#include <RoeSolver.h>

Inheritance diagram for Nektar::RoeSolver:

Collaboration diagram for Nektar::RoeSolver:

Static Public Member Functions
static RiemannSolverSharedPtr	create ()

Static Public Attributes
static std::string	solverName

Protected Member Functions
	RoeSolver ()
virtual void	v_PointSolve (double rhoL, double rhouL, double rhovL, double rhowL, double EL, double rhoR, double rhouR, double rhovR, double rhowR, double ER, double &rhof, double &rhouf, double &rhovf, double &rhowf, double &Ef)
	Roe Riemann solver.
Protected Member Functions inherited from Nektar::CompressibleSolver
	CompressibleSolver ()
virtual void	v_Solve (const int nDim, const Array< OneD, const Array< OneD, NekDouble > > &Fwd, const Array< OneD, const Array< OneD, NekDouble > > &Bwd, Array< OneD, Array< OneD, NekDouble > > &flux)
virtual void	v_ArraySolve (const Array< OneD, const Array< OneD, NekDouble > > &Fwd, const Array< OneD, const Array< OneD, NekDouble > > &Bwd, Array< OneD, Array< OneD, NekDouble > > &flux)
virtual void	v_PointSolveVisc (NekDouble rhoL, NekDouble rhouL, NekDouble rhovL, NekDouble rhowL, NekDouble EL, NekDouble EpsL, NekDouble rhoR, NekDouble rhouR, NekDouble rhovR, NekDouble rhowR, NekDouble ER, NekDouble EpsR, NekDouble &rhof, NekDouble &rhouf, NekDouble &rhovf, NekDouble &rhowf, NekDouble &Ef, NekDouble &Epsf)
Protected Member Functions inherited from Nektar::SolverUtils::RiemannSolver
SOLVER_UTILS_EXPORT	RiemannSolver ()
void	GenerateRotationMatrices (const Array< OneD, const Array< OneD, NekDouble > > &normals)
	Generate rotation matrices for 3D expansions.
void	FromToRotation (Array< OneD, const NekDouble > &from, Array< OneD, const NekDouble > &to, NekDouble *mat)
	A function for creating a rotation matrix that rotates a vector from into another vector to.
SOLVER_UTILS_EXPORT void	rotateToNormal (const Array< OneD, const Array< OneD, NekDouble > > &inarray, const Array< OneD, const Array< OneD, NekDouble > > &normals, const Array< OneD, const Array< OneD, NekDouble > > &vecLocs, Array< OneD, Array< OneD, NekDouble > > &outarray)
	Rotate a vector field to trace normal.
SOLVER_UTILS_EXPORT void	rotateFromNormal (const Array< OneD, const Array< OneD, NekDouble > > &inarray, const Array< OneD, const Array< OneD, NekDouble > > &normals, const Array< OneD, const Array< OneD, NekDouble > > &vecLocs, Array< OneD, Array< OneD, NekDouble > > &outarray)
	Rotate a vector field from trace normal.
bool	CheckScalars (std::string name)
	Determine whether a scalar has been defined in m_scalars.
bool	CheckVectors (std::string name)
	Determine whether a vector has been defined in m_vectors.
bool	CheckParams (std::string name)
	Determine whether a parameter has been defined in m_params.
bool	CheckAuxScal (std::string name)
	Determine whether a scalar has been defined in m_auxScal.
bool	CheckAuxVec (std::string name)
	Determine whether a vector has been defined in m_auxVec.

