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Fixed a lot of little things to get multi-component phase envelopes to build.

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Testing of mixture derivatives entirely refactored - much cleaner

Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
2014-09-07 21:56:34 +02:00
parent 3e7c92d5a8
commit af03189c5b
4 changed files with 464 additions and 490 deletions
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814
src/Backends/Helmholtz/MixtureDerivatives.cpp
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@@ -10,7 +10,7 @@ long double MixtureDerivatives::dalphar_dxi(HelmholtzEOSMixtureBackend &HEOS, st
else if(xN_flag == XN_DEPENDENT){
std::vector<long double> &x = HEOS.mole_fractions;
std::size_t N = x.size();
if (i==N-1) return 0;
if (i == N-1) return 0;
double dar_dxi = HEOS.components[i]->pEOS->baser(HEOS._tau, HEOS._delta) - HEOS.components[N-1]->pEOS->baser(HEOS._tau, HEOS._delta);
double FiNariN = HEOS.Excess.F[i][N-1]*HEOS.Excess.DepartureFunctionMatrix[i][N-1]->alphar(HEOS._tau, HEOS._delta);
dar_dxi += (1-2*x[i])*FiNariN;
@@ -18,7 +18,7 @@ long double MixtureDerivatives::dalphar_dxi(HelmholtzEOSMixtureBackend &HEOS, st
if (i==k) continue;
double Fikarik = HEOS.Excess.F[i][k]*HEOS.Excess.DepartureFunctionMatrix[i][k]->alphar(HEOS._tau, HEOS._delta);
double FkNarkN = HEOS.Excess.F[k][N-1]*HEOS.Excess.DepartureFunctionMatrix[k][N-1]->alphar(HEOS._tau, HEOS._delta);
dar_dxi += x[i]*(Fikarik - FiNariN - FkNarkN);
dar_dxi += x[k]*(Fikarik - FiNariN - FkNarkN);
}
return dar_dxi;
}
@@ -42,7 +42,7 @@ long double MixtureDerivatives::d2alphar_dxi_dTau(HelmholtzEOSMixtureBackend &HE
if (i==k) continue;
double Fikarik = HEOS.Excess.F[i][k]*HEOS.Excess.DepartureFunctionMatrix[i][k]->dalphar_dTau(HEOS._tau, HEOS._delta);
double FkNarkN = HEOS.Excess.F[k][N-1]*HEOS.Excess.DepartureFunctionMatrix[k][N-1]->dalphar_dTau(HEOS._tau, HEOS._delta);
d2ar_dxi_dTau += x[i]*(Fikarik - FiNariN - FkNarkN);
d2ar_dxi_dTau += x[k]*(Fikarik - FiNariN - FkNarkN);
}
return d2ar_dxi_dTau;
}
@@ -67,7 +67,7 @@ long double MixtureDerivatives::d2alphar_dxi_dDelta(HelmholtzEOSMixtureBackend &
if (i==k) continue;
double Fikarik = HEOS.Excess.F[i][k]*HEOS.Excess.DepartureFunctionMatrix[i][k]->dalphar_dDelta(HEOS._tau, HEOS._delta);
double FkNarkN = HEOS.Excess.F[k][N-1]*HEOS.Excess.DepartureFunctionMatrix[k][N-1]->dalphar_dDelta(HEOS._tau, HEOS._delta);
d2ar_dxi_dDelta += x[i]*(Fikarik - FiNariN - FkNarkN);
d2ar_dxi_dDelta += x[k]*(Fikarik - FiNariN - FkNarkN);
}
return d2ar_dxi_dDelta;
}
@@ -83,10 +83,9 @@ long double MixtureDerivatives::d2alphardxidxj(HelmholtzEOSMixtureBackend &HEOS,
}
else if(xN_flag == XN_DEPENDENT){
std::size_t N = HEOS.mole_fractions.size();
if (i == N-1){ return 0;}
if (i == N-1 || j == N-1){ return 0;}
double FiNariN = HEOS.Excess.F[i][N-1]*HEOS.Excess.DepartureFunctionMatrix[i][N-1]->alphar(HEOS._tau, HEOS._delta);
if (i == j) { return -2*FiNariN; }
if (j == N-1){ return 0; }
double Fijarij = HEOS.Excess.F[i][j]*HEOS.Excess.DepartureFunctionMatrix[i][j]->alphar(HEOS._tau, HEOS._delta);
double FjNarjN = HEOS.Excess.F[j][N-1]*HEOS.Excess.DepartureFunctionMatrix[j][N-1]->alphar(HEOS._tau, HEOS._delta);
@@ -358,446 +357,409 @@ long double MixtureDerivatives::d_ndalphardni_dTau(HelmholtzEOSMixtureBackend &H
using namespace CoolProp;
TEST_CASE("Mixture derivative checks", "[mixtures],[mixture_derivs]")
{
/* Set up a test class for the mixture tests */
std::vector<std::string> names(2);
names[0] = "Ethane"; names[1] = "Propane";
std::vector<long double> z(2);
z[0] = 0.25; z[1] = 1-z[0];
shared_ptr<HelmholtzEOSMixtureBackend> HEOS(new HelmholtzEOSMixtureBackend(names));
HelmholtzEOSMixtureBackend &rHEOS = *(HEOS.get());
rHEOS.set_mole_fractions(z);
x_N_dependency_flag xN_flag = XN_DEPENDENT;
// These ones only require the i index
for (std::size_t i = 0; i< z.size();++i)
for (std::size_t Ncomp = 2; Ncomp <= 3; Ncomp++)
{
std::ostringstream ss0;
ss0 << "dln_fugacity_i_dT__constrho_n, i=" << i;
SECTION(ss0.str(),"")
std::ostringstream ss00;
ss00 << "Mixture with " << Ncomp << " components";
SECTION(ss00.str(),"")
{
std::vector<std::string> names;
std::vector<long double> z;
shared_ptr<HelmholtzEOSMixtureBackend> HEOS, HEOS_plusT_constrho, HEOS_plusrho_constT, HEOS_minusT_constrho, HEOS_minusrho_constT;
names.resize(Ncomp);
z.resize(Ncomp);
/* Set up a test class for the mixture tests */
if (Ncomp == 2)
{
names[0] = "Ethane"; names[1] = "Propane";
z[0] = 0.3; z[1] = 0.7;
}
else if (Ncomp == 3)
{
