test(tests): added test suite

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.

tests/sandbox/equations_sandbox.cpp

@@ -0,0 +1,48 @@
+#include <cmath>
+#include <print>
+
+#include "serif/eos/evaluation.hpp"
+#include "serif/eos/models/polytropic.hpp"
+#include "serif/equations/barotropic_density.hpp"
+#include "serif/equations/surface_potential.hpp"
+
+/** @brief Evaluate manufactured interior and surface samples and inspect their exact derivatives. */
+int main() {
+    namespace equations = serif::equations;
+    namespace dimensions = serif::dimensions;
+
+    const serif::eos::models::Polytrope eos{1.0, 0.8};
+    const double density = 0.5, angular_velocity = 0.3, surface_level = 1.2;
+    const dimensions::PressureValue surface_pressure{0.0};
+    const equations::BarotropicDensityBalance density_balance{eos, surface_pressure};
+    const equations::SurfacePotentialBalance surface;
+    using Balance = decltype(density_balance);
+
+    // Density supplies the pressure potential through the EOS; it is not another solved field.
+    const auto surface_density = serif::eos::evaluate<dimensions::MassDensity>(eos, surface_pressure);
+    const double pressure_potential = serif::eos::evaluate<dimensions::BarotropicPressurePotential>(eos, dimensions::DensityValue{density}).value();
+    const double surface_pressure_potential = serif::eos::evaluate<dimensions::BarotropicPressurePotential>(eos, surface_density).value();
+    equations::EquationPoint<Balance::Operands> mechanics;
+    mechanics.position = {0.3, 0.4, 0.0};
+    mechanics.fields.get<Balance::Density>() = density;
+    mechanics.fields.get<Balance::AngularVelocity>() = angular_velocity;
+    mechanics.fields.get<Balance::SurfaceLevel>() = surface_level;
+    mechanics.fields.get<Balance::Potential>() = surface_level - pressure_potential + surface_pressure_potential +
+        angular_velocity * angular_velocity * density_balance.rotation().centrifugal_potential(mechanics.position);
+    const auto interior_balance = density_balance.evaluate(mechanics);
+
+    equations::EquationPoint<decltype(surface)::Operands> boundary;
+    boundary.position = mechanics.position;
+    boundary.fields.get<decltype(surface)::Potential>() = surface_level +
+        angular_velocity * angular_velocity * surface.rotation().centrifugal_potential(boundary.position);
+    boundary.fields.get<decltype(surface)::SurfaceLevel>() = surface_level;
+    boundary.fields.get<decltype(surface)::AngularVelocity>() = angular_velocity;
+    const auto surface_balance = surface.evaluate(boundary);
+
+    std::println("Density balance residual = {:.3e}; angular-velocity derivative = {}",
+        interior_balance.residual, interior_balance.field_derivatives.get<Balance::AngularVelocity>());
+    std::println("Surface potential residual = {:.3e}; derivative with respect to surface level = {}",
+        surface_balance.residual, surface_balance.field_derivatives.get<decltype(surface)::SurfaceLevel>());
+    // complete_sandbox assembles these same physical equations on its finite-element mesh.
+    return std::abs(interior_balance.residual) < 1.0e-12 && std::abs(surface_balance.residual) < 1.0e-12 ? 0 : 1;
+}