class MixtureDerivatives{
CoolPropDbl RT = HEOS.gas_constant()*HEOS.T();
return 1/RT*nd_ndln_fugacity_i_dnj_dnk__constT_V_xi(HEOS, i, j, k, xN_flag) - nAij(HEOS, i, j, xN_flag);
}
static CoolPropDbl d_nAij_dX(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag, parameters WRT)
{
if (WRT == iTau){
return 1/(HEOS.gas_constant()*HEOS.T_reducing())*MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi(HEOS, i, j, xN_flag)
+ 1/(HEOS.gas_constant()*HEOS.T())*MixtureDerivatives::d_ndln_fugacity_i_dnj_dtau__constdelta_x(HEOS, i, j, xN_flag);
}
else if (WRT == iDelta){
return 1/(HEOS.gas_constant()*HEOS.T())*MixtureDerivatives::d_ndln_fugacity_i_dnj_ddelta__consttau_x(HEOS, i, j, xN_flag);
}
else{
throw ValueError(format("wrong WRT"));
}
}
static CoolPropDbl d_n2Aijk_dX(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag, parameters WRT){
CoolPropDbl RT = HEOS.gas_constant()*HEOS.T();
if (WRT == iTau){
double summer = 0;
summer += d2_ndln_fugacity_i_dnj_dtau2__constdelta_x(HEOS, i, j, xN_flag)*ndtaudni__constT_V_nj(HEOS, k, xN_flag);
summer += d_ndln_fugacity_i_dnj_dtau__constdelta_x(HEOS, i, j, xN_flag)*d_ndtaudni_dTau(HEOS, k, xN_flag);
summer += d2_ndln_fugacity_i_dnj_ddelta_dtau__constx(HEOS, i, j, xN_flag)*nddeltadni__constT_V_nj(HEOS, k, xN_flag);
summer += d2_ndln_fugacity_i_dnj_dxk_dTau__constdelta(HEOS, i, j, k, xN_flag);
std::size_t mmax = HEOS.mole_fractions.size();
if (xN_flag == XN_DEPENDENT){ mmax--; }
for (std::size_t m = 0; m < mmax; ++m){
summer -= HEOS.mole_fractions[m]*d2_ndln_fugacity_i_dnj_dxk_dTau__constdelta(HEOS, i, j, m, xN_flag);
}
return 1/RT*summer + 1/(HEOS.gas_constant()*HEOS.T_reducing())*nd_ndln_fugacity_i_dnj_dnk__constT_V_xi(HEOS,i,j,k,xN_flag) - d_nAij_dX(HEOS, i, j, xN_flag, WRT);
}
else if (WRT== iDelta){
double summer = 0;
summer += d2_ndln_fugacity_i_dnj_ddelta_dtau__constx(HEOS, i, j, xN_flag)*ndtaudni__constT_V_nj(HEOS, k, xN_flag);
summer += d2_ndln_fugacity_i_dnj_ddelta2__consttau_x(HEOS, i, j, xN_flag)*nddeltadni__constT_V_nj(HEOS, k, xN_flag);
summer += d_ndln_fugacity_i_dnj_ddelta__consttau_x(HEOS, i, j, xN_flag)*d_nddeltadni_dDelta(HEOS, k, xN_flag);
summer += d2_ndln_fugacity_i_dnj_dxk_dDelta__consttau(HEOS, i, j, k, xN_flag);
std::size_t mmax = HEOS.mole_fractions.size();
if (xN_flag == XN_DEPENDENT){ mmax--; }
for (std::size_t m = 0; m < mmax; ++m){
summer -= HEOS.mole_fractions[m]*d2_ndln_fugacity_i_dnj_dxk_dDelta__consttau(HEOS, i, j, m, xN_flag);
}
return 1/RT*summer - d_nAij_dX(HEOS, i, j, xN_flag, iDelta);
}
else{
return _HUGE;
}
}
static Eigen::MatrixXd Lstar(HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag){
std::size_t N = HEOS.mole_fractions.size();
Eigen::MatrixXd L;
@@ -198,16 +247,7 @@ class MixtureDerivatives{
Eigen::MatrixXd dLstar_dX(N, N);
for (std::size_t i = 0; i < N; ++i){
for (std::size_t j = i; j < N; ++j){
if (WRT == iTau){
dLstar_dX(i, j) = 1/(HEOS.gas_constant()*HEOS.T_reducing())*MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi(HEOS, i, j, xN_flag)
+ 1/(HEOS.gas_constant()*HEOS.T())*MixtureDerivatives::d_ndln_fugacity_i_dnj_dtau__constdelta_x(HEOS, i, j, xN_flag);
}
else if (WRT == iDelta){
dLstar_dX(i, j) = 1/(HEOS.gas_constant()*HEOS.T())*MixtureDerivatives::d_ndln_fugacity_i_dnj_ddelta__consttau_x(HEOS, i, j, xN_flag);
}
else{
throw ValueError(format("dLstar_dX invalid WRT"));
}
dLstar_dX(i, j) = d_nAij_dX(HEOS, i, j, xN_flag, WRT);
}
}
// Fill in the symmetric elements
@@ -244,7 +284,9 @@ class MixtureDerivatives{
static Eigen::MatrixXd Mstar(HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag){
std::size_t N = HEOS.mole_fractions.size();
Eigen::MatrixXd L = Lstar(HEOS, xN_flag), M = L;
Eigen::MatrixXd L = Lstar(HEOS, xN_flag),
