616 lines
22 KiB
C++
616 lines
22 KiB
C++
#include <algorithm>
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#include <array>
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#include <cmath>
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#include <limits>
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#include <stdexcept>
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#include <utility>
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#include <catch2/catch_test_macros.hpp>
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#include <catch2/matchers/catch_matchers_floating_point.hpp>
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#include <mfem.hpp>
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import mean_field;
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import test_helpers;
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namespace eos = mean_field::eos;
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namespace polytropic_eos_test_utils {
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template <typename Function>
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double centered_derivative(
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Function &&function,
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const double position,
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const double step
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) {
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return (function(position + step) - function(position - step)) / (2.0 * step);
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}
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template <typename Integrand>
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double integrate_cube(
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const mfem::IntegrationRule &integrationRule,
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Integrand &&integrand
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) {
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double integral = 0.0;
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for (int pointIndex = 0; pointIndex < integrationRule.GetNPoints(); ++pointIndex) {
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const mfem::IntegrationPoint &integrationPoint = integrationRule.IntPoint(pointIndex);
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integral += integrationPoint.weight * integrand(integrationPoint);
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}
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return integral;
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}
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} // namespace polytropic_eos_test_utils
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TEST_CASE(
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"Polytropic EOS Satisfies Its Thermodynamic Identities",
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tags::barotrope_eos_unit
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) {
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constexpr std::array<double, 3> polytropicIndices{1.0, 1.5, 3.0};
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constexpr std::array<double, 4> densities{1.0e-4, 0.02, 0.37, 2.4};
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constexpr double polytropicConstant = 0.73;
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for (const double polytropicIndex : polytropicIndices) {
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DYNAMIC_SECTION("polytropic index n = " << polytropicIndex) {
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const mean_field::eos::Polytrope barotrope(polytropicIndex, polytropicConstant);
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const double expectedEnthalpyScale = (polytropicIndex + 1.0) * polytropicConstant;
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CHECK(barotrope.polytropic_index() == polytropicIndex);
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CHECK(barotrope.polytropic_constant() == polytropicConstant);
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CHECK(barotrope.enthalpy_scale() == expectedEnthalpyScale);
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for (const double density : densities) {
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CAPTURE(polytropicIndex, polytropicConstant, density);
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const double expectedPressure = polytropicConstant * std::pow(density, 1.0 + 1.0 / polytropicIndex);
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const double expectedEnthalpy = expectedEnthalpyScale * std::pow(density, 1.0 / polytropicIndex);
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const double pressureFromDensity =
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eos::evaluate<eos::quantity::Pressure>(barotrope, eos::DensityValue{density}).value();
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const double enthalpyFromDensity =
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eos::evaluate<eos::quantity::SpecificEnthalpy>(barotrope, eos::DensityValue{density}).value();
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const double recoveredDensity =
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eos::evaluate<eos::quantity::Density>(barotrope, eos::SpecificEnthalpyValue{enthalpyFromDensity})
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.value();
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const double pressureFromEnthalpy =
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eos::evaluate<eos::quantity::Pressure>(barotrope, eos::SpecificEnthalpyValue{enthalpyFromDensity})
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.value();
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CHECK_THAT(pressureFromDensity, Catch::Matchers::WithinRel(expectedPressure, 2.0e-13));
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CHECK_THAT(enthalpyFromDensity, Catch::Matchers::WithinRel(expectedEnthalpy, 2.0e-13));
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CHECK_THAT(recoveredDensity, Catch::Matchers::WithinRel(density, 5.0e-13));
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CHECK_THAT(pressureFromEnthalpy, Catch::Matchers::WithinRel(expectedPressure, 5.0e-13));
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/*
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* Polytropic identity:
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*
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* P = rho h / (n + 1).
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*/
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CHECK_THAT(
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pressureFromEnthalpy,
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Catch::Matchers::WithinRel(density * enthalpyFromDensity / (polytropicIndex + 1.0), 5.0e-13)
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);
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/*
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* Polytropic identity:
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*
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* dP / dh = rho.
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*
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* The implementation should return the same
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* value as the density from specific enthalpy relation.
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*/
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CHECK(
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(eos::partialDerivative<eos::quantity::Pressure, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{enthalpyFromDensity}
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)
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.value() == recoveredDensity)
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);
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/*
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* Since
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*
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* h = (n + 1) K rho^(1/n),
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*
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* it follows that
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*
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* dP / d rho = h / n.
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*/
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CHECK_THAT(
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(eos::partialDerivative<eos::quantity::Pressure, eos::quantity::Density>(
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barotrope, eos::DensityValue{density}
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)
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.value()),
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Catch::Matchers::WithinRel(enthalpyFromDensity / polytropicIndex, 5.0e-13)
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);
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}
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}
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}
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}
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TEST_CASE(
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"Polytropic EOS Pressure Derivatives Match Centered Differences",
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tags::barotrope_eos_jacobian
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) {
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constexpr std::array<double, 3> polytropicIndices{1.0, 1.5, 3.0};
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constexpr std::array<double, 3> positiveValues{0.2, 0.73, 1.8};
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constexpr double polytropicConstant = 0.61;
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for (const double polytropicIndex : polytropicIndices) {
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const mean_field::eos::Polytrope barotrope(polytropicIndex, polytropicConstant);
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DYNAMIC_SECTION("polytropic index n = " << polytropicIndex) {
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for (const double enthalpy : positiveValues) {
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const double step = 2.0e-6 * std::max(1.0, std::abs(enthalpy));
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const double numericalDerivative = polytropic_eos_test_utils::centered_derivative(
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[&barotrope](const double perturbedEnthalpy) {
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return eos::evaluate<eos::quantity::Pressure>(
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barotrope, eos::SpecificEnthalpyValue{perturbedEnthalpy}
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)
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.value();
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},
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enthalpy, step
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);
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const double analyticDerivative =
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eos::partialDerivative<eos::quantity::Pressure, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{enthalpy}
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)
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.value();
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CAPTURE(polytropicIndex, enthalpy, step, numericalDerivative, analyticDerivative);
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CHECK_THAT(numericalDerivative, Catch::Matchers::WithinRel(analyticDerivative, 5.0e-8));
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}
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for (const double density : positiveValues) {
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const double step = 2.0e-6 * std::max(1.0, std::abs(density));
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const double numericalDerivative = polytropic_eos_test_utils::centered_derivative(
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[&barotrope](const double perturbedDensity) {
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return eos::evaluate<eos::quantity::Pressure>(barotrope, eos::DensityValue{perturbedDensity})
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.value();
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},
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density, step
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);
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const double analyticDerivative =
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eos::partialDerivative<eos::quantity::Pressure, eos::quantity::Density>(
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barotrope, eos::DensityValue{density}
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)
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.value();
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CAPTURE(polytropicIndex, density, step, numericalDerivative, analyticDerivative);
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CHECK_THAT(numericalDerivative, Catch::Matchers::WithinRel(analyticDerivative, 5.0e-8));
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}
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}
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}
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}
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TEST_CASE(
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"Polytropic EOS Density Derivative Matches Centered Differences",
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tags::barotrope_eos_jacobian
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) {
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constexpr std::array<double, 3> polytropicIndices{1.0, 1.5, 3.0};
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constexpr std::array<double, 3> enthalpies{0.2, 0.73, 1.8};
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constexpr double polytropicConstant = 0.61;
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for (const double polytropicIndex : polytropicIndices) {
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const mean_field::eos::Polytrope barotrope(polytropicIndex, polytropicConstant);
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DYNAMIC_SECTION("polytropic index n = " << polytropicIndex) {
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for (const double enthalpy : enthalpies) {
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const double step = 2.0e-6 * std::max(1.0, std::abs(enthalpy));
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const double numericalDerivative = polytropic_eos_test_utils::centered_derivative(
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[&barotrope](const double perturbedEnthalpy) {
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return eos::evaluate<eos::quantity::Density>(
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barotrope, eos::SpecificEnthalpyValue{perturbedEnthalpy}
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)
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.value();
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},
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enthalpy, step
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);
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const double analyticDerivative =
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eos::partialDerivative<eos::quantity::Density, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{enthalpy}
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)
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.value();
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CAPTURE(polytropicIndex, enthalpy, step, numericalDerivative, analyticDerivative);
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CHECK_THAT(numericalDerivative, Catch::Matchers::WithinRel(analyticDerivative, 5.0e-8));
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}
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}
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}
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}
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TEST_CASE(
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"Polytropic EOS Defines Consistent Surface And Exterior Behavior",
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tags::barotrope_eos_unit
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) {
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constexpr std::array<double, 3> polytropicIndices{1.0, 1.5, 3.0};
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constexpr double polytropicConstant = 0.47;
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constexpr double exteriorEnthalpy = -0.3;
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for (const double polytropicIndex : polytropicIndices) {
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const mean_field::eos::Polytrope barotrope(polytropicIndex, polytropicConstant);
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DYNAMIC_SECTION("polytropic index n = " << polytropicIndex) {
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/*
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* Exact surface values.
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*/
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CHECK(eos::evaluate<eos::quantity::Density>(barotrope, eos::SpecificEnthalpyValue{0.0}).value() == 0.0);
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CHECK(eos::evaluate<eos::quantity::Pressure>(barotrope, eos::SpecificEnthalpyValue{0.0}).value() == 0.0);
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CHECK(
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(eos::partialDerivative<eos::quantity::Pressure, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{0.0}
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)
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.value() == 0.0)
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);
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CHECK(eos::evaluate<eos::quantity::Pressure>(barotrope, eos::DensityValue{0.0}).value() == 0.0);
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CHECK(eos::evaluate<eos::quantity::SpecificEnthalpy>(barotrope, eos::DensityValue{0.0}).value() == 0.0);
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CHECK(
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(eos::partialDerivative<eos::quantity::Pressure, eos::quantity::Density>(
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barotrope, eos::DensityValue{0.0}
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)
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.value() == 0.0)
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);
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/*
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* Positive-part extension into h < 0.
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*/
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CHECK(
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eos::evaluate<eos::quantity::Density>(barotrope, eos::SpecificEnthalpyValue{exteriorEnthalpy})
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.value() == 0.0
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);
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CHECK(
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eos::evaluate<eos::quantity::Pressure>(barotrope, eos::SpecificEnthalpyValue{exteriorEnthalpy})
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.value() == 0.0
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);
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CHECK(
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(eos::partialDerivative<eos::quantity::Density, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{exteriorEnthalpy}
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)
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.value() == 0.0)
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);
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CHECK(
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(eos::partialDerivative<eos::quantity::Pressure, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{exteriorEnthalpy}
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)
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.value() == 0.0)
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);
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/*
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* At h = 0, rho(h) has a nonzero right
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* derivative only for n = 1.
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*/
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const double expectedSurfaceDensityDerivative =
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polytropicIndex == 1.0 ? 1.0 / barotrope.enthalpy_scale() : 0.0;
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CHECK(
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(eos::partialDerivative<eos::quantity::Density, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{0.0}
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)
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.value() == expectedSurfaceDensityDerivative)
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);
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}
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}
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}
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TEST_CASE(
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"Polytropic EOS Rejects Invalid Physical Inputs",
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tags::barotrope_eos_unit
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) {
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CHECK_THROWS_AS(mean_field::eos::Polytrope(0.999, 1.0), std::invalid_argument);
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CHECK_THROWS_AS(mean_field::eos::Polytrope(std::numeric_limits<double>::infinity(), 1.0), std::invalid_argument);
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CHECK_THROWS_AS(mean_field::eos::Polytrope(3.0, 0.0), std::invalid_argument);
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CHECK_THROWS_AS(mean_field::eos::Polytrope(3.0, -1.0), std::invalid_argument);
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const mean_field::eos::Polytrope barotrope(3.0, 0.75);
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CHECK_THROWS_AS(eos::evaluate<eos::quantity::Pressure>(barotrope, eos::DensityValue{-0.1}), std::domain_error);
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CHECK_THROWS_AS(
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eos::evaluate<eos::quantity::SpecificEnthalpy>(barotrope, eos::DensityValue{-0.1}), std::domain_error
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);
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CHECK_THROWS_AS(
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(eos::partialDerivative<eos::quantity::Pressure, eos::quantity::Density>(barotrope, eos::DensityValue{-0.1})),
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std::domain_error
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);
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constexpr std::array<double, 3> nonfiniteValues{
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std::numeric_limits<double>::infinity(), -std::numeric_limits<double>::infinity(),
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std::numeric_limits<double>::quiet_NaN()
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};
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for (const double nonfiniteValue : nonfiniteValues) {
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CAPTURE(nonfiniteValue);
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CHECK_THROWS_AS(
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eos::evaluate<eos::quantity::Density>(barotrope, eos::SpecificEnthalpyValue{nonfiniteValue}),
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std::domain_error
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);
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CHECK_THROWS_AS(
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eos::evaluate<eos::quantity::Pressure>(barotrope, eos::SpecificEnthalpyValue{nonfiniteValue}),
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std::domain_error
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);
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CHECK_THROWS_AS(
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(eos::partialDerivative<eos::quantity::Density, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{nonfiniteValue}
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)),
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std::domain_error
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);
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CHECK_THROWS_AS(
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(eos::partialDerivative<eos::quantity::Pressure, eos::quantity::SpecificEnthalpy>(
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barotrope, eos::SpecificEnthalpyValue{nonfiniteValue}
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)),
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std::domain_error
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);
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}
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}
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TEST_CASE(
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"Pressure Force And Pressure Integral Have Distinct Registered Forms",
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tags::barotrope_pressure_quadrature_unit
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) {
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using EnthalpyField = mean_field::field::Field<mean_field::field::Enthalpy>;
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/*
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* For the registered H1 order p = 3 and n = 3:
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*
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* h has degree p,
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* P(h) has degree 4p,
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*
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* so the nonlinear EOS contributes an additional
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*
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* 4p - p = 3p = 9
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*
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* beyond the registered enthalpy operand.
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*/
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constexpr int enthalpyOrder = mean_field::field::Enthalpy::Scalar::familyOrder;
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constexpr int pressureExtraOrder = 3 * enthalpyOrder;
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constexpr int geometryWeightOrder = 2;
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constexpr mean_field::quadrature::Query pressureIntegralQuery =
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EnthalpyField::make_query<mean_field::field::Enthalpy::Form::PressureIntegral>(
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mean_field::quadrature::QuadratureRole::diagnostic, geometryWeightOrder,
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std::array<int, 1>{pressureExtraOrder}, mean_field::utils::DOMAINS::STELLAR,
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mean_field::quadrature::MappingKind::general
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);
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constexpr mean_field::quadrature::Query pressureForceQuery =
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EnthalpyField::make_query<mean_field::field::Enthalpy::Form::PressureForce>(
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mean_field::quadrature::QuadratureRole::discretization, geometryWeightOrder,
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std::array<int, 1>{pressureExtraOrder}, mean_field::utils::DOMAINS::STELLAR,
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mean_field::quadrature::MappingKind::general
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);
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STATIC_CHECK(mean_field::field::Enthalpy::Form::PressureIntegral::dynamicOrderCount == 1);
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STATIC_CHECK(mean_field::field::Enthalpy::Form::PressureForce::dynamicOrderCount == 1);
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STATIC_CHECK(
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mean_field::field::Enthalpy::Form::PressureIntegral::policyKey !=
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mean_field::field::Enthalpy::Form::PressureForce::policyKey
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);
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REQUIRE(pressureIntegralQuery.base_order.has_value());
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REQUIRE(pressureForceQuery.base_order.has_value());
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/*
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* Pressure integral:
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*
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* degree(P) + degree(J)
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* = 12 + 2
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* = 14.
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*/
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CHECK(*pressureIntegralQuery.base_order == 14);
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/*
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* Pressure force:
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*
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* degree(P)
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* + degree(grad w)
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* + degree(J)
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*
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* = 12 + 2 + 2
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* = 16.
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*/
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CHECK(*pressureForceQuery.base_order == 16);
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CHECK(pressureIntegralQuery.term == mean_field::quadrature::Term::pressure_integral);
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CHECK(pressureForceQuery.term == mean_field::quadrature::Term::pressure_force);
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CHECK(pressureIntegralQuery.role == mean_field::quadrature::QuadratureRole::diagnostic);
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CHECK(pressureForceQuery.role == mean_field::quadrature::QuadratureRole::discretization);
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CHECK(pressureIntegralQuery.domain == mean_field::utils::DOMAINS::STELLAR);
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CHECK(pressureForceQuery.domain == mean_field::utils::DOMAINS::STELLAR);
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/*
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* Verify that the two terms route to independent policy
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* controls.
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*/
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mean_field::quadrature::RuleSet ruleSet =
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mean_field::quadrature::make_rule_set(mean_field::quadrature::Mode::production);
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ruleSet.pressure_integral.boost = 3;
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ruleSet.pressure_force.boost = 5;
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const mean_field::quadrature::Policy policy(std::move(ruleSet));
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const mean_field::quadrature::Resolution pressureIntegralResolution = policy.resolve(pressureIntegralQuery);
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const mean_field::quadrature::Resolution pressureForceResolution = policy.resolve(pressureForceQuery);
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CHECK(pressureIntegralResolution.base_order == 14);
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CHECK(pressureIntegralResolution.boost == 3);
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CHECK(pressureIntegralResolution.order == 17);
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|
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|
CHECK(pressureForceResolution.base_order == 16);
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|
|
|
CHECK(pressureForceResolution.boost == 5);
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|
|
|
CHECK(pressureForceResolution.order == 21);
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|
}
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|
|
|
TEST_CASE(
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|
"Pressure Quadrature Exactly Integrates An N Three Polynomial",
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|
tags::barotrope_pressure_quadrature_accuracy
|
|
) {
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|
using EnthalpyField = mean_field::field::Field<mean_field::field::Enthalpy>;
|
|
|
|
constexpr int enthalpyOrder = mean_field::field::Enthalpy::Scalar::familyOrder;
|
|
|
|
constexpr int pressureExtraOrder = 3 * enthalpyOrder;
|
|
|
|
/*
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|
* K = 1/4 and n = 3 give
|
|
*
|
|
* (n + 1) K = 1,
|
|
* rho(h) = h^3,
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|
* P(h) = h^4 / 4.
|
|
*/
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|
const mean_field::eos::Polytrope barotrope(3.0, 0.25);
|
|
|
|
constexpr mean_field::quadrature::Query pressureIntegralQuery =
|
|
EnthalpyField::make_query<mean_field::field::Enthalpy::Form::PressureIntegral>(
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|
mean_field::quadrature::QuadratureRole::diagnostic, 0, std::array<int, 1>{pressureExtraOrder},
|
|
mean_field::utils::DOMAINS::STELLAR, mean_field::quadrature::MappingKind::affine
|
|
);
|
|
|
|
constexpr mean_field::quadrature::Query pressureForceQuery =
|
|
EnthalpyField::make_query<mean_field::field::Enthalpy::Form::PressureForce>(
|
|
mean_field::quadrature::QuadratureRole::discretization, 0, std::array<int, 1>{pressureExtraOrder},
|
|
mean_field::utils::DOMAINS::STELLAR, mean_field::quadrature::MappingKind::affine
|
|
);
|
|
|
|
const mean_field::quadrature::RuleFactory ruleFactory{
|
|
mean_field::quadrature::Policy(mean_field::quadrature::make_rule_set(mean_field::quadrature::Mode::production))
|
|
};
|
|
|
|
const mean_field::quadrature::MfemRule pressureIntegralRule =
|
|
ruleFactory.get(pressureIntegralQuery, mfem::Geometry::CUBE);
|
|
|
|
const mean_field::quadrature::MfemRule pressureForceRule =
|
|
ruleFactory.get(pressureForceQuery, mfem::Geometry::CUBE);
|
|
|
|
/*
|
|
* On the reference cube [0,1]^3 choose
|
|
*
|
|
* h = x^3 y^3 z^3.
|
|
*
|
|
* This is representable by the order-three H1 space.
|
|
* Then
|
|
*
|
|
* P = x^12 y^12 z^12 / 4.
|
|
*/
|
|
const double numericalPressureIntegral = polytropic_eos_test_utils::integrate_cube(
|
|
*pressureIntegralRule.integration_rule, [&barotrope](const mfem::IntegrationPoint &integrationPoint) {
|
|
const double coordinateProduct = integrationPoint.x * integrationPoint.y * integrationPoint.z;
|
|
|
|
const double enthalpy = std::pow(coordinateProduct, 3.0);
|
|
|
|
return eos::evaluate<eos::quantity::Pressure>(barotrope, eos::SpecificEnthalpyValue{enthalpy}).value();
|
|
}
|
|
);
|
|
|
|
const double analyticPressureIntegral = 0.25 / std::pow(13.0, 3.0);
|
|
|
|
/*
|
|
* Choose a representable vector test function whose
|
|
* divergence is
|
|
*
|
|
* div(w) = x^2 y^2 z^2.
|
|
*
|
|
* Therefore
|
|
*
|
|
* -P div(w)
|
|
* = -x^14 y^14 z^14 / 4.
|
|
*/
|
|
const double numericalPressureForceIntegral = polytropic_eos_test_utils::integrate_cube(
|
|
*pressureForceRule.integration_rule, [&barotrope](const mfem::IntegrationPoint &integrationPoint) {
|
|
const double coordinateProduct = integrationPoint.x * integrationPoint.y * integrationPoint.z;
|
|
|
|
const double enthalpy = std::pow(coordinateProduct, 3.0);
|
|
|
|
const double pressure =
|
|
eos::evaluate<eos::quantity::Pressure>(barotrope, eos::SpecificEnthalpyValue{enthalpy}).value();
|
|
|
|
const double testDivergence = integrationPoint.x * integrationPoint.x * integrationPoint.y *
|
|
integrationPoint.y * integrationPoint.z * integrationPoint.z;
|
|
|
|
return -pressure * testDivergence;
|
|
}
|
|
);
|
|
|
|
const double analyticPressureForceIntegral = -0.25 / std::pow(15.0, 3.0);
|
|
|
|
INFO("Pressure-integral quadrature order = " << pressureIntegralRule.resolution.order);
|
|
|
|
INFO("Pressure-force quadrature order = " << pressureForceRule.resolution.order);
|
|
|
|
INFO("Numerical pressure integral = " << numericalPressureIntegral);
|
|
|
|
INFO("Analytic pressure integral = " << analyticPressureIntegral);
|
|
|
|
INFO("Numerical pressure-force integral = " << numericalPressureForceIntegral);
|
|
|
|
INFO("Analytic pressure-force integral = " << analyticPressureForceIntegral);
|
|
|
|
CHECK(pressureIntegralRule.resolution.base_order == 12);
|
|
|
|
CHECK(pressureIntegralRule.resolution.order == 12);
|
|
|
|
CHECK(pressureForceRule.resolution.base_order == 14);
|
|
|
|
CHECK(pressureForceRule.resolution.order == 14);
|
|
|
|
CHECK_THAT(numericalPressureIntegral, Catch::Matchers::WithinAbs(analyticPressureIntegral, 5.0e-14));
|
|
|
|
CHECK_THAT(numericalPressureForceIntegral, Catch::Matchers::WithinAbs(analyticPressureForceIntegral, 5.0e-14));
|
|
}
|