names[0] = "Ethane"; names[1] = "Propane"; names[2] = "Methane";
z[0] = 0.3; z[1] = 0.4; z[2] = 0.3;
}
double T1 = 300, rho1 = 300, dT = 1e-3, drho = 1e-3, dz = 1e-6;
HEOS.reset(new HelmholtzEOSMixtureBackend(names));
HEOS->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS = *(HEOS.get());
rHEOS.set_mole_fractions(z);
double T1 = 300, dT = 1e-3, rho1 = 300;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, rho1, T1);
double analytic = MixtureDerivatives::dln_fugacity_i_dT__constrho_n(rHEOS, i, xN_flag);
rHEOS.update(DmolarT_INPUTS, rho1, T1 + dT);
double v1 = log(MixtureDerivatives::fugacity_i(rHEOS, i, xN_flag));
rHEOS.update(DmolarT_INPUTS, rho1, T1 - dT);
double v2 = log(MixtureDerivatives::fugacity_i(rHEOS, i, xN_flag));
rHEOS.unspecify_phase();
double numeric = (v1 - v2)/(2*dT);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss0b;
ss0b << "dln_fugacity_i_drho__constT_n, i=" << i;
SECTION(ss0b.str(), "")
{
if (i==1){break;}
double drho = 1e-3;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double analytic = MixtureDerivatives::dln_fugacity_i_drho__constT_n(rHEOS, i, xN_flag);
HEOS_plusT_constrho.reset(new HelmholtzEOSMixtureBackend(names));
HEOS_plusT_constrho->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS_plusT_constrho = *(HEOS_plusT_constrho.get());
rHEOS_plusT_constrho.set_mole_fractions(z);
rHEOS_plusT_constrho.update(DmolarT_INPUTS, rho1, T1 + dT);
rHEOS.update(DmolarT_INPUTS, 300 + drho, 300);
double v1 = log(MixtureDerivatives::fugacity_i(rHEOS, i, xN_flag));
rHEOS.update(DmolarT_INPUTS, 300 - drho, 300);
double v2 = log(MixtureDerivatives::fugacity_i(rHEOS, i, xN_flag));
HEOS_minusT_constrho.reset(new HelmholtzEOSMixtureBackend(names));
HEOS_minusT_constrho->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS_minusT_constrho = *(HEOS_minusT_constrho.get());
rHEOS_minusT_constrho.set_mole_fractions(z);
rHEOS_minusT_constrho.update(DmolarT_INPUTS, rho1, T1 - dT);
double numeric = (v1 - v2)/(2*drho);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss1;
ss1 << "dln_fugacity_coefficient_dT__constp_n, i=" << i;
SECTION(ss1.str(), "")
{
double T1 = 300, dT = 1e-3;
rHEOS.specify_phase(iphase_gas);
HEOS_plusrho_constT.reset(new HelmholtzEOSMixtureBackend(names));
HEOS_plusrho_constT->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS_plusrho_constT = *(HEOS_plusrho_constT.get());
rHEOS_plusrho_constT.set_mole_fractions(z);
rHEOS_plusrho_constT.update(DmolarT_INPUTS, rho1 + drho, T1);
rHEOS.update(PT_INPUTS, 101325, T1);
double analytic = MixtureDerivatives::dln_fugacity_coefficient_dT__constp_n(rHEOS, i, xN_flag);
HEOS_minusrho_constT.reset(new HelmholtzEOSMixtureBackend(names));
HEOS_minusrho_constT->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS_minusrho_constT = *(HEOS_minusrho_constT.get());
rHEOS_minusrho_constT.set_mole_fractions(z);
rHEOS_minusrho_constT.update(DmolarT_INPUTS, rho1 - drho, T1);
rHEOS.update(PT_INPUTS, 101325, T1 + dT);
double v1 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS, i, xN_flag);
rHEOS.update(PT_INPUTS, 101325, T1 - dT);
double v2 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS, i, xN_flag);
double numeric = (v1 - v2)/(2*dT);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
rHEOS.update(DmolarT_INPUTS, rho1, T1);
std::ostringstream ss2;
ss2 << "dln_fugacity_coefficient_dp__constT_n, i=" << i;
SECTION(ss2.str(), "")
{
double p0 = 101325, drho = 1e-4;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(PT_INPUTS, p0, 300);
double analytic = MixtureDerivatives::dln_fugacity_coefficient_dp__constT_n(rHEOS, i, xN_flag);
double rho1 = rHEOS.rhomolar();
rHEOS.update(DmolarT_INPUTS, rho1 + drho, 300);
double v1 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS, i, xN_flag), p1 = rHEOS.p();
rHEOS.update(DmolarT_INPUTS, rho1 - drho, 300);
double v2 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS, i, xN_flag), p2 = rHEOS.p();
double numeric = (v1 - v2)/(p1 - p2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3;
ss3 << "d_ndalphardni_dDelta, i=" << i;
SECTION(ss3.str(), "")
{
double p1 = 101325, dP = 1e-1;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(PT_INPUTS, p1, 300);
double analytic = MixtureDerivatives::d_ndalphardni_dDelta(rHEOS, i, xN_flag);
rHEOS.update(PT_INPUTS, p1 + dP, 300);
double v1 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS, i, xN_flag), delta1 = rHEOS.delta();
rHEOS.update(PT_INPUTS, p1 - dP, 300);
double v2 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS, i, xN_flag), delta2 = rHEOS.delta();
double numeric = (v1 - v2)/(delta1 - delta2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3a;
ss3a << "d2alphar_dxi_dDelta, i=" << i;
SECTION(ss3a.str(), "")
{
if (i==1){break;}
double p1 = 101325, dP = 1e-1;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(PT_INPUTS, p1, 300);
double analytic = MixtureDerivatives::d2alphar_dxi_dDelta(rHEOS, i, xN_flag);
rHEOS.update(PT_INPUTS, p1 + dP, 300);
double v1 = MixtureDerivatives::dalphar_dxi(rHEOS, i, xN_flag), delta1 = rHEOS.delta();
rHEOS.update(PT_INPUTS, p1 - dP, 300);
double v2 = MixtureDerivatives::dalphar_dxi(rHEOS, i, xN_flag), delta2 = rHEOS.delta();
double numeric = (v1 - v2)/(delta1 - delta2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss4;
ss4 << "d_ndalphardni_dTau, i=" << i;
SECTION(ss4.str(), "")
{
double p1 = 101325, dT = 1e-2;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(PT_INPUTS, 101325, 300);
double rho1 = rHEOS.rhomolar();
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double analytic = MixtureDerivatives::d_ndalphardni_dTau(rHEOS, i, xN_flag);
rHEOS.update(DmolarT_INPUTS, rho1, 300 + dT);
double v1 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS, i, xN_flag), tau1 = rHEOS.tau();
rHEOS.update(DmolarT_INPUTS, rho1, 300 - dT);
double v2 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS, i, xN_flag), tau2 = rHEOS.tau();
double numeric = (v1 - v2)/(tau1 - tau2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss4a;
ss4a << "d2alphar_dxi_dTau, i=" << i;
SECTION(ss4a.str(), "")
{
if (i == 1){ break; }
double p1 = 101325, dT = 1e-2;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(PT_INPUTS, 101325, 300);
double rho1 = rHEOS.rhomolar();
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double analytic = MixtureDerivatives::d2alphar_dxi_dTau(rHEOS, i, xN_flag);
rHEOS.update(DmolarT_INPUTS, rho1, 300 + dT);
double v1 = MixtureDerivatives::dalphar_dxi(rHEOS, i, xN_flag), tau1 = rHEOS.tau();
rHEOS.update(DmolarT_INPUTS, rho1, 300 - dT);
double v2 = MixtureDerivatives::dalphar_dxi(rHEOS, i, xN_flag), tau2 = rHEOS.tau();
double numeric = (v1 - v2)/(tau1 - tau2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss5;
ss5 << "dpdxj__constT_V_xi, i=" << i;
SECTION(ss5.str(), "")
{
if (i==1){break;}
double dz = 1e-6;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double rho1 = rHEOS.rhomolar();
double analytic = MixtureDerivatives::dpdxj__constT_V_xi(rHEOS, i, xN_flag);
std::vector<long double> zp = z; /// Copy base composition
zp[i] += dz; zp[1-i] -= dz;
rHEOS.set_mole_fractions(zp);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v1 = rHEOS.p();
std::vector<long double> zm = z; /// Copy base composition
zm[i] -= dz; zm[1-i] += dz;
rHEOS.set_mole_fractions(zm);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v2 = rHEOS.p();
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss6;
ss6 << "d_dalpharddelta_dxj__constT_V_xi, i=" << i;
SECTION(ss6.str(), "")
{
if (i==1){break;}
double dz = 1e-6;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double rho1 = rHEOS.rhomolar();
double analytic = MixtureDerivatives::d_dalpharddelta_dxj__constT_V_xi(rHEOS, i, xN_flag);
// Increment mole fraction
std::vector<long double> zp = z; /// Copy base composition
zp[i] += dz; zp[1-i] -= dz;
rHEOS.set_mole_fractions(zp);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v1 = rHEOS.dalphar_dDelta();
// Decrement mole fraction
std::vector<long double> zm = z; /// Copy base composition
zm[i] -= dz; zm[1-i] += dz;
rHEOS.set_mole_fractions(zm);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v2 = rHEOS.dalphar_dDelta();
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
// These derivatives depend on both the i and j indices
for (std::size_t j = 0; j < z.size(); ++j){
std::ostringstream ss1;
ss1 << "dln_fugacity_coefficient_dxj__constT_p_xi, i=" << i << ", j=" << j;
SECTION(ss1.str(), "")
x_N_dependency_flag xN_flag = XN_DEPENDENT;
// These ones only require the i index
for (std::size_t i = 0; i< z.size();++i)
{
if (j == 1){break;}
double dz = 1e-6;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double p = rHEOS.p();
CAPTURE(p);
double rho1 = rHEOS.rhomolar();
double analytic = MixtureDerivatives::dln_fugacity_coefficient_dxj__constT_p_xi(rHEOS, i, j, xN_flag);
shared_ptr<HelmholtzEOSMixtureBackend> HEOS, HEOS_pluszi, HEOS_minuszi;
HEOS_pluszi.reset(new HelmholtzEOSMixtureBackend(names));
HEOS_pluszi->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS_pluszi = *(HEOS_pluszi.get());
std::vector<long double> zp = z; /// Copy base composition
zp[j] += dz; zp[1-j] -= dz;
rHEOS.set_mole_fractions(zp);
rHEOS.update(PT_INPUTS, p, 300);
double v1 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS, i, xN_flag);
zp[i] += dz; zp[z.size()-1] -= dz;
rHEOS_pluszi.set_mole_fractions(zp);
rHEOS_pluszi.update(DmolarT_INPUTS, rho1, T1);
HEOS_minuszi.reset(new HelmholtzEOSMixtureBackend(names));
HEOS_minuszi->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS_minuszi = *(HEOS_minuszi.get());
std::vector<long double> zm = z; /// Copy base composition
zm[j] -= dz; zm[1-j] += dz;
rHEOS.set_mole_fractions(zm);
rHEOS.update(PT_INPUTS, p, 300);
double v2 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS, i, xN_flag);
zm[i] -= dz; zm[z.size()-1] += dz;
rHEOS_minuszi.set_mole_fractions(zm);
rHEOS_minuszi.update(DmolarT_INPUTS, rho1, T1);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
std::ostringstream ss0;
ss0 << "dln_fugacity_i_dT__constrho_n, i=" << i;
SECTION(ss0.str(),"")
{
double analytic = MixtureDerivatives::dln_fugacity_i_dT__constrho_n(rHEOS, i, xN_flag);
double v1 = log(MixtureDerivatives::fugacity_i(rHEOS_plusT_constrho, i, xN_flag));
double v2 = log(MixtureDerivatives::fugacity_i(rHEOS_minusT_constrho, i, xN_flag));
double numeric = (v1 - v2)/(2*dT);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss0b;
ss0b << "dln_fugacity_i_drho__constT_n, i=" << i;
SECTION(ss0b.str(), "")
{
double analytic = MixtureDerivatives::dln_fugacity_i_drho__constT_n(rHEOS, i, xN_flag);
double v1 = log(MixtureDerivatives::fugacity_i(rHEOS_plusrho_constT, i, xN_flag));
double v2 = log(MixtureDerivatives::fugacity_i(rHEOS_minusrho_constT, i, xN_flag));
double numeric = (v1 - v2)/(2*dT);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss2;
ss2 << "dln_fugacity_coefficient_dp__constT_n, i=" << i;
SECTION(ss2.str(), "")
{
double analytic = MixtureDerivatives::dln_fugacity_coefficient_dp__constT_n(rHEOS, i, xN_flag);
double v1 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS_plusrho_constT, i, xN_flag), p1 = rHEOS_plusrho_constT.p();
double v2 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS_minusrho_constT, i, xN_flag), p2 = rHEOS_minusrho_constT.p();
double numeric = (v1 - v2)/(p1 - p2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss1;
ss1 << "dln_fugacity_coefficient_dT__constp_n, i=" << i;
SECTION(ss1.str(), "")
{
double T1 = 300, dT = 1e-3;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(PT_INPUTS, 101325, T1);
double analytic = MixtureDerivatives::dln_fugacity_coefficient_dT__constp_n(rHEOS, i, xN_flag);
rHEOS.update(PT_INPUTS, 101325, T1 + dT);
double v1 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS, i, xN_flag);
rHEOS.update(PT_INPUTS, 101325, T1 - dT);
double v2 = MixtureDerivatives::ln_fugacity_coefficient(rHEOS, i, xN_flag);
double numeric = (v1 - v2)/(2*dT);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss1a;
ss1a << "dln_fugacity_dxj__constT_rho_xi, i=" << i << ", j=" << j;
SECTION(ss1a.str(), "")
{
if (j == 1){break;}
double dz = 1e-6;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double p = rHEOS.p();
CAPTURE(p);
std::ostringstream ss3;
ss3 << "d_ndalphardni_dDelta, i=" << i;
SECTION(ss3.str(), "")
{
double analytic = MixtureDerivatives::d_ndalphardni_dDelta(rHEOS, i, xN_flag);
double v1 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS_plusrho_constT, i, xN_flag), delta1 = rHEOS_plusrho_constT.delta();
double v2 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS_minusrho_constT, i, xN_flag), delta2 = rHEOS_minusrho_constT.delta();
double numeric = (v1 - v2)/(delta1 - delta2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3a;
ss3a << "d2alphar_dxi_dDelta, i=" << i;
SECTION(ss3a.str(), "")
{
if (i == z.size()-1){break;}
double analytic = MixtureDerivatives::d2alphar_dxi_dDelta(rHEOS, i, xN_flag);
double v1 = MixtureDerivatives::dalphar_dxi(rHEOS_plusrho_constT, i, xN_flag), delta1 = rHEOS_plusrho_constT.delta();
double v2 = MixtureDerivatives::dalphar_dxi(rHEOS_minusrho_constT, i, xN_flag), delta2 = rHEOS_minusrho_constT.delta();
double numeric = (v1 - v2)/(delta1 - delta2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss4a;
ss4a << "d2alphar_dxi_dTau, i=" << i;
SECTION(ss4a.str(), "")
{
if (i == z.size()-1){ break; }
double analytic = MixtureDerivatives::d2alphar_dxi_dTau(rHEOS, i, xN_flag);
double v1 = MixtureDerivatives::dalphar_dxi(rHEOS_plusT_constrho, i, xN_flag), tau1 = rHEOS_plusT_constrho.tau();
double v2 = MixtureDerivatives::dalphar_dxi(rHEOS_minusT_constrho, i, xN_flag), tau2 = rHEOS_minusT_constrho.tau();
double numeric = (v1 - v2)/(tau1 - tau2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss4;
ss4 << "d_ndalphardni_dTau, i=" << i;
SECTION(ss4.str(), "")
{
double analytic = MixtureDerivatives::d_ndalphardni_dTau(rHEOS, i, xN_flag);
double v1 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS_plusT_constrho, i, xN_flag), tau1 = rHEOS_plusT_constrho.tau();
double v2 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS_minusT_constrho, i, xN_flag), tau2 = rHEOS_minusT_constrho.tau();
double numeric = (v1 - v2)/(tau1 - tau2);
double err = std::abs((numeric-analytic)/analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss5;
ss5 << "dpdxj__constT_V_xi, i=" << i;
SECTION(ss5.str(), "")
{
if (i==z.size()-1){break;}
double analytic = MixtureDerivatives::dpdxj__constT_V_xi(rHEOS, i, xN_flag);
double v1 = rHEOS_pluszi.p();
double v2 = rHEOS_minuszi.p();
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss5a;
ss5a << "dtaudxj__constT_V_xi, i=" << i;
SECTION(ss5a.str(), "")
{
if (i==z.size()-1){break;}
double analytic = MixtureDerivatives::dtau_dxj__constT_V_xi(rHEOS, i, xN_flag);
double v1 = rHEOS_pluszi.tau();
double v2 = rHEOS_minuszi.tau();
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss5b;
ss5b << "ddeltadxj__constT_V_xi, i=" << i;
SECTION(ss5b.str(), "")
{
if (i==z.size()-1){break;}
double analytic = MixtureDerivatives::ddelta_dxj__constT_V_xi(rHEOS, i, xN_flag);
double v1 = rHEOS_pluszi.delta();
double v2 = rHEOS_minuszi.delta();
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss6;
ss6 << "d_dalpharddelta_dxj__constT_V_xi, i=" << i;
SECTION(ss6.str(), "")
{
if (i==z.size()-1){break;}
double analytic = MixtureDerivatives::d_dalpharddelta_dxj__constT_V_xi(rHEOS, i, xN_flag);
double v1 = rHEOS_pluszi.dalphar_dDelta();
double v2 = rHEOS_minuszi.dalphar_dDelta();
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss7;
ss7 << "dTrdxi__constxj, i=" << i;
SECTION(ss7.str(), "")
{
if (i == z.size()-1){break;}
double analytic = rHEOS.Reducing->dTrdxi__constxj(rHEOS.get_const_mole_fractions(), i, xN_flag);
double v1 = rHEOS_pluszi.Reducing->Tr(rHEOS_pluszi.get_const_mole_fractions());
double v2 = rHEOS_minuszi.Reducing->Tr(rHEOS_minuszi.get_const_mole_fractions());
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss8;
ss8 << "drhormolardxi__constxj, i=" << i;
SECTION(ss8.str(), "")
{
if (i == z.size()-1){break;}
double analytic = rHEOS.Reducing->drhormolardxi__constxj(rHEOS.get_const_mole_fractions(), i, xN_flag);
double v1 = rHEOS_pluszi.Reducing->rhormolar(rHEOS_pluszi.get_const_mole_fractions());
double v2 = rHEOS_minuszi.Reducing->rhormolar(rHEOS_minuszi.get_const_mole_fractions());
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3c;
ss3c << "d2Trdxi2__constxj, i=" << i;
SECTION(ss3c.str(), "")
{
if (i == z.size()-1){break;}
double analytic = rHEOS.Reducing->d2Trdxi2__constxj(z, i, xN_flag);
double v1 = rHEOS_pluszi.Reducing->dTrdxi__constxj(rHEOS_pluszi.get_const_mole_fractions(), i, xN_flag);
double v2 = rHEOS_minuszi.Reducing->dTrdxi__constxj(rHEOS_minuszi.get_const_mole_fractions(), i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3d;
ss3d << "dalphar_dxi, i=" << i;
SECTION(ss3d.str(), "")
{
if (i == z.size()-1){break;}
double analytic = MixtureDerivatives::dalphar_dxi(rHEOS, i, xN_flag);
double v1 = rHEOS_pluszi.alphar();
double v2 = rHEOS_minuszi.alphar();
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
double rho1 = rHEOS.rhomolar();
double analytic = MixtureDerivatives::dln_fugacity_dxj__constT_rho_xi(rHEOS, i, j, xN_flag);
std::vector<long double> zp = z; /// Copy base composition
zp[j] += dz; zp[1-j] -= dz;
rHEOS.set_mole_fractions(zp);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double v1 = log(MixtureDerivatives::fugacity_i(rHEOS, i, xN_flag));
std::vector<long double> zm = z; /// Copy base composition
zm[j] -= dz; zm[1-j] += dz;
rHEOS.set_mole_fractions(zm);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double v2 = log(MixtureDerivatives::fugacity_i(rHEOS, i, xN_flag));
// These derivatives depend on both the i and j indices
for (std::size_t j = 0; j < z.size(); ++j){
shared_ptr<HelmholtzEOSMixtureBackend> HEOS, HEOS_pluszj, HEOS_minuszj;
HEOS_pluszj.reset(new HelmholtzEOSMixtureBackend(names));
HEOS_pluszj->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS_pluszj = *(HEOS_pluszj.get());
std::vector<long double> zp = z; /// Copy base composition
zp[j] += dz; zp[z.size()-1] -= dz;
rHEOS_pluszj.set_mole_fractions(zp);
rHEOS_pluszj.update(DmolarT_INPUTS, rho1, T1);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
HEOS_minuszj.reset(new HelmholtzEOSMixtureBackend(names));
HEOS_minuszj->specify_phase(iphase_gas);
HelmholtzEOSMixtureBackend &rHEOS_minuszj = *(HEOS_minuszj.get());
std::vector<long double> zm = z; /// Copy base composition
zm[j] -= dz; zm[z.size()-1] += dz;
rHEOS_minuszj.set_mole_fractions(zm);
rHEOS_minuszj.update(DmolarT_INPUTS, rho1, T1);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss2;
ss2 << "d_ndTrdni_dxj, i=" << i << ", j=" << j;
SECTION(ss2.str(), "")
{
if (j == 1){break;}
double dz = 1e-6;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double rho1 = rHEOS.rhomolar();
double analytic = rHEOS.Reducing->d_ndTrdni_dxj__constxi(rHEOS.get_const_mole_fractions(), i, j, xN_flag);
// Increment mole fraction
std::vector<long double> zp = z; /// Copy base composition
zp[j] += dz; zp[1-j] -= dz;
rHEOS.set_mole_fractions(zp);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v1 = rHEOS.Reducing->ndTrdni__constnj(rHEOS.get_const_mole_fractions(), i, xN_flag);
// Decrement mole fraction
std::vector<long double> zm = z; /// Copy base composition
zm[j] -= dz; zm[1-j] += dz;
rHEOS.set_mole_fractions(zm);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v2 = rHEOS.Reducing->ndTrdni__constnj(rHEOS.get_const_mole_fractions(), i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss4;
ss4 << "d_ndrhomolarrdni_dxj, i=" << i << ", j=" << j;
SECTION(ss4.str(), "")
{
if (j == 1){break;}
double dz = 1e-6;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double rho1 = rHEOS.rhomolar();
double analytic = rHEOS.Reducing->d_ndrhorbardni_dxj__constxi(rHEOS.get_const_mole_fractions(), i, j, xN_flag);
// Increment mole fraction
std::vector<long double> zp = z; /// Copy base composition
zp[j] += dz; zp[1-j] -= dz;
rHEOS.set_mole_fractions(zp);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v1 = rHEOS.Reducing->ndrhorbardni__constnj(rHEOS.get_const_mole_fractions(), i, xN_flag);
// Decrement mole fraction
std::vector<long double> zm = z; /// Copy base composition
zm[j] -= dz; zm[1-j] += dz;
rHEOS.set_mole_fractions(zm);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v2 = rHEOS.Reducing->ndrhorbardni__constnj(rHEOS.get_const_mole_fractions(), i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3;
ss3 << "d_ndalphardni_dxj__constT_V_xi, i=" << i << ", j=" << j;
SECTION(ss3.str(), "")
{
if (j == 1){break;}
double dz = 1e-6;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double rho1 = rHEOS.rhomolar();
double analytic = MixtureDerivatives::d_ndalphardni_dxj__constT_V_xi(rHEOS, i, j, xN_flag);
// Increment mole fraction
std::vector<long double> zp = z; /// Copy base composition
zp[j] += dz; zp[1-j] -= dz;
rHEOS.set_mole_fractions(zp);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v1 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS, i, xN_flag);
// Decrement mole fraction
std::vector<long double> zm = z; /// Copy base composition
zm[j] -= dz; zm[1-j] -= dz;
rHEOS.set_mole_fractions(zm);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v2 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS, i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3a;
ss3a << "d2alphardxidxj, i=" << i << ", j=" << j;
SECTION(ss3a.str(), "")
{
if (j == 1){break;}
double dz = 1e-6;
rHEOS.specify_phase(iphase_gas);
rHEOS.update(DmolarT_INPUTS, 300, 300);
double rho1 = rHEOS.rhomolar();
double analytic = MixtureDerivatives::d2alphardxidxj(rHEOS,i,j,xN_flag);
// Increment mole fraction
std::vector<long double> zp = z; /// Copy base composition
zp[j] += dz; zp[1-j] -= dz;
rHEOS.set_mole_fractions(zp);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v1 = MixtureDerivatives::dalphar_dxi(rHEOS, i, xN_flag);
// Decrement mole fraction
std::vector<long double> zm = z; /// Copy base composition
zm[j] -= dz; zm[1-j] -= dz;
rHEOS.set_mole_fractions(zm);
rHEOS.update(DmolarT_INPUTS, rho1, 300);
double v2 = MixtureDerivatives::dalphar_dxi(rHEOS, i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
std::ostringstream ss1a;
ss1a << "dln_fugacity_dxj__constT_rho_xi, i=" << i << ", j=" << j;
SECTION(ss1a.str(), "")
{
if (j == z.size()-1){break;}
double analytic = MixtureDerivatives::dln_fugacity_dxj__constT_rho_xi(rHEOS, i, j, xN_flag);
double v1 = log(MixtureDerivatives::fugacity_i(rHEOS_pluszj, i, xN_flag));
double v2 = log(MixtureDerivatives::fugacity_i(rHEOS_minuszj, i, xN_flag));
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss2;
ss2 << "d_ndTrdni_dxj, i=" << i << ", j=" << j;
SECTION(ss2.str(), "")
{
if (j == z.size()-1){break;}
double analytic = rHEOS.Reducing->d_ndTrdni_dxj__constxi(rHEOS.get_const_mole_fractions(), i, j, xN_flag);
double v1 = rHEOS_pluszj.Reducing->ndTrdni__constnj(rHEOS_pluszj.get_const_mole_fractions(), i, xN_flag);
double v2 = rHEOS_minuszj.Reducing->ndTrdni__constnj(rHEOS_minuszj.get_const_mole_fractions(), i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss4;
ss4 << "d_ndrhomolarrdni_dxj, i=" << i << ", j=" << j;
SECTION(ss4.str(), "")
{
if (j == z.size()-1){break;}
double analytic = rHEOS.Reducing->d_ndrhorbardni_dxj__constxi(rHEOS.get_const_mole_fractions(), i, j, xN_flag);
double v1 = rHEOS_pluszj.Reducing->ndrhorbardni__constnj(rHEOS_pluszj.get_const_mole_fractions(), i, xN_flag);
double v2 = rHEOS_minuszj.Reducing->ndrhorbardni__constnj(rHEOS_minuszj.get_const_mole_fractions(), i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3;
ss3 << "d_ndalphardni_dxj__constT_V_xi, i=" << i << ", j=" << j;
SECTION(ss3.str(), "")
{
if (j == z.size()-1){break;}
double analytic = MixtureDerivatives::d_ndalphardni_dxj__constT_V_xi(rHEOS, i, j, xN_flag);
double v1 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS_pluszj, i, xN_flag);
double v2 = MixtureDerivatives::ndalphar_dni__constT_V_nj(rHEOS_minuszj, i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3a;
ss3a << "d2alphardxidxj, i=" << i << ", j=" << j;
SECTION(ss3a.str(), "")
{
if (j == z.size()-1){break;}
double analytic = MixtureDerivatives::d2alphardxidxj(rHEOS,i,j,xN_flag);
double v1 = MixtureDerivatives::dalphar_dxi(rHEOS_pluszj, i, xN_flag);
double v2 = MixtureDerivatives::dalphar_dxi(rHEOS_minuszj, i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
if (std::abs(numeric) < DBL_EPSILON && std::abs(analytic) < DBL_EPSILON){break;}
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
std::ostringstream ss3b;
ss3b << "d2Trdxidxj, i=" << i << ", j=" << j;
SECTION(ss3b.str(), "")
{
if (j == z.size()-1 || i == j){break;}
double analytic = rHEOS.Reducing->d2Trdxidxj(z, i, j, xN_flag);
double v1 = rHEOS.Reducing->dTrdxi__constxj(rHEOS_pluszj.get_const_mole_fractions(), i, xN_flag);
double v2 = rHEOS.Reducing->dTrdxi__constxj(rHEOS_minuszj.get_const_mole_fractions(), i, xN_flag);
double numeric = (v1 - v2)/(2*dz);
double err = std::abs((numeric-analytic)/analytic);
if (std::abs(numeric) < DBL_EPSILON && std::abs(analytic) < DBL_EPSILON){break;}
CAPTURE(numeric);
CAPTURE(analytic);
CHECK(err < 1e-8);
}
}
}
}
}
}
#endif

2
src/Backends/Helmholtz/PhaseEnvelopeRoutines.cpp
View File

@@ -41,7 +41,7 @@ void PhaseEnvelopeRoutines::build(HelmholtzEOSMixtureBackend &HEOS)
IO.rhomolar_vap = io.rhomolar_vap;
IO.T = io.T;
IO.p = io.p;
IO.Nstep_max = 100;
IO.Nstep_max = 30;
bool dont_extrapolate = false;

19
src/Backends/Helmholtz/ReducingFunctions.cpp
View File

@@ -176,7 +176,7 @@ long double GERG2008ReducingFunction::dYrdxi__constxj(const std::vector<long dou
}
for (std::size_t k = i+1; k < N-1; k++)
{
dYr_dxi += c_Y_ij(i, k, beta, gamma, Y_c_ij)*dfYkidxi__constxk(x,i,k,beta);
dYr_dxi += c_Y_ij(i, k, beta, gamma, Y_c_ij)*dfYikdxi__constxk(x,i,k,beta);
}
double beta_Y_iN = beta[i][N-1], xN = x[N-1];
dYr_dxi += c_Y_ij(i, N-1, beta, gamma, Y_c_ij)*(xN*(x[i]+xN)/(pow(beta_Y_iN,2)*x[i]+xN)+(1-beta_Y_iN*beta_Y_iN)*x[i]*xN*xN/pow(beta_Y_iN*beta_Y_iN*x[i]+xN, 2));
@@ -216,7 +216,7 @@ long double GERG2008ReducingFunction::d2Yrdxi2__constxj(const std::vector<long d
}
for (std::size_t k = i+1; k < N-1; k++)
{
d2Yr_dxi2 += c_Y_ij(i, k, beta, gamma, Y_c_ij)*d2fYkidxi2__constxk(x,i,k,beta);
d2Yr_dxi2 += c_Y_ij(i, k, beta, gamma, Y_c_ij)*d2fYikdxi2__constxk(x,i,k,beta);
}
double beta_Y_iN = beta[i][N-1], xN = x[N-1];
d2Yr_dxi2 += 2*c_Y_ij(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)));
@@ -255,14 +255,17 @@ long double GERG2008ReducingFunction::d2Yrdxidxj__constxj(const std::vector<long
for (std::size_t k = 0; k < N-1; k++)
{
double beta_Y_kN = beta[k][N-1];
long double beta_Y_kN = beta[k][N-1];
d2Yr_dxidxj += 2*c_Y_ij(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_ij(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_ij(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));
{
long double beta_Y_iN = beta[i][N-1];
d2Yr_dxidxj += c_Y_ij(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));
}
{
long double beta_Y_jN = beta[j][N-1];
d2Yr_dxidxj += -c_Y_ij(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{

119
src/Backends/Helmholtz/VLERoutines.cpp
View File

@@ -812,73 +812,78 @@ void SaturationSolvers::newton_raphson_saturation::check_Jacobian()
long double T0 = T;
std::vector<long double> r0 = r, x0 = x;
STLMatrix J0 = J;
long double rhomolar_liq = rSatL.rhomolar();
long double rhomolar_vap = rSatV.rhomolar();
long double rhomolar_liq0 = rSatL.rhomolar();
long double rhomolar_vap0 = rSatV.rhomolar();
// Derivatives with respect to T
double dT = 1e-3, T1 = T+dT, T2 = T-dT;
this->T = T1;
this->rhomolar_liq = rhomolar_liq;
this->rhomolar_vap = rhomolar_vap;
build_arrays();
std::vector<long double> r1 = r;
this->T = T2;
this->rhomolar_liq = rhomolar_liq;
this->rhomolar_vap = rhomolar_vap;
build_arrays();
std::vector<long double> r2 = r;
std::vector<long double> diffn(N+1, _HUGE);
for (std::size_t i = 0; i < N+1; ++i){
diffn[i] = (r1[i]-r2[i])/(2*dT);
{
// Derivatives with respect to T
double dT = 1e-3, T1 = T+dT, T2 = T-dT;
this->T = T1;
this->rhomolar_liq = rhomolar_liq0;
this->rhomolar_vap = rhomolar_vap0;
build_arrays();
std::vector<long double> r1 = r;
this->T = T2;
this->rhomolar_liq = rhomolar_liq0;
this->rhomolar_vap = rhomolar_vap0;
build_arrays();
std::vector<long double> r2 = r;
std::vector<long double> diffn(N+1, _HUGE);
for (std::size_t i = 0; i < N+1; ++i){
diffn[i] = (r1[i]-r2[i])/(2*dT);
}
std::cout << format("For T\n");
std::cout << "numerical: " << vec_to_string(diffn, "%0.11Lg") << std::endl;
std::cout << "analytic: " << vec_to_string(get_col(J0, N-1), "%0.11Lg") << std::endl;
}
std::cout << format("For T\n");
std::cout << "numerical: " << vec_to_string(diffn, "%0.11Lg") << std::endl;
std::cout << "analytic: " << vec_to_string(get_col(J0, N-1), "%0.11Lg") << std::endl;
// Derivatives with respect to rho'
double drho = 1;
this->T = T0;
this->rhomolar_liq = rhomolar_liq+drho;
this->rhomolar_vap = rhomolar_vap;
build_arrays();
std::vector<long double> rr1 = r;
this->T = T0;
this->rhomolar_liq = rhomolar_liq-drho;
this->rhomolar_vap = rhomolar_vap;
build_arrays();
std::vector<long double> rr2 = r;
std::vector<long double> difffn(N+1, _HUGE);
for (std::size_t i = 0; i < N+1; ++i){
difffn[i] = (rr1[i]-rr2[i])/(2*drho);
{
// Derivatives with respect to rho'
double drho = 1;
this->T = T0;
this->rhomolar_liq = rhomolar_liq0+drho;
this->rhomolar_vap = rhomolar_vap0;
build_arrays();
std::vector<long double> rr1 = r;
this->T = T0;
this->rhomolar_liq = rhomolar_liq0-drho;
this->rhomolar_vap = rhomolar_vap0;
build_arrays();
std::vector<long double> rr2 = r;
std::vector<long double> difffn(N+1, _HUGE);
for (std::size_t i = 0; i < N+1; ++i){
difffn[i] = (rr1[i]-rr2[i])/(2*drho);
}
std::cout << format("For rho\n");
std::cout << "numerical: " << vec_to_string(difffn, "%0.11Lg") << std::endl;
std::cout << "analytic: " << vec_to_string(get_col(J0, N), "%0.11Lg") << std::endl;
}
std::cout << format("For rho\n");
std::cout << "numerical: " << vec_to_string(difffn, "%0.11Lg") << std::endl;
std::cout << "analytic: " << vec_to_string(get_col(J0, N), "%0.11Lg") << std::endl;
for (std::size_t i = 0; i < x.size()-1; ++i)
{
// Derivatives with respect to x0
// Derivatives with respect to x[i]
double dx = 1e-5;
x = x0; x[i] += dx; x[x.size()-1] -= dx;
this->x = x0;
this->x[i] += dx; this->x[x.size()-1] -= dx;
this->T = T0;
this->rhomolar_liq = rhomolar_liq;
this->rhomolar_vap = rhomolar_vap;
rSatL.set_mole_fractions(x);
build_arrays(); r1 = r;
this->rhomolar_liq = rhomolar_liq0;
this->rhomolar_vap = rhomolar_vap0;
build_arrays();
std::vector<long double> r1 = this->r;
x = x0; x[i] -= dx; x[x.size()-1] += dx;
rSatL.set_mole_fractions(x);
this->x = x0;
this->x[i] -= dx; this->x[x.size()-1] += dx;
this->T = T0;
this->rhomolar_liq = rhomolar_liq;
this->rhomolar_vap = rhomolar_vap;
build_arrays(); r2 = r;
this->rhomolar_liq = rhomolar_liq0;
this->rhomolar_vap = rhomolar_vap0;
build_arrays();
std::vector<long double> r2 = this->r;
std::vector<long double> diffn(N+1, _HUGE);
for (std::size_t j = 0; j < N+1; ++j){
diffn[i] = (r1[j]-r2[j])/(2*dx);
diffn[j] = (r1[j]-r2[j])/(2*dx);
}
std::cout << format("For x%d\n", i);
std::cout << format("For x%d N %d\n", i, N);
std::cout << "numerical: " << vec_to_string(diffn, "%0.11Lg") << std::endl;
std::cout << "analytic: " << vec_to_string(get_col(J0, i), "%0.11Lg") << std::endl;
}
@@ -944,6 +949,10 @@ void SaturationSolvers::newton_raphson_saturation::call(HelmholtzEOSMixtureBacke
//std::cout << format("\t%Lg ", this->error_rms) << T << " " << rhomolar_liq << " " << rhomolar_vap << " " << vec_to_string(v, "%0.10Lg") << " " << vec_to_string(x, "%0.10Lg") << std::endl;
iter++;
if (iter == IO.Nstep_max){
throw ValueError(format("newton_raphson_saturation::call reached max number of iterations [%d]",IO.Nstep_max));
}
}
while(this->error_rms > 1e-7 && max_rel_change > 1000*LDBL_EPSILON && min_abs_change > 100*DBL_EPSILON && iter < IO.Nstep_max);
IO.Nsteps = iter;