meson-mfem/src/lib/serif/eos/models/polytropic.cpp

#include "serif/eos/models/polytropic.hpp"
#include "serif/utils/misc/finite.hpp"
#include "serif/eos/exceptions.hpp"

namespace serif::eos::models {
    using utils::misc::validate_finite;
    using utils::misc::validate_greater_than;
    using utils::misc::validate_less_than;
    using utils::misc::validate_nonnegativity;

    using namespace dimensions;
    using namespace relations;

    Polytrope::Polytrope(const PolytropeParameters& parameters) : Polytrope(parameters.n, parameters.K) {}

    Polytrope::Polytrope(const double n, const double K):
    m_polytropic_index(n),
    m_polytropic_constant(K),
    m_enthalpy_scale((n + 1.0) * K) {
        validate_finite<EOSEvaluationError>(m_polytropic_index, EOSEvaluationErrorCode::outside_domain);
        validate_greater_than<EOSEvaluationError>(m_polytropic_index, 1.0, EOSEvaluationErrorCode::outside_domain);
        validate_finite<EOSEvaluationError>(m_polytropic_constant, EOSEvaluationErrorCode::outside_domain);
        validate_greater_than<EOSEvaluationError>(m_polytropic_constant, 0.0, EOSEvaluationErrorCode::outside_domain);
    }

    [[nodiscard]] double Polytrope::polytropic_index() const noexcept {
        return m_polytropic_index;
    }

    [[nodiscard]] double Polytrope::polytropic_constant() const noexcept {
        return m_polytropic_constant;
    }

    [[nodiscard]] double Polytrope::enthalpy_scale() const noexcept {
        return m_enthalpy_scale;
    }

    [[nodiscard]] PressureValue Polytrope::evaluate(PressureFromDensity, const DensityValue density) const {
        validate_nonnegativity<EOSEvaluationError>(density.value(), EOSEvaluationErrorCode::invalid_thermodynamic_input);

        if (density.value() == 0.0) {
            // P = 0
            return PressureValue{0.0};
        }

        // P = K * (ρ)^(1 + 1/n)
        return PressureValue{
            m_polytropic_constant * std::pow(density.value(), 1.0 + 1.0 / m_polytropic_index)
        };
    }

    [[nodiscard]] SpecificEnthalpyValue Polytrope::evaluate(SpecificEnthalpyFromDensity, const DensityValue density) const {
        validate_nonnegativity<EOSEvaluationError>(density.value(), EOSEvaluationErrorCode::invalid_thermodynamic_input);
        if (density.value() == 0.0) {
            // h = 0
            return SpecificEnthalpyValue{0.0};
        }

        // h = hs * (ρ)^(1/n)
        return SpecificEnthalpyValue{
            m_enthalpy_scale * std::pow(density.value(), 1.0 / m_polytropic_index)
        };
    }

    [[nodiscard]] DensityValue Polytrope::evaluate(DensityFromSpecificEnthalpy, SpecificEnthalpyValue specific_enthalpy) const {
        validate_finite<EOSEvaluationError>(specific_enthalpy.value(), EOSEvaluationErrorCode::invalid_thermodynamic_input);

        if (specific_enthalpy.value() <= 0.0) {
            // ρ = 0
            return DensityValue{0.0};
        }

        // ρ = (h/hs)^n
        return DensityValue{std::pow(specific_enthalpy.value() / m_enthalpy_scale, m_polytropic_index)};
    }

    [[nodiscard]] PressureValue Polytrope::evaluate(PressureFromSpecificEnthalpy, SpecificEnthalpyValue specific_enthalpy) const {
        const DensityValue density = evaluate(DensityFromSpecificEnthalpy{}, specific_enthalpy);
        if (specific_enthalpy.value() <= 0.0) {
            // P = 0
            return PressureValue{0.0};
        }

        // P = ρ * h / (n + 1)
        return PressureValue{density.value() * specific_enthalpy.value()/ (m_polytropic_index + 1.0)};
    }

    [[nodiscard]] SpecificEnthalpyValue Polytrope::evaluate(SpecificEnthalpyFromPressure, PressureValue pressure) const {
        validate_nonnegativity<EOSEvaluationError>(pressure.value(), EOSEvaluationErrorCode::invalid_thermodynamic_input);
        if (pressure.value() == 0.0) {
            // h = 0
            return SpecificEnthalpyValue{0.0};
        }

        const double indexPlusOne = m_polytropic_index + 1.0;

        // h = (n+1) * (K^(n/(n+1))) * (P^(1/(n+1)))
        return SpecificEnthalpyValue{
            indexPlusOne * std::pow(m_polytropic_constant, m_polytropic_index / indexPlusOne) *
            std::pow(pressure.value(), 1.0 / indexPlusOne)
        };
    }

    [[nodiscard]] PartialDerivative<Density, SpecificEnthalpy> Polytrope::partial_derivative(DensityFromSpecificEnthalpy, WithRespectTo<SpecificEnthalpy>, const SpecificEnthalpyValue specific_enthalpy) const {
        validate_finite<EOSEvaluationError>(specific_enthalpy.value(), EOSEvaluationErrorCode::invalid_thermodynamic_input);

        if (specific_enthalpy.value() < 0.0) {
            // dρ/dh = 0
            return PartialDerivative<Density, SpecificEnthalpy>{0.0};
        }

        if (specific_enthalpy.value() == 0.0) {
            // dρ/dh = n == 1 -> 1/hs
            // dρ/dh = else   -> 0
            return PartialDerivative<Density, SpecificEnthalpy>{
                m_polytropic_index == 1.0 ? 1.0 / m_enthalpy_scale : 0.0
            };
        }

        // dρ/dh = (n/hs) * (h/hs)^(n-1)
        return PartialDerivative<Density, SpecificEnthalpy>{
            m_polytropic_index / m_enthalpy_scale * std::pow(specific_enthalpy.value() / m_enthalpy_scale, m_polytropic_index - 1.0)
        };
    }

    [[nodiscard]] PartialDerivative<Pressure, SpecificEnthalpy> Polytrope::partial_derivative(PressureFromSpecificEnthalpy, WithRespectTo<SpecificEnthalpy>, const SpecificEnthalpyValue specific_enthalpy) const {
        const DensityValue density = evaluate(DensityFromSpecificEnthalpy{}, specific_enthalpy);

        // dP/dh = ρ
        return PartialDerivative<Pressure, SpecificEnthalpy>{density.value()};
    }

    [[nodiscard]] PartialDerivative<Pressure, Density> Polytrope::partial_derivative(PressureFromDensity, WithRespectTo<Density>, const DensityValue density) const {
        validate_nonnegativity<EOSEvaluationError>(density.value(), EOSEvaluationErrorCode::invalid_thermodynamic_input);

        if (density.value() == 0.0) {
            // dP/dρ = 0
            return PartialDerivative<Pressure, Density>{0.0};
        }

        // dP/dρ = K * (1 + 1/n) * (ρ)^(1/n)
        return PartialDerivative<Pressure, Density>{
            m_polytropic_constant * (1.0 + 1.0 / m_polytropic_index) * std::pow(density.value(), 1.0 / m_polytropic_index)
        };
    }
}