M = L,
adjL = adjugate(L);
// Last row
for (std::size_t i = 0; i < N; ++i){
@@ -252,18 +294,39 @@ class MixtureDerivatives{
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
n2dLdni(k, j) = n2dLdni(j, k);
}
}
// 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)*n2dLdni).trace();
M(N-1, i) = (adjL*n2dLdni).trace();
}
return M;
}
static Eigen::MatrixXd dMstar_dX(HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag, parameters WRT){
std::size_t N = HEOS.mole_fractions.size();
Eigen::MatrixXd L = Lstar(HEOS, xN_flag),
dL_dX = dLstar_dX(HEOS, xN_flag, WRT),
dMstar = dL_dX,
adjL = adjugate(L),
d_adjL_dX = adjugate_derivative(L, dL_dX);
// Last row in the d(Mstar)/d(X) requires derivatives of
for (std::size_t i = 0; i < N; ++i){
Eigen::MatrixXd n2dLdni(N, N), d_n2dLdni_dX(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);
d_n2dLdni_dX(j, k) = d_n2Aijk_dX(HEOS, j, k, i, xN_flag, WRT);
// Fill in the symmetric elements
n2dLdni(k, j) = n2dLdni(j, k);
d_n2dLdni_dX(k, j) = d_n2dLdni_dX(j, k);
}
}
dMstar(N-1, i) = (n2dLdni*d_adjL_dX + adjL*d_n2dLdni_dX).trace();
}
return dMstar;
}
/** \brief Table B4, Kunz, JCED, 2012 for the original term and the subsequent substitutions
*
@@ -497,6 +560,8 @@ class MixtureDerivatives{
*/
static CoolPropDbl d2_ndalphardni_dxj_dTau__constdelta_xi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d3_ndalphardni_dxj_dTau2__constdelta_xi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d3_ndalphardni_dxj_dDelta2__consttau_xi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d3_ndalphardni_dxj_dDelta_dTau__constxi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
/** \brief GERG 2004 Monograph equation 7.41
*
@@ -540,6 +605,8 @@ class MixtureDerivatives{
*/
static CoolPropDbl d_nd_ndalphardni_dnj_dTau__constdelta_x(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_nd_ndalphardni_dnj_dTau2__constdelta_x(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_nd_ndalphardni_dnj_dDelta2__consttau_x(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_nd_ndalphardni_dnj_dDelta_dTau__constx(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
/* \brief \f$\delta\f$ derivative of GERG 2004 7.47
*
@@ -550,6 +617,9 @@ class MixtureDerivatives{
*
*/
static CoolPropDbl d_nd_ndalphardni_dnj_dxk__consttau_delta(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_nd_ndalphardni_dnj_dxk_dTau__constdelta(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_nd_ndalphardni_dnj_dxk_dDelta__consttau(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
/** \brief GERG 2004 Monograph equation 7.48
*
@@ -567,6 +637,8 @@ class MixtureDerivatives{
static CoolPropDbl d_nddeltadni_dxj__constdelta_tau(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_nddeltadni_dxj_dDelta__consttau(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
/** \brief GERG 2004 Monograph equation 7.49
*
* The derivative term
@@ -583,6 +655,8 @@ class MixtureDerivatives{
static CoolPropDbl d_ndtaudni_dxj__constdelta_tau(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
static CoolPropDbl d2_ndtaudni_dxj_dTau__constdelta(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag);
/** \brief GERG 2004 Monograph equation 7.52
*
* The derivative term
@@ -605,6 +679,9 @@ class MixtureDerivatives{
*/
static CoolPropDbl d2_ndalphardni_dxj_dxk__constdelta_tau_xi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
static CoolPropDbl d3_ndalphardni_dxj_dxk_dTau__constdelta_xi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
static CoolPropDbl d3_ndalphardni_dxj_dxk_dDelta__consttau_xi(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag);
}; /* class MixtureDerivatives */
} /* namepsace CoolProp*/