Additional Inherited Members
Public Member Functions inherited from Nektar::SolverUtils::RiemannSolver
SOLVER_UTILS_EXPORT void	Solve (const int nDim, const Array< OneD, const Array< OneD, NekDouble > > &Fwd, const Array< OneD, const Array< OneD, NekDouble > > &Bwd, Array< OneD, Array< OneD, NekDouble > > &flux)
	Perform the Riemann solve given the forwards and backwards spaces.
template<typename FuncPointerT , typename ObjectPointerT >
void	SetScalar (std::string name, FuncPointerT func, ObjectPointerT obj)
void	SetScalar (std::string name, RSScalarFuncType fp)
template<typename FuncPointerT , typename ObjectPointerT >
void	SetVector (std::string name, FuncPointerT func, ObjectPointerT obj)
void	SetVector (std::string name, RSVecFuncType fp)
template<typename FuncPointerT , typename ObjectPointerT >
void	SetParam (std::string name, FuncPointerT func, ObjectPointerT obj)
void	SetParam (std::string name, RSParamFuncType fp)
template<typename FuncPointerT , typename ObjectPointerT >
void	SetAuxScal (std::string name, FuncPointerT func, ObjectPointerT obj)
template<typename FuncPointerT , typename ObjectPointerT >
void	SetAuxVec (std::string name, FuncPointerT func, ObjectPointerT obj)
std::map< std::string, RSScalarFuncType > &	GetScalars ()
std::map< std::string, RSVecFuncType > &	GetVectors ()
std::map< std::string, RSParamFuncType > &	GetParams ()
Public Attributes inherited from Nektar::SolverUtils::RiemannSolver
int	m_spacedim
Protected Attributes inherited from Nektar::CompressibleSolver
bool	m_pointSolve

Detailed Description

Definition at line 43 of file RoeSolver.h.

Constructor & Destructor Documentation

Nektar::RoeSolver::RoeSolver ( )

protected

Definition at line 46 of file RoeSolver.cpp.

Referenced by create().

                         : CompressibleSolver()
    {
    }

Member Function Documentation

static RiemannSolverSharedPtr Nektar::RoeSolver::create ( )

inlinestatic

Definition at line 46 of file RoeSolver.h.

References RoeSolver().

        {
            return RiemannSolverSharedPtr(
                new RoeSolver());
        }

void Nektar::RoeSolver::v_PointSolve	(	double	rhoL,
		double	rhouL,
		double	rhovL,
		double	rhowL,
		double	EL,
		double	rhoR,
		double	rhouR,
		double	rhovR,
		double	rhowR,
		double	ER,
		double &	rhof,
		double &	rhouf,
		double &	rhovf,
		double &	rhowf,
		double &	Ef
	)

protectedvirtual

Roe Riemann solver.

Stated equations numbers are from:

"Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction", E. F. Toro (3rd edition, 2009).

We follow the algorithm prescribed following equation 11.70.

Parameters

rhoL	Density left state.
rhoR	Density right state.
rhouL	x-momentum component left state.
rhouR	x-momentum component right state.
rhovL	y-momentum component left state.
rhovR	y-momentum component right state.
rhowL	z-momentum component left state.
rhowR	z-momentum component right state.
EL	Energy left state.
ER	Energy right state.
rhof	Computed Riemann flux for density.
rhouf	Computed Riemann flux for x-momentum component
rhovf	Computed Riemann flux for y-momentum component
rhowf	Computed Riemann flux for z-momentum component
Ef	Computed Riemann flux for energy.

Reimplemented from Nektar::CompressibleSolver.

Definition at line 77 of file RoeSolver.cpp.

References Nektar::SolverUtils::RiemannSolver::m_params.

    {        
        static NekDouble gamma = m_params["gamma"]();
        
        // Left and right velocities
        NekDouble uL = rhouL / rhoL;
        NekDouble vL = rhovL / rhoL;
        NekDouble wL = rhowL / rhoL;
        NekDouble uR = rhouR / rhoR;
        NekDouble vR = rhovR / rhoR;
        NekDouble wR = rhowR / rhoR;
        // Left and right pressures
        NekDouble pL = (gamma - 1.0) *
            (EL - 0.5 * (rhouL * uL + rhovL * vL + rhowL * wL));
        NekDouble pR = (gamma - 1.0) *
            (ER - 0.5 * (rhouR * uR + rhovR * vR + rhowR * wR));
        
        // Left and right enthalpy
        NekDouble hL = (EL + pL) / rhoL;
        NekDouble hR = (ER + pR) / rhoR;
        // Square root of rhoL and rhoR.
        NekDouble srL  = sqrt(rhoL);
        NekDouble srR  = sqrt(rhoR);
        NekDouble srLR = srL + srR;
        
        // Velocity, enthalpy and sound speed Roe averages (equation 11.60).
        NekDouble uRoe   = (srL * uL + srR * uR) / srLR;
        NekDouble vRoe   = (srL * vL + srR * vR) / srLR;
        NekDouble wRoe   = (srL * wL + srR * wR) / srLR;
        NekDouble hRoe   = (srL * hL + srR * hR) / srLR;
        NekDouble URoe   = (uRoe * uRoe + vRoe * vRoe + wRoe * wRoe);
        NekDouble cRoe   = sqrt((gamma - 1.0)*(hRoe - 0.5 * URoe));
        
        // Compute eigenvectors (equation 11.59).
        NekDouble k[5][5] = {
            {1, uRoe - cRoe, vRoe, wRoe, hRoe - uRoe * cRoe},
            {1, uRoe,        vRoe, wRoe, 0.5 * URoe},
            {0, 0,           1,    0,    vRoe},
            {0, 0,           0,    1,    wRoe},
            {1, uRoe+cRoe,  vRoe,  wRoe, hRoe + uRoe*cRoe}
        };
        // Calculate jumps \Delta u_i (defined preceding equation 11.67).
        NekDouble jump[5] = {
            rhoR  - rhoL,
            rhouR - rhouL,
            rhovR - rhovL,
            rhowR - rhowL,
            ER    - EL
        };
        // Define \Delta u_5 (equation 11.70).
        NekDouble jumpbar = jump[4] - (jump[2]-vRoe*jump[0])*vRoe -
            (jump[3]-wRoe*jump[0])*wRoe;
        
        // Compute wave amplitudes (equations 11.68, 11.69).
        NekDouble alpha[5];
        alpha[1] = (gamma-1.0)*(jump[0]*(hRoe - uRoe*uRoe) + uRoe*jump[1] -
                                jumpbar)/(cRoe*cRoe);
        alpha[0] = (jump[0]*(uRoe + cRoe) - jump[1] - cRoe*alpha[1])/(2.0*cRoe);
        alpha[4] = jump[0] - (alpha[0] + alpha[1]);
        alpha[2] = jump[2] - vRoe * jump[0];
        alpha[3] = jump[3] - wRoe * jump[0];
        
        // Compute average of left and right fluxes needed for equation 11.29.
        rhof  = 0.5*(rhoL*uL + rhoR*uR);
        rhouf = 0.5*(pL + rhoL*uL*uL + pR + rhoR*uR*uR);
        rhovf = 0.5*(rhoL*uL*vL + rhoR*uR*vR);
        rhowf = 0.5*(rhoL*uL*wL + rhoR*uR*wR);
        Ef    = 0.5*(uL*(EL + pL) + uR*(ER + pR));
        // Compute eigenvalues \lambda_i (equation 11.58).
        NekDouble uRoeAbs = fabs(uRoe);
        NekDouble lambda[5] = { 
            fabs(uRoe - cRoe),
            uRoeAbs,
            uRoeAbs,
            uRoeAbs,
            fabs(uRoe + cRoe)
        };
        // Finally perform summation (11.29).
        for (int i = 0; i < 5; ++i)
        {
            NekDouble ahat = 0.5*alpha[i]*lambda[i];
            rhof  -= ahat*k[i][0];
            rhouf -= ahat*k[i][1];
            rhovf -= ahat*k[i][2];
            rhowf -= ahat*k[i][3];
            Ef    -= ahat*k[i][4];
        }
    }

Member Data Documentation

std::string Nektar::RoeSolver::solverName

static

Initial value:

        SolverUtils::GetRiemannSolverFactory().RegisterCreatorFunction(
            "Roe",
            RoeSolver::create,
            "Roe Riemann solver")

Definition at line 52 of file RoeSolver.h.

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation