equation_of_state_van_der_waals.h

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//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// Copyright (C) 2023 - 2026 by the ryujin authors
//
 
#pragma once
 
#include <ryujin/base/compile_time_options.h>
#include <ryujin/euler_aeos/equation_of_state.h>
 
namespace ryujin
{
  namespace EquationsOfState
  {
    class VanDerWaals : public EquationOfState
    {
    public:
      using EquationOfState::pressure;
      using EquationOfState::specific_internal_energy;
      using EquationOfState::speed_of_sound;
      using EquationOfState::temperature;
 
      VanDerWaals(const std::string &subsection)
          : EquationOfState("van der waals", subsection)
      {
        gamma_ = 7. / 5.;
        this->add_parameter("gamma", gamma_, "The ratio of specific heats");
 
        a_ = 0.;
        this->add_parameter("vdw a", a_, "The vdw a constant");
 
        b_ = 0.;
        this->add_parameter(
            "covolume b", b_, "The maximum compressibility constant");
 
        /*
         * R is the specific gas constant with units [J / (Kg K)]. More details
         * can be found at:
         * https://en.wikipedia.org/wiki/Gas_constant#Specific_gas_constant
         */
        R_ = 0.4;
        this->add_parameter(
            "gas constant R", R_, "The specific gas constant R");
 
        cv_ = R_ / (gamma_ - 1.);
 
        /* Update the EOS interpolation parameters on parameter read in
         * and the specific heat at constant volume:
         */
        ParameterAcceptor::parse_parameters_call_back.connect([this] {
          this->covolume_constant_ = b_;
          cv_ = R_ / (gamma_ - 1.);
          /*
           * FIXME: The van der Waals EOS allows for negative pressures. We
           * should thus come up with a sensible way of setting
           * "interpolation_pinfty_"...
           */
        });
      }
 
      double pressure(double rho, double e) const final
      {
        const auto intermolecular = a_ * rho * rho;
        const auto numerator = rho * e + intermolecular;
        const auto covolume = 1. - b_ * rho;
        return (gamma_ - 1.) * numerator / covolume - intermolecular;
      }
 
      double specific_internal_energy(double rho, double p) const final
      {
        const auto intermolecular = a_ * rho * rho;
        const auto covolume = 1. - b_ * rho;
        const auto numerator = (p + intermolecular) * covolume;
        const auto denominator = rho * (gamma_ - 1.);
        return numerator / denominator - a_ * rho;
      }
 
      double temperature(double rho, double e) const final
      {
        return (e + a_ * rho) / cv_;
      }
 
      double cold_curve_bound(double rho) const final
      {
        return -a_ * rho;
      }
 
      double specific_entropy(double rho, double e) const final
      {
        const auto first_term = cv_ * std::log((e + a_ * rho) / cv_);
        const auto second_term = R_ * std::log(1. / rho - b_);
        return first_term + second_term;
      }
 
      double speed_of_sound(double rho, double e) const final
      {
        const auto covolume = 1. - b_ * rho;
        const auto numerator = gamma_ * (gamma_ - 1.) * (e + a_ * rho);
        return std::sqrt(numerator / (covolume * covolume) - 2. * a_ * rho);
      }
 
    private:
      double gamma_;
      double b_;
      double a_;
      double R_;
      double cv_;
    };
  } // namespace EquationsOfState
} // namespace ryujin