Implementation of the HHO scheme for Navier-Stokes with variable density. More...

Namespaces
namespace	HArDCore2D::NSASolutions

Classes
struct	HArDCore2D::VarDensityNavierStokes
	Class for Navier-Stokes model. More...

struct	HArDCore2D::NSASolutions::IExactSolution

struct	HArDCore2D::NSASolutions::Linear

struct	HArDCore2D::NSASolutions::Trigonometric

struct	HArDCore2D::NSASolutions::CaiEtAl

struct	HArDCore2D::NSASolutions::GuermondQuartapelle

struct	HArDCore2D::NSASolutions::LidDrivenCavity

struct	HArDCore2D::NSASolutions::RayleighTaylor

struct	HArDCore2D::NSASolutions::DamBreak

Typedefs
typedef Eigen::SparseMatrix< double >	HArDCore2D::VarDensityNavierStokes::systemMatrixType

typedef std::function< VectorRd(const VectorRd &)>	HArDCore2D::VarDensityNavierStokes::MomentumForcingTermType

typedef std::function< double(const VectorRd &)>	HArDCore2D::VarDensityNavierStokes::CompressibilityForcingTermType

typedef std::function< double(const VectorRd &)>	HArDCore2D::VarDensityNavierStokes::DensityForcingTermType

typedef std::function< VectorRd(const VectorRd &)>	HArDCore2D::VarDensityNavierStokes::VelocityType

typedef std::function< MatrixRd(const VectorRd &)>	HArDCore2D::VarDensityNavierStokes::VelocityGradientType

typedef std::function< double(const VectorRd &)>	HArDCore2D::VarDensityNavierStokes::PressureType

typedef std::function< VectorRd(const VectorRd &)>	HArDCore2D::VarDensityNavierStokes::PressureGradientType

typedef std::function< double(const VectorRd &)>	HArDCore2D::VarDensityNavierStokes::VolumicFractionType

typedef IntegralWeight	HArDCore2D::VarDensityNavierStokes::ViscosityType

Functions
	HArDCore2D::VarDensityNavierStokes::VarDensityNavierStokes (const VHHOSpace &vhho_space, const GlobalDOFSpace &p_space, const GlobalDOFSpace &phi_space, const BoundaryConditions &BC, bool use_threads, bool stokes=false, std::ostream &output=std::cout)
	Constructor.

void	HArDCore2D::VarDensityNavierStokes::assembleLinearHHOSystem (const MomentumForcingTermType &f, const CompressibilityForcingTermType &g, const VolumicFractionType &rhog, const ViscosityType &mu, const Eigen::VectorXd &u0, const Eigen::VectorXd &uold, const double &time_step)
	Assemble the global system

void	HArDCore2D::VarDensityNavierStokes::assembleLinearDGSystem (const CompressibilityForcingTermType &h, const Eigen::VectorXd &uprho, const VolumicFractionType &rho, const double &time_step)
	DG ADVECTION SYSTEM.

size_t	HArDCore2D::VarDensityNavierStokes::nloc_sc_u () const
	Returns the local number of velocity statically condensed DOFs.

size_t	HArDCore2D::VarDensityNavierStokes::nloc_sc_p () const
	Returns the local number of pressure statically condensed DOFs.

size_t	HArDCore2D::VarDensityNavierStokes::numSCDOFs_u () const
	Returns the number of velocity statically condensed DOFs.

size_t	HArDCore2D::VarDensityNavierStokes::numSCDOFs_p () const
	Returns the number of pressure statically condensed DOFs.

size_t	HArDCore2D::VarDensityNavierStokes::numSCDOFs () const
	Returns the number of statically condensed DOFs.

size_t	HArDCore2D::VarDensityNavierStokes::numDirDOFs () const
	Returns the number of Dirichlet DOFs.

size_t	HArDCore2D::VarDensityNavierStokes::dimVelocity () const
	Returns the dimension of velocity space.

size_t	HArDCore2D::VarDensityNavierStokes::dimPressure () const
	Returns the dimension of pressure space.

size_t	HArDCore2D::VarDensityNavierStokes::dimVolumicFraction () const
	Returns the dimension of pressure space.

size_t	HArDCore2D::VarDensityNavierStokes::numNonSCDOFs () const
	Returns the number of DOFs after SC and with Lagrange multiplier, but before eliminating Dirichlet DOFs.

size_t	HArDCore2D::VarDensityNavierStokes::sizeSystemHHO () const
	Returns the size of the final system with Lagrange multiplier, after application of SC and removal of Dirichlet BCs.

size_t	HArDCore2D::VarDensityNavierStokes::sizeSystemDG () const

const VHHOSpace &	HArDCore2D::VarDensityNavierStokes::vhhospace () const
	Returns the velocity space.

const GlobalDOFSpace &	HArDCore2D::VarDensityNavierStokes::pspace () const
	Returns the pressure space.

const GlobalDOFSpace &	HArDCore2D::VarDensityNavierStokes::phispace () const
	Returns the pressure space.

const Mesh &	HArDCore2D::VarDensityNavierStokes::mesh () const
	Returns the mesh.

const systemMatrixType &	HArDCore2D::VarDensityNavierStokes::systemMatrixHHO () const
	Returns the linear system matrix.

systemMatrixType &	HArDCore2D::VarDensityNavierStokes::systemMatrixHHO ()
	Returns the linear system matrix.

const Eigen::VectorXd &	HArDCore2D::VarDensityNavierStokes::systemVector () const
	Returns the linear system right-hand side vector.

Eigen::VectorXd &	HArDCore2D::VarDensityNavierStokes::systemVector ()
	Returns the linear system right-hand side vector.

const double &	HArDCore2D::VarDensityNavierStokes::stabilizationParameter () const
	Returns the stabilization parameter (scaling)

double &	HArDCore2D::VarDensityNavierStokes::stabilizationParameter ()
	Returns the stabilization parameter.

const systemMatrixType &	HArDCore2D::VarDensityNavierStokes::scMatrix () const
	Returns the static condensation recovery operator.

Eigen::VectorXd &	HArDCore2D::VarDensityNavierStokes::scVector ()
	Returns the static condensation rhs.

const systemMatrixType &	HArDCore2D::VarDensityNavierStokes::systemMatrixDG () const
	Returns the linear system matrix.

systemMatrixType &	HArDCore2D::VarDensityNavierStokes::systemMatrixDG ()
	Returns the linear system matrix.

const Eigen::VectorXd &	HArDCore2D::VarDensityNavierStokes::systemVectorDG () const
	Returns the linear system right-hand side vector.

Eigen::VectorXd &	HArDCore2D::VarDensityNavierStokes::systemVectorDG ()
	Returns the linear system right-hand side vector.

bool &	HArDCore2D::VarDensityNavierStokes::isStokes ()
	Returns the Stokes status.

Eigen::VectorXd	HArDCore2D::VarDensityNavierStokes::interpolate (const VelocityType &u, const PressureType &p, const VolumicFractionType &phi, const int doe_cell=-1, const int doe_face=-1) const
	Interpolates velocity and pressure.

std::vector< double >	HArDCore2D::VarDensityNavierStokes::computeEnergyNorms (const std::vector< Eigen::VectorXd > &list_dofs) const
	Compute the discrete energy norm of a family of vectors representing the dofs.

std::vector< double >	HArDCore2D::VarDensityNavierStokes::computePressureL2Norm (const std::vector< Eigen::VectorXd > &list_dofs) const
	Compute the discrete L2 norm of the pressure.

std::vector< std::tuple< double, double, double > >	HArDCore2D::VarDensityNavierStokes::computeDGNorms (const std::vector< Eigen::VectorXd > &list_dofs, const VelocityType &u) const
	Compute the discrete energy norm of a family of vectors representing the dofs.

std::vector< double >	HArDCore2D::VarDensityNavierStokes::computePhysicalEnergies (const Eigen::VectorXd &uprho, const MomentumForcingTermType &f, const ViscosityType &mu) const
	UTILS.

Eigen::VectorXd	HArDCore2D::VarDensityNavierStokes::pressureVertexValues (const Eigen::VectorXd &p) const
	Create vertex values for the pressure (from the element values), for plotting.

Eigen::VectorXd	HArDCore2D::VarDensityNavierStokes::volumicFractionVertexValues (const Eigen::VectorXd &phi) const
	Create vertex values for volumic fraction.

void	HArDCore2D::VarDensityNavierStokes::writeToVtuFile (const Eigen::VectorXd &upphi, const Eigen::VectorXd &upphiI, const std::unique_ptr< Mesh > &mesh_ptr, const std::string &solution_name, const std::string &mesh_name, const size_t &degree, const int &time_it, const double &reynolds, const std::vector< std::string > &plot_variables, const std::string &output_path)
	Write solution to vut file.

void	HArDCore2D::VarDensityNavierStokes::writeTimeStepData (const std::string &filename, const int &time_it, const double &time, const double &dt, const double &L2_u_err, const double &H1_u_err, const double &Energy_err, const double &L2_rho_err, const double &cf_rho_err, const double &upw_rho_err, const double &E_kinetic, const double &E_potential, const double &E_dissipation) const
	Writing data to txt file.

void	HArDCore2D::VarDensityNavierStokes::writeFileHeader (const std::string &filename, const std::string &solution_name, const int &solution_number, const std::string &mesh_name, const size_t &degree, const std::unique_ptr< Mesh > &mesh_ptr, const double &viscosity) const
	Writing file header with simulation metadata.

Eigen::VectorXd	HArDCore2D::VarDensityNavierStokes::imposingBC (const VelocityType &u, const Eigen::VectorXd &uph) const
	impose boundary conditions

double	HArDCore2D::VarDensityNavierStokes::getUpwindDensity (const size_t &iE, const size_t &iT, const Eigen::VectorXd &uprho) const
	get upwind value of the density at the face E

Eigen::VectorXd	HArDCore2D::VarDensityNavierStokes::newtonRaphson (LinearSolver< VarDensityNavierStokes::systemMatrixType > &solver, const std::unique_ptr< Mesh > &mesh_ptr, const size_t &newton_maxit, const double &newton_tol, const Eigen::VectorXd &u_newt, const Eigen::VectorXd &un, const MomentumForcingTermType &f, const CompressibilityForcingTermType &g, const VolumicFractionType &rhog, const ViscosityType &mu, const double &time_step)
	newton method

	HArDCore2D::NSASolutions::IExactSolution::IExactSolution (std::string name, bool is_stokes, double viscosity)

virtual	HArDCore2D::NSASolutions::IExactSolution::~IExactSolution ()

std::string	HArDCore2D::NSASolutions::IExactSolution::name () const
	Return the solution name.

bool	HArDCore2D::NSASolutions::IExactSolution::isStokes () const

double	HArDCore2D::NSASolutions::IExactSolution::viscosity () const
	Return the viscosity.

virtual Eigen::Vector2d	HArDCore2D::NSASolutions::IExactSolution::momentumForcingTerm (const Eigen::Vector2d &x, const double &t=0) const =0

virtual double	HArDCore2D::NSASolutions::IExactSolution::compressibilityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const =0

virtual double	HArDCore2D::NSASolutions::IExactSolution::densityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const =0

virtual Eigen::Vector2d	HArDCore2D::NSASolutions::IExactSolution::velocity (const Eigen::Vector2d &x, const double &t=0) const =0

virtual double	HArDCore2D::NSASolutions::IExactSolution::pressure (const Eigen::Vector2d &x, const double &t=0) const =0

virtual Eigen::Matrix2d	HArDCore2D::NSASolutions::IExactSolution::velocityGradient (const Eigen::Vector2d &x, const double &t=0) const =0

virtual Eigen::Vector2d	HArDCore2D::NSASolutions::IExactSolution::pressureGradient (const Eigen::Vector2d &x, const double &t=0) const =0

virtual double	HArDCore2D::NSASolutions::IExactSolution::volumicFraction (const Eigen::Vector2d &x, const double &t=0) const =0

	HArDCore2D::NSASolutions::Linear::Linear (const int &stokes)

Eigen::Vector2d	HArDCore2D::NSASolutions::Linear::momentumForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::Linear::compressibilityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::Linear::densityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::Linear::velocity (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::Linear::pressure (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Matrix2d	HArDCore2D::NSASolutions::Linear::velocityGradient (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::Linear::pressureGradient (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::Linear::volumicFraction (const Eigen::Vector2d &x, const double &t=0) const

