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Fix d_ndln_fugacity_i_dnj_ddxk__consttau_delta and M1_star

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This commit is contained in:
Ian Bell
2015-05-31 21:41:22 -06:00
parent 3fd77d57ba
commit 26fb36c370
2 changed files with 58 additions and 12 deletions
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57
src/Backends/Helmholtz/MixtureDerivatives.cpp
View File

@@ -338,7 +338,8 @@ CoolPropDbl MixtureDerivatives::d_ndln_fugacity_i_dnj_ddelta__consttau_x(Helmhol
return d_ndalphardni_dDelta(HEOS, j, xN_flag) + d_nd_ndalphardni_dnj_dDelta__consttau_x(HEOS, i, j, xN_flag);
}
CoolPropDbl MixtureDerivatives::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){
return d_ndalphardni_dxj__constdelta_tau_xi(HEOS, i, j, xN_flag) + d_nd_ndalphardni_dnj_dxk__consttau_delta(HEOS, i, j, k, xN_flag);
CoolPropDbl s = -Kronecker_delta(i, j)*Kronecker_delta(i, k)/pow(HEOS.mole_fractions[i], 2);
return s + d_ndalphardni_dxj__constdelta_tau_xi(HEOS, j, k, xN_flag) + d_nd_ndalphardni_dnj_dxk__consttau_delta(HEOS, i, j, k, xN_flag);
}
CoolPropDbl MixtureDerivatives::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){
double sum = d_ndln_fugacity_i_dnj_dtau__constdelta_x(HEOS, i, j, xN_flag)*ndtaudni__constT_V_nj(HEOS, k, xN_flag)
@@ -1387,6 +1388,33 @@ TEST_CASE("Mixture derivative checks", "[mixtures],[mixture_derivs]")
CAPTURE(analytic);
CHECK(err < 1e-7);
}
std::ostringstream ss3o1; ss3o1 << "d_ndln_fugacity_i_dnj_ddelta__consttau_x, i=" << i;
SECTION(ss3o1.str(), "")
{
if (i == Ncomp-1){ break; }
double analytic = MixtureDerivatives::d_ndln_fugacity_i_dnj_ddelta__consttau_x(rHEOS, i, j, xN_flag);
double v1 = MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi(rHEOS_plusrho_constT, i, j, xN_flag), delta1 = rHEOS_plusrho_constT.delta();
double v2 = MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi(rHEOS_minusrho_constT, i, j, xN_flag), delta2 = rHEOS_minusrho_constT.delta();
double numeric = (v1 - v2)/(delta1 - delta2);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-7);
}
std::ostringstream ss3o2; ss3o2 << "d_ndln_fugacity_i_dnj_dtau__constdelta_x, i=" << i;
SECTION(ss3o2.str(), "")
{
if (i == Ncomp-1){ break; }
double analytic = MixtureDerivatives::d_ndln_fugacity_i_dnj_dtau__constdelta_x(rHEOS, i, j, xN_flag);
double v1 = MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi(rHEOS_plusT_constrho, i, j, xN_flag), tau1 = rHEOS_plusT_constrho.tau();
double v2 = MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi(rHEOS_minusT_constrho, i, j, xN_flag), tau2 = rHEOS_minusT_constrho.tau();
double numeric = (v1 - v2)/(tau1 - tau2);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-7);
}
std::ostringstream ss3p; ss3p << "d_nd_ndalphardni_dnj_dTau__constdelta_x, i=" << i;
SECTION(ss3p.str(), "")
{
@@ -1517,7 +1545,7 @@ TEST_CASE("Mixture derivative checks", "[mixtures],[mixture_derivs]")
std::ostringstream ss7; ss7 << "d2_ndalphardni_dxj_dxk__constdelta_tau_xi, i=" << i << ", j=" << j << ", k=" << k;
SECTION(ss7.str(), "")
{
if (i == Ncomp-1){ break; }
if ((xN_flag == XN_DEPENDENT) && (i == Ncomp-1 || j == Ncomp-1 || k == Ncomp-1)){ break; }
double analytic = MixtureDerivatives::d2_ndalphardni_dxj_dxk__constdelta_tau_xi(rHEOS, i, j, k, xN_flag);
double v1 = MixtureDerivatives::d_ndalphardni_dxj__constdelta_tau_xi(rHEOS_pluszk_consttaudelta, i, j, xN_flag);
double v2 = MixtureDerivatives::d_ndalphardni_dxj__constdelta_tau_xi(rHEOS_minuszk_consttaudelta, i, j, xN_flag);
