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#define CATCH_CONFIG_MAIN
#include "catch/catch.hpp"
#include "teqp/core.hpp"
auto build_vdW_argon() {
double Omega_b = 1.0 / 8, Omega_a = 27.0 / 64;
double Tcrit = 150.687, pcrit = 4863000.0; // Argon
double R = get_R_gas<double>(); // Universal gas constant
double b = Omega_b * R * Tcrit / pcrit;
double ba = Omega_b / Omega_a / Tcrit / R;
double a = b / ba;
auto vdW = vdWEOS1(a, b);
return vdW;
}
auto build_simple() {
// Argon + Xenon
std::valarray<double> Tc_K = { 150.687, 289.733 };
std::valarray<double> pc_Pa = { 4863000.0, 5842000.0 };
auto R = 1.380649e-23 * 6.02214076e23; ///< Exact value, given by k_B*N_A
int i = 0;
double ai = 27.0 / 64.0 * pow(R * Tc_K[i], 2) / pc_Pa[i];
double bi = 1.0 / 8.0 * R * Tc_K[i] / pc_Pa[i];
return vdWEOS1(ai, bi);
}
auto build_vdW() {
// Argon + Xenon
std::valarray<double> Tc_K = { 150.687, 289.733 };
std::valarray<double> pc_Pa = { 4863000.0, 5842000.0 };
return vdWEOS(Tc_K, pc_Pa);
}
TEST_CASE("Check virial coefficients for vdW", "[virial]")
{
auto vdW = build_vdW_argon();
double Omega_b = 1.0 / 8, Omega_a = 27.0 / 64;
double Tcrit = 150.687, pcrit = 4863000.0; // Argon
double R = get_R_gas<double>(); // Universal gas constant
double b = Omega_b * R * Tcrit / pcrit;
double ba = Omega_b / Omega_a / Tcrit / R;
double a = b / ba;
auto T = 300.0;
std::valarray<double> molefrac = { 1.0 };
auto Bn = get_Bnvir<Nvir, ADBackends::autodiff>(vdW, T, molefrac);
auto Bnmcx = get_Bnvir<Nvir, ADBackends::multicomplex>(vdW, T, molefrac);
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// Exact solutions for virial coefficients for van der Waals
auto get_vdW_exacts = [a, b, R, T](int Nmax) {
std::map<int, double> o = { {2, b - a / (R * T)} };
for (auto i = 3; i <= Nmax; ++i) {
o[i] = pow(b, i - 1);
}
return o;
};
auto Bnexact = get_vdW_exacts(Nvir);
// This one with complex step derivatives as another check
double B2 = get_B2vir(vdW, T, molefrac);
double B2exact = b - a / (R * T);
CHECK(std::abs(B2exact-Bnexact[2]) < 1e-15);
CHECK(std::abs(B2-Bnexact[2]) < 1e-15);
// And all the remaining derivatives
for (auto i = 2; i <= Nvir; ++i) {
auto numeric = Bn[i];
auto exact = Bnexact[i];
auto err = std::abs(numeric-exact);
auto relerr = err / std::abs(Bn[i]);
CAPTURE(numeric);
CAPTURE(exact);
CAPTURE(i);
CAPTURE(relerr);
CHECK(relerr < 1e-15);
}
}
TEST_CASE("Check Hessian of Psir", "[virial]")
{
double T = 298.15;
double rho = 3.0;
const std::valarray<double> rhovec = { rho / 2, rho / 2 };
auto get_worst_error = [&T, &rhovec](const auto &model){
auto H1 = build_Psir_Hessian_autodiff(model, T, rhovec);
auto H2 = build_Psir_Hessian_mcx(model, T, rhovec);
auto err = (H1.array() - H2).abs().maxCoeff();
CAPTURE(err);
CHECK(err < 1e-15);
return;
};
SECTION("simple") {
get_worst_error(build_simple());
}
SECTION("less_simple") {
get_worst_error(build_vdW());
}
}
TEST_CASE("Check p three ways for vdW", "[virial][p]")
{
auto model = build_simple();
const double T = 298.15;
const double rho = 3000.0;
const std::valarray<double> rhovec = { rho / 2, rho / 2 }, molefrac = {0.5, 0.5};
// Exact solution from EOS
auto pexact = model.p(T, 1/rho);
// Numerical solution from alphar
auto pfromderiv = rho*model.R*T + get_pr(model, T, rhovec);
// Numerical solution from virial expansion
constexpr int Nvir = 8;
auto Bn = get_Bnvir<Nvir>(model, T, molefrac);
auto Z = 1.0;
for (auto i = 2; i <= Nvir; ++i){
Z += Bn[i]*pow(rho, i-1);
auto pvir = Z * rho * model.R * T;
}
auto pvir = Z*rho*model.R*T;
CHECK(std::abs(pfromderiv - pexact)/pexact < 1e-15);
CHECK(std::abs(pvir - pexact)/pexact < 1e-8);
}
TEST_CASE("Trace critical locus for vdW", "[vdW][crit]")
{
// Argon + Xenon
std::valarray<double> Tc_K = { 150.687, 289.733 };
std::valarray<double> pc_Pa = { 4863000.0, 5842000.0 };
vdWEOS<double> vdW(Tc_K, pc_Pa);
auto Zc = 3.0/8.0;
auto rhoc0 = pc_Pa[0] / (vdW.R * Tc_K[0]) / Zc;
double T0 = Tc_K[0];
std::valarray<double> rhovec0 = { rhoc0, 0.0 };
auto tic0 = std::chrono::steady_clock::now();
std::string filename = "";
trace_critical_arclength_binary(vdW, T0, rhovec0, filename);
auto tic1 = std::chrono::steady_clock::now();