ns-solutions.hpp

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#ifndef NS_SOLUTIONS_HPP
#define NS_SOLUTIONS_HPP
 
#include <Eigen/Dense>
 
#include "MeshBuilder2D.hpp"
 
namespace HArDCore2D
{
  namespace NavierStokesSolutions
  {   
    //------------------------------------------------------------------------------
    // Interface for exact solutions
 
    struct IExactSolution {
      IExactSolution(std::string name, bool is_stokes, double viscosity);
      virtual ~IExactSolution();
      
      inline std::string name() const {
        return m_name;
      }
 
      inline bool isStokes() const {
        return m_is_stokes;
      }
 
      inline double viscosity() const {
        return m_viscosity;
      }
    
      virtual Eigen::Vector2d momentumForcingTerm(const Eigen::Vector2d & x, const double & t=0) const = 0;
      virtual double compressibilityForcingTerm(const Eigen::Vector2d & x, const double & t=0) const = 0;
      virtual Eigen::Vector2d velocity(const Eigen::Vector2d & x, const double & t=0) const = 0;
      virtual double pressure(const Eigen::Vector2d & x, const double & t=0) const = 0;
      virtual Eigen::Matrix2d velocityGradient(const Eigen::Vector2d & x, const double & t=0) const = 0;
      virtual Eigen::Vector2d pressureGradient(const Eigen::Vector2d & x, const double & t=0) const = 0;
 
    protected:
      std::string m_name;
      bool m_is_stokes;
      double m_viscosity;
    };
  
    //------------------------------------------------------------------------------
    // Linear
 
    struct Linear : public IExactSolution {
      Linear();
      
      Eigen::Vector2d momentumForcingTerm(const Eigen::Vector2d & x, const double & t = 0) const;
      double compressibilityForcingTerm(const Eigen::Vector2d & x, const double & t = 0) const;    
      Eigen::Vector2d velocity(const Eigen::Vector2d & x, const double & t = 0) const;   
      double pressure(const Eigen::Vector2d & x, const double & t = 0) const;
      Eigen::Matrix2d velocityGradient(const Eigen::Vector2d & x, const double & t = 0) const;    
      Eigen::Vector2d pressureGradient(const Eigen::Vector2d & x, const double & t = 0) const;
    };  
    
    //------------------------------------------------------------------------------
    // Linear temporal
 
    struct LinearTemporal : public IExactSolution {
      LinearTemporal();
      
      Eigen::Vector2d momentumForcingTerm(const Eigen::Vector2d & x, const double & t = 0) const;
      double compressibilityForcingTerm(const Eigen::Vector2d & x, const double & t = 0) const;    
      Eigen::Vector2d velocity(const Eigen::Vector2d & x, const double & t = 0) const;   
      double pressure(const Eigen::Vector2d & x, const double & t = 0) const;
      Eigen::Matrix2d velocityGradient(const Eigen::Vector2d & x, const double & t = 0) const;    
      Eigen::Vector2d pressureGradient(const Eigen::Vector2d & x, const double & t = 0) const;
    };
 
    //------------------------------------------------------------------------------
    // Trigonometric
 
    struct Trigonometric : public IExactSolution {
      Trigonometric();
    
      Eigen::Vector2d momentumForcingTerm(const Eigen::Vector2d & x, const double & t = 0) const;
      double compressibilityForcingTerm(const Eigen::Vector2d & x, const double & t = 0) const;    
      Eigen::Vector2d velocity(const Eigen::Vector2d & x, const double & t = 0) const;   
      double pressure(const Eigen::Vector2d & x, const double & t = 0) const;
      Eigen::Matrix2d velocityGradient(const Eigen::Vector2d & x, const double & t = 0) const;    
      Eigen::Vector2d pressureGradient(const Eigen::Vector2d & x, const double & t = 0) const;
    };    
 
    //------------------------------------------------------------------------------
    // Kovasznay
 
    struct Kovasznay : public IExactSolution {
      Kovasznay(const double & Re, std::ostream & output = std::cout);
 
      static inline Mesh2D::MeshBuilder::TransformationType domain_transformation = [](const std::array<double, 2> & x) {
        return std::array<double, 2>{2. * x[0] - 0.5, 2. * x[1]};
      };
    
      Eigen::Vector2d momentumForcingTerm(const Eigen::Vector2d & x, const double & t = 0) const;
      double compressibilityForcingTerm(const Eigen::Vector2d & x, const double & t = 0) const;
      Eigen::Vector2d velocity(const Eigen::Vector2d & x, const double & t = 0) const;   
      double pressure(const Eigen::Vector2d & x, const double & t = 0) const;
      Eigen::Matrix2d velocityGradient(const Eigen::Vector2d & x, const double & t = 0) const;    
      Eigen::Vector2d pressureGradient(const Eigen::Vector2d & x, const double & t = 0) const;
 
    private:
      double m_Re;
      double m_lambda;
    };
    
    //------------------------------------------------------------------------------
    // Kim and Moin
    
    struct KimMoin : public IExactSolution {
      KimMoin();
      
      Eigen::Vector2d momentumForcingTerm(const Eigen::Vector2d & x, const double & t) const;
      double compressibilityForcingTerm(const Eigen::Vector2d & x, const double & t) const;    
      Eigen::Vector2d velocity(const Eigen::Vector2d & x, const double & t) const;
      double pressure(const Eigen::Vector2d & x, const double & t) const;
      Eigen::Matrix2d velocityGradient(const Eigen::Vector2d & x, const double & t) const;   
      Eigen::Vector2d pressureGradient(const Eigen::Vector2d & x, const double & t) const;
    };
 
  } // namespace NavierStokesSolutions
 
} // namespace HArDCore2D
#endif