	HArDCore2D::NSASolutions::Trigonometric::Trigonometric (const int &stokes)

Eigen::Vector2d	HArDCore2D::NSASolutions::Trigonometric::momentumForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::Trigonometric::compressibilityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::Trigonometric::densityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::Trigonometric::velocity (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::Trigonometric::pressure (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Matrix2d	HArDCore2D::NSASolutions::Trigonometric::velocityGradient (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::Trigonometric::pressureGradient (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::Trigonometric::volumicFraction (const Eigen::Vector2d &x, const double &t=0) const

	HArDCore2D::NSASolutions::CaiEtAl::CaiEtAl (const int &stokes)

Eigen::Vector2d	HArDCore2D::NSASolutions::CaiEtAl::momentumForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::CaiEtAl::compressibilityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::CaiEtAl::densityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::CaiEtAl::velocity (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::CaiEtAl::pressure (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Matrix2d	HArDCore2D::NSASolutions::CaiEtAl::velocityGradient (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::CaiEtAl::pressureGradient (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::CaiEtAl::volumicFraction (const Eigen::Vector2d &x, const double &t=0) const

	HArDCore2D::NSASolutions::GuermondQuartapelle::GuermondQuartapelle (const int &stokes)

Eigen::Vector2d	HArDCore2D::NSASolutions::GuermondQuartapelle::momentumForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::GuermondQuartapelle::compressibilityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::GuermondQuartapelle::densityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::GuermondQuartapelle::velocity (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::GuermondQuartapelle::pressure (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Matrix2d	HArDCore2D::NSASolutions::GuermondQuartapelle::velocityGradient (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::GuermondQuartapelle::pressureGradient (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::GuermondQuartapelle::volumicFraction (const Eigen::Vector2d &x, const double &t=0) const

	HArDCore2D::NSASolutions::LidDrivenCavity::LidDrivenCavity (const int &stokes)

Eigen::Vector2d	HArDCore2D::NSASolutions::LidDrivenCavity::momentumForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::LidDrivenCavity::compressibilityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::LidDrivenCavity::densityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::LidDrivenCavity::velocity (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::LidDrivenCavity::pressure (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Matrix2d	HArDCore2D::NSASolutions::LidDrivenCavity::velocityGradient (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::LidDrivenCavity::pressureGradient (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::LidDrivenCavity::volumicFraction (const Eigen::Vector2d &x, const double &t=0) const

	HArDCore2D::NSASolutions::RayleighTaylor::RayleighTaylor (const double &rho_min, const double &rho_max, const double &Re, const double &L, const double &a, const double &g)

Eigen::Vector2d	HArDCore2D::NSASolutions::RayleighTaylor::momentumForcingTerm (const Eigen::Vector2d &x, const double &t=0) const
	A function to transform the unit domain to \((-L/2,L/2)\times (-2L,2L)\).

double	HArDCore2D::NSASolutions::RayleighTaylor::compressibilityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::RayleighTaylor::densityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::RayleighTaylor::velocity (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::RayleighTaylor::pressure (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Matrix2d	HArDCore2D::NSASolutions::RayleighTaylor::velocityGradient (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::RayleighTaylor::pressureGradient (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::RayleighTaylor::volumicFraction (const Eigen::Vector2d &x, const double &t=0) const

	HArDCore2D::NSASolutions::DamBreak::DamBreak (const double &rho_min, const double &rho_max, const double &Re, const double &L, const double &H, const double &g)

Eigen::Vector2d	HArDCore2D::NSASolutions::DamBreak::momentumForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::DamBreak::compressibilityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::DamBreak::densityForcingTerm (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::DamBreak::velocity (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::DamBreak::pressure (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Matrix2d	HArDCore2D::NSASolutions::DamBreak::velocityGradient (const Eigen::Vector2d &x, const double &t=0) const

Eigen::Vector2d	HArDCore2D::NSASolutions::DamBreak::pressureGradient (const Eigen::Vector2d &x, const double &t=0) const

double	HArDCore2D::NSASolutions::DamBreak::volumicFraction (const Eigen::Vector2d &x, const double &t=0) const

Variables
std::string	HArDCore2D::NSASolutions::IExactSolution::m_name

bool	HArDCore2D::NSASolutions::IExactSolution::m_is_stokes

double	HArDCore2D::NSASolutions::IExactSolution::m_viscosity

static double	HArDCore2D::NSASolutions::RayleighTaylor::s_L = 0.0

Detailed Description

Implementation of the HHO scheme for Navier-Stokes with variable density.

Typedef Documentation

◆ CompressibilityForcingTermType

typedef std::function<double(const VectorRd &)> HArDCore2D::VarDensityNavierStokes::CompressibilityForcingTermType

◆ DensityForcingTermType

typedef std::function<double(const VectorRd &)> HArDCore2D::VarDensityNavierStokes::DensityForcingTermType

◆ MomentumForcingTermType

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::VarDensityNavierStokes::MomentumForcingTermType

◆ PressureGradientType

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::VarDensityNavierStokes::PressureGradientType

◆ PressureType

typedef std::function<double(const VectorRd &)> HArDCore2D::VarDensityNavierStokes::PressureType

◆ systemMatrixType

typedef Eigen::SparseMatrix<double> HArDCore2D::VarDensityNavierStokes::systemMatrixType

◆ VelocityGradientType

typedef std::function<MatrixRd(const VectorRd &)> HArDCore2D::VarDensityNavierStokes::VelocityGradientType

◆ VelocityType

typedef std::function<VectorRd(const VectorRd &)> HArDCore2D::VarDensityNavierStokes::VelocityType

◆ ViscosityType

typedef IntegralWeight HArDCore2D::VarDensityNavierStokes::ViscosityType

◆ VolumicFractionType

typedef std::function<double(const VectorRd &)> HArDCore2D::VarDensityNavierStokes::VolumicFractionType

Function Documentation

◆ assembleLinearDGSystem()

void VarDensityNavierStokes::assembleLinearDGSystem	(	const CompressibilityForcingTermType &	h,
		const Eigen::VectorXd &	uprho,
		const VolumicFractionType &	rho,
		const double &	time_step
	)

DG ADVECTION SYSTEM.

◆ assembleLinearHHOSystem()

void VarDensityNavierStokes::assembleLinearHHOSystem	(	const MomentumForcingTermType &	f,
		const CompressibilityForcingTermType &	g,
		const VolumicFractionType &	rhog,
		const ViscosityType &	mu,
		const Eigen::VectorXd &	u0,
		const Eigen::VectorXd &	uold,
		const double &	time_step
	)

Assemble the global system

HHO NAVIER-STOKES SYSTEM.

Parameters

f	Forcing term
g	Forcing term for the divergence equation
rhog	denisty on the boundary
mu	Viscosity
u0	solution at previous time step
uold	solution at previous Newton iteration
time_step	time step

◆ CaiEtAl()

CaiEtAl::CaiEtAl ( const int & stokes )

◆ compressibilityForcingTerm() [1/8]

double Linear::compressibilityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ compressibilityForcingTerm() [2/8]

double Trigonometric::compressibilityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ compressibilityForcingTerm() [3/8]

double CaiEtAl::compressibilityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ compressibilityForcingTerm() [4/8]

double GuermondQuartapelle::compressibilityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ compressibilityForcingTerm() [5/8]

double LidDrivenCavity::compressibilityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ compressibilityForcingTerm() [6/8]

double RayleighTaylor::compressibilityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ compressibilityForcingTerm() [7/8]

double DamBreak::compressibilityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ compressibilityForcingTerm() [8/8]

virtual double HArDCore2D::NSASolutions::IExactSolution::compressibilityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

pure virtual

Implemented in HArDCore2D::NSASolutions::Linear, HArDCore2D::NSASolutions::Trigonometric, HArDCore2D::NSASolutions::CaiEtAl, HArDCore2D::NSASolutions::GuermondQuartapelle, HArDCore2D::NSASolutions::LidDrivenCavity, HArDCore2D::NSASolutions::RayleighTaylor, and HArDCore2D::NSASolutions::DamBreak.

◆ computeDGNorms()

std::vector< std::tuple< double, double, double > > VarDensityNavierStokes::computeDGNorms	(	const std::vector< Eigen::VectorXd > &	list_dofs,
		const VelocityType &	u
	)		const

Compute the discrete energy norm of a family of vectors representing the dofs.

◆ computeEnergyNorms()

std::vector< double > VarDensityNavierStokes::computeEnergyNorms ( const std::vector< Eigen::VectorXd > & list_dofs ) const

Compute the discrete energy norm of a family of vectors representing the dofs.

Parameters

list_dofs The list of vectors representing the dofs

◆ computePhysicalEnergies()

std::vector< double > VarDensityNavierStokes::computePhysicalEnergies	(	const Eigen::VectorXd &	uprho,
		const MomentumForcingTermType &	f,
		const ViscosityType &	mu
	)		const

UTILS.

Parameters

uprho	Solution vector
f	Momentum forcing term
mu	Viscosity

◆ computePressureL2Norm()

std::vector< double > VarDensityNavierStokes::computePressureL2Norm ( const std::vector< Eigen::VectorXd > & list_dofs ) const

Compute the discrete L2 norm of the pressure.

Parameters

list_dofs The list of vectors representing the dofs

◆ DamBreak()

DamBreak::DamBreak	(	const double &	rho_min,
		const double &	rho_max,
		const double &	Re,
		const double &	L,
		const double &	H,
		const double &	g
	)

◆ densityForcingTerm() [1/8]

double Linear::densityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ densityForcingTerm() [2/8]

double Trigonometric::densityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ densityForcingTerm() [3/8]

double CaiEtAl::densityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ densityForcingTerm() [4/8]

double GuermondQuartapelle::densityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ densityForcingTerm() [5/8]

double LidDrivenCavity::densityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ densityForcingTerm() [6/8]

double RayleighTaylor::densityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ densityForcingTerm() [7/8]

double DamBreak::densityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ densityForcingTerm() [8/8]

virtual double HArDCore2D::NSASolutions::IExactSolution::densityForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

pure virtual

Implemented in HArDCore2D::NSASolutions::Linear, HArDCore2D::NSASolutions::Trigonometric, HArDCore2D::NSASolutions::CaiEtAl, HArDCore2D::NSASolutions::GuermondQuartapelle, HArDCore2D::NSASolutions::LidDrivenCavity, HArDCore2D::NSASolutions::RayleighTaylor, and HArDCore2D::NSASolutions::DamBreak.

◆ dimPressure()

size_t HArDCore2D::VarDensityNavierStokes::dimPressure ( ) const

inline

Returns the dimension of pressure space.

◆ dimVelocity()

size_t HArDCore2D::VarDensityNavierStokes::dimVelocity ( ) const

inline

Returns the dimension of velocity space.

◆ dimVolumicFraction()

size_t HArDCore2D::VarDensityNavierStokes::dimVolumicFraction ( ) const

inline

Returns the dimension of pressure space.

◆ getUpwindDensity()

double HArDCore2D::VarDensityNavierStokes::getUpwindDensity	(	const size_t &	iE,
		const size_t &	iT,
		const Eigen::VectorXd &	uprho
	)		const

get upwind value of the density at the face E

◆ GuermondQuartapelle()

GuermondQuartapelle::GuermondQuartapelle ( const int & stokes )

◆ IExactSolution()

IExactSolution::IExactSolution	(	std::string	name,
		bool	is_stokes,
		double	viscosity
	)

◆ imposingBC()

Eigen::VectorXd VarDensityNavierStokes::imposingBC	(	const VelocityType &	u,
		const Eigen::VectorXd &	uph
	)		const

impose boundary conditions

◆ interpolate()

Eigen::VectorXd VarDensityNavierStokes::interpolate	(	const VelocityType &	u,
		const PressureType &	p,
		const VolumicFractionType &	phi,
		const int	doe_cell = `-1`,
		const int	doe_face = `-1`
	)		const

Interpolates velocity and pressure.

INTERPOLATION.

Parameters

u	Continuous velocity to interpolate
p	Continuous pressure to interpolate
doe_cell	The optional degre of cell quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.
doe_face	The optional degre of face quadrature rules to compute the interpolate. If negative, then 2*degree()+3 will be used.

◆ isStokes() [1/2]

bool & HArDCore2D::VarDensityNavierStokes::isStokes ( )

inline

Returns the Stokes status.

◆ isStokes() [2/2]

bool HArDCore2D::NSASolutions::IExactSolution::isStokes ( ) const

inline

Return true if the solution is for the Stokes problem, false if it is for the Navier-Stokes problem

◆ LidDrivenCavity()

LidDrivenCavity::LidDrivenCavity ( const int & stokes )

◆ Linear()

Linear::Linear ( const int & stokes )

◆ mesh()

const Mesh & HArDCore2D::VarDensityNavierStokes::mesh ( ) const

inline

Returns the mesh.

◆ momentumForcingTerm() [1/8]

Eigen::Vector2d Linear::momentumForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ momentumForcingTerm() [2/8]

Eigen::Vector2d Trigonometric::momentumForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ momentumForcingTerm() [3/8]

Eigen::Vector2d CaiEtAl::momentumForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ momentumForcingTerm() [4/8]

Eigen::Vector2d GuermondQuartapelle::momentumForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ momentumForcingTerm() [5/8]

Eigen::Vector2d LidDrivenCavity::momentumForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ momentumForcingTerm() [6/8]

Eigen::Vector2d RayleighTaylor::momentumForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

A function to transform the unit domain to \((-L/2,L/2)\times (-2L,2L)\).

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ momentumForcingTerm() [7/8]

Eigen::Vector2d DamBreak::momentumForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ momentumForcingTerm() [8/8]

virtual Eigen::Vector2d HArDCore2D::NSASolutions::IExactSolution::momentumForcingTerm	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

pure virtual

Implemented in HArDCore2D::NSASolutions::Linear, HArDCore2D::NSASolutions::Trigonometric, HArDCore2D::NSASolutions::CaiEtAl, HArDCore2D::NSASolutions::GuermondQuartapelle, HArDCore2D::NSASolutions::LidDrivenCavity, HArDCore2D::NSASolutions::RayleighTaylor, and HArDCore2D::NSASolutions::DamBreak.

◆ name()

std::string HArDCore2D::NSASolutions::IExactSolution::name ( ) const

inline

Return the solution name.

◆ newtonRaphson()

Eigen::VectorXd VarDensityNavierStokes::newtonRaphson	(	LinearSolver< VarDensityNavierStokes::systemMatrixType > &	solver,
		const std::unique_ptr< Mesh > &	mesh_ptr,
		const size_t &	newton_maxit,
		const double &	newton_tol,
		const Eigen::VectorXd &	u_newt,
		const Eigen::VectorXd &	un,
		const MomentumForcingTermType &	f,
		const CompressibilityForcingTermType &	g,
		const VolumicFractionType &	rhog,
		const ViscosityType &	mu,
		const double &	time_step
	)

newton method

initializing parameters

◆ nloc_sc_p()

size_t HArDCore2D::VarDensityNavierStokes::nloc_sc_p ( ) const

inline

Returns the local number of pressure statically condensed DOFs.

◆ nloc_sc_u()

size_t HArDCore2D::VarDensityNavierStokes::nloc_sc_u ( ) const

inline

Returns the local number of velocity statically condensed DOFs.

◆ numDirDOFs()

size_t HArDCore2D::VarDensityNavierStokes::numDirDOFs ( ) const

inline

Returns the number of Dirichlet DOFs.

◆ numNonSCDOFs()

size_t HArDCore2D::VarDensityNavierStokes::numNonSCDOFs ( ) const

inline

Returns the number of DOFs after SC and with Lagrange multiplier, but before eliminating Dirichlet DOFs.

◆ numSCDOFs()

size_t HArDCore2D::VarDensityNavierStokes::numSCDOFs ( ) const

inline

Returns the number of statically condensed DOFs.

◆ numSCDOFs_p()

size_t HArDCore2D::VarDensityNavierStokes::numSCDOFs_p ( ) const

inline

Returns the number of pressure statically condensed DOFs.

◆ numSCDOFs_u()

size_t HArDCore2D::VarDensityNavierStokes::numSCDOFs_u ( ) const

inline

Returns the number of velocity statically condensed DOFs.

◆ phispace()

const GlobalDOFSpace & HArDCore2D::VarDensityNavierStