Emily Boudreaux
cb20faeb3d
The test suite is extensive. Note that LLMs were used to aid in the development of the test suite. All LLM generated code was manually reviewed.
144 lines
9.5 KiB
C++
144 lines
9.5 KiB
C++
#include <cmath>
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#include <catch2/catch_test_macros.hpp>
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#include "serif/equations/barotropic_density.hpp"
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#include "serif/tests/equations/barotropic_eos.hpp"
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#include "serif/tests/equations/gravity_fixture.hpp"
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namespace {
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using Balance = serif::equations::BarotropicDensityBalance<serif::tests::equations::MixedPowerBarotrope>;
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}
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TEST_CASE("Barotropic density assembles a nonpolytropic value balance and complete ALE tangent", "[equations][barotropic_density][unit]") {
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using namespace serif::tests::equations;
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for (const auto geometry : {::mfem::Element::HEXAHEDRON, ::mfem::Element::TETRAHEDRON}) {
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gravity::GravityFixture fixture(geometry);
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auto density = fixture.density(), potential = fixture.potential();
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auto surface_level = constant(1, -0.8), omega = constant(1, 0.2), displacement = fixture.displacement(0.3);
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/** @brief Bind exactly the four physical inputs; the EOS supplies every thermodynamic value. */
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const auto fields = [&](const auto& rho, const auto& phi, const auto& level, const auto& rotation) {
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return backend::make_term_coefficients(backend::bind(fixture.density_binding, rho),
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backend::bind(fixture.potential_binding, phi), backend::bind(fixture.constant_binding, level),
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backend::bind(fixture.angular_velocity_binding, rotation));
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};
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const Balance balance{MixedPowerBarotrope{.gauge = 7.5}, serif::dimensions::PressureValue{0.3125},
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{1.0, 2.0, 3.0}, {0.2, -0.1, 0.3}};
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VolumeEquationFixture equation{balance, fixture.density_binding, fixture.displacement_binding,
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fixture.compactification, fixture.mapper, gravity::reference_policy()};
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equation.prepare(fields(density, potential, surface_level, omega), constant(displacement.Size(), 0.0), fixture.workspace);
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::mfem::Vector residual;
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equation.residual(fixture.workspace, residual);
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/** @brief Integrate the analytic physical residual independently of the equation's evaluator. */
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::mfem::FunctionCoefficient expected_balance([](const ::mfem::Vector& position) {
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const double rho = 0.55 + 0.025 * position[0] - 0.010 * position[1] + 0.006 * position[2];
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const double phi = -0.5 + 0.1 * position[0] * position[1] - 0.07 * position[2] * position[2];
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const double x = position[0] - 0.2, y = position[1] + 0.1, z = position[2] - 0.3;
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const double axial_projection = x + 2.0 * y + 3.0 * z;
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const double centrifugal = 0.5 * (x * x + y * y + z * z - axial_projection * axial_projection / 14.0);
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// P_surface = 5/16 fixes rho_surface = 1/2 and A_surface - gauge = 7/6.
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return 2.0 * rho + (4.0 / 3.0) * rho * rho * rho - 7.0 / 6.0 + phi - 0.04 * centrifugal + 0.8;
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});
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::mfem::LinearForm reference(&fixture.density_space);
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::mfem::Array<int> stellar{1, 1, 0};
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const auto& rule = ::mfem::IntRules.Get(fixture.mesh.GetElementBaseGeometry(0), gravity::reference_order);
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auto* integrator = new ::mfem::DomainLFIntegrator(expected_balance);
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integrator->SetIntRule(&rule);
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reference.AddDomainIntegrator(integrator, stellar);
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reference.Assemble();
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CHECK(relative_error(residual, fixture.density_binding.gather(reference)) < 3.0e-12);
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const auto density_direction = deterministic(density.Size(), 0.1), potential_direction = deterministic(potential.Size(), 0.3);
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const auto level_direction = constant(1, -0.05), omega_direction = constant(1, 0.07), displacement_direction = fixture.displacement(0.2);
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equation.prepare(fields(density, potential, surface_level, omega), displacement, fixture.workspace);
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::mfem::Vector action, transpose;
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equation.apply_jacobian(fields(density_direction, potential_direction, level_direction, omega_direction),
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displacement_direction, fixture.workspace, action);
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const auto dual = deterministic(residual.Size(), 0.7);
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equation.apply_jacobian_transpose(dual, fixture.workspace, transpose);
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const auto direction = packed(packed(density_direction, potential_direction, level_direction), omega_direction, displacement_direction);
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CHECK(std::abs(dual * action - direction * transpose) < 4.0e-11);
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constexpr double step = 1.0e-6;
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auto plus_density = density, minus_density = density, plus_potential = potential, minus_potential = potential;
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auto plus_level = surface_level, minus_level = surface_level, plus_omega = omega, minus_omega = omega;
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auto plus_displacement = displacement, minus_displacement = displacement;
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plus_density.Add(step, density_direction);
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minus_density.Add(-step, density_direction);
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plus_potential.Add(step, potential_direction);
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minus_potential.Add(-step, potential_direction);
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plus_level.Add(step, level_direction);
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minus_level.Add(-step, level_direction);
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plus_omega.Add(step, omega_direction);
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minus_omega.Add(-step, omega_direction);
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plus_displacement.Add(step, displacement_direction);
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minus_displacement.Add(-step, displacement_direction);
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::mfem::Vector positive, negative;
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equation.prepare(fields(plus_density, plus_potential, plus_level, plus_omega), plus_displacement, fixture.workspace);
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equation.residual(fixture.workspace, positive);
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equation.prepare(fields(minus_density, minus_potential, minus_level, minus_omega), minus_displacement, fixture.workspace);
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equation.residual(fixture.workspace, negative);
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positive -= negative;
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positive /= 2.0 * step;
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CHECK(relative_error(action, positive) < 4.0e-8);
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}
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}
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TEST_CASE("Reconstructed density retains the field and geometry Jacobian including its transpose", "[equations][unit][reconstruction]") {
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using namespace serif::tests::equations;
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namespace reconstruction = serif::discretization::reconstruction;
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namespace discretization_backend = serif::discretization::backend::mfem;
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using Density = blocks::density::mass;
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using PolytropicBalance = serif::equations::BarotropicDensityBalance<serif::eos::models::Polytrope>;
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gravity::GravityFixture fixture(::mfem::Mesh::MakeCartesian3D(2, 1, 1, ::mfem::Element::HEXAHEDRON));
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const double exponent = 5.0 / 3.0;
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const auto reconstruction_plan = discretization_backend::make_reconstruction(
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reconstruction::SurfacePower<Density>{.density_exponent = exponent}, fixture.density_binding);
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discretization_backend::TermBinding<Density, Schema> density_binding(fixture.density_space, reconstruction_plan);
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auto density = fixture.project(density_binding, [exponent](const ::mfem::Vector& point) {
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return std::pow(point[2], exponent) * (1.0 + 0.1 * point[0]);
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});
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const auto density_direction = fixture.project(density_binding, [exponent](const ::mfem::Vector& point) {
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return 0.1 * std::pow(point[2], exponent) * (point[0] - 0.3 * point[1]);
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});
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const auto potential = fixture.potential(), level = constant(1, -0.8), omega = constant(1, 0.2);
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const auto displacement = fixture.displacement(0.3), displacement_direction = fixture.displacement(0.2);
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const auto fields = [&](const auto& rho) {
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return backend::make_term_coefficients(backend::bind(density_binding, rho),
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backend::bind(fixture.potential_binding, potential), backend::bind(fixture.constant_binding, level),
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backend::bind(fixture.angular_velocity_binding, omega));
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};
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VolumeEquationFixture equation{PolytropicBalance{serif::eos::models::Polytrope{exponent, 0.7}, serif::dimensions::PressureValue{0.0}},
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density_binding, fixture.displacement_binding, fixture.compactification, fixture.mapper, gravity::reference_policy()};
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equation.prepare(fields(density), displacement, fixture.workspace);
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CHECK(equation.integration_order(0) == ::mfem::IntRules.Get(::mfem::Geometry::CUBE, gravity::reference_order).GetOrder());
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::mfem::Vector action, transpose;
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const auto potential_direction = constant(potential.Size(), 0.0), level_direction = constant(1, 0.0), omega_direction = constant(1, 0.0);
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equation.apply_jacobian(backend::make_term_coefficients(backend::bind(density_binding, density_direction),
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backend::bind(fixture.potential_binding, potential_direction), backend::bind(fixture.constant_binding, level_direction),
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backend::bind(fixture.angular_velocity_binding, omega_direction)), displacement_direction, fixture.workspace, action);
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const auto dual = deterministic(density_binding.size(), 0.7);
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equation.apply_jacobian_transpose(dual, fixture.workspace, transpose);
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const auto direction = packed(packed(density_direction, potential_direction, level_direction), omega_direction, displacement_direction);
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CHECK(std::abs(dual * action - direction * transpose) < 4e-11);
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for (const double step : {1e-5, 1e-6}) {
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auto plus_density = density, minus_density = density;
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auto plus_displacement = displacement, minus_displacement = displacement;
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plus_density.Add(step, density_direction);
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minus_density.Add(-step, density_direction);
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plus_displacement.Add(step, displacement_direction);
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minus_displacement.Add(-step, displacement_direction);
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::mfem::Vector plus, minus;
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equation.prepare(fields(plus_density), plus_displacement, fixture.workspace);
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equation.residual(fixture.workspace, plus);
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equation.prepare(fields(minus_density), minus_displacement, fixture.workspace);
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equation.residual(fixture.workspace, minus);
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plus -= minus;
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plus /= 2.0 * step;
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CHECK(relative_error(action, plus) < 4e-8);
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}
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}
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