@@ -1530,7 +1558,7 @@ TEST_CASE("Mixture derivative checks", "[mixtures],[mixture_derivs]")
std::ostringstream ss8; ss8 << "d3alphardxidxjdxk, i=" << i << ", j=" << j << ", k=" << k;
SECTION(ss8.str(), "")
{
if (j == Ncomp-1){ break; }
if ((xN_flag == XN_DEPENDENT) && (i == Ncomp-1 || j == Ncomp-1 || k == Ncomp-1)){ break; }
double analytic = MixtureDerivatives::d3alphardxidxjdxk(rHEOS, i, j, k, xN_flag);
double v1 = MixtureDerivatives::d2alphardxidxj(rHEOS_pluszk_consttaudelta, i, j, xN_flag);
double v2 = MixtureDerivatives::d2alphardxidxj(rHEOS_minuszk_consttaudelta, i, j, xN_flag);
@@ -1552,7 +1580,7 @@ TEST_CASE("Mixture derivative checks", "[mixtures],[mixture_derivs]")
std::ostringstream ss9; ss9 << "d_nd_ndalphardni_dnj_dxk__consttau_delta, i=" << i << ", j=" << j << ", k=" << k;
SECTION(ss9.str(), "")
{
if (j == Ncomp-1){ break; }
if ((xN_flag == XN_DEPENDENT) && (i == Ncomp-1 || j == Ncomp-1 || k == Ncomp-1)){ break; }
double analytic = MixtureDerivatives::d_nd_ndalphardni_dnj_dxk__consttau_delta(rHEOS, i, j, k, xN_flag);
double v1 = MixtureDerivatives::nd_ndalphardni_dnj__constT_V(rHEOS_pluszk_consttaudelta, i, j, xN_flag);
double v2 = MixtureDerivatives::nd_ndalphardni_dnj__constT_V(rHEOS_minuszk_consttaudelta, i, j, xN_flag);
@@ -1566,6 +1594,27 @@ TEST_CASE("Mixture derivative checks", "[mixtures],[mixture_derivs]")
err = numeric-analytic;
}
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss10; ss10 << "d_ndln_fugacity_i_dnj_ddxk__consttau_delta, i=" << i << ", j=" << j << ", k=" << k;
SECTION(ss10.str(), "")
{
if ((xN_flag == XN_DEPENDENT) && (i == Ncomp-1 || j == Ncomp-1 || k == Ncomp-1)){ break; }
double analytic = MixtureDerivatives::d_ndln_fugacity_i_dnj_ddxk__consttau_delta(rHEOS, i, j, k, xN_flag);
double v1 = MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi(rHEOS_pluszk_consttaudelta, i, j, xN_flag);
double v2 = MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi(rHEOS_minuszk_consttaudelta, i, j, xN_flag);
double numeric = (v1 - v2)/(2*dz);
if (std::abs(numeric) < DBL_EPSILON && std::abs(analytic) < DBL_EPSILON){ break; }
double err;
if (std::abs(analytic) > DBL_EPSILON){
err = std::abs((numeric-analytic)/analytic);
}
else{
err = numeric-analytic;
}
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);

13
src/Backends/Helmholtz/MixtureDerivatives.h
View File

@@ -163,26 +163,23 @@ class MixtureDerivatives{
}
static CoolPropDbl n2Aijk(HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag){
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);
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 L1_star(HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag){
Eigen::Matrix2d L1;
CoolPropDbl RT = HEOS.gas_constant()*HEOS.T();
L1(0, 0) = nAij(HEOS, 0, 0, xN_flag);
L1(1, 0) = nAij(HEOS, 1, 0, xN_flag);
L1(0, 1) = L1(1,0);
L1(0, 1) = nAij(HEOS, 0, 1, xN_flag);
L1(1, 0) = L1(0, 1);
L1(1, 1) = nAij(HEOS, 1, 1, xN_flag);
return L1.determinant();
}
static CoolPropDbl M1_star(HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag){
Eigen::Matrix2d M1;
CoolPropDbl RT = HEOS.gas_constant()*HEOS.T();
M1(0, 0) = nAij(HEOS, 0, 0, xN_flag);
M1(0, 1) = nAij(HEOS, 0, 1, xN_flag);
double dL1_dn0 = 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);
double dL1_dn1 = 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);
M1(1, 0) = dL1_dn0;
M1(1, 1) = dL1_dn1;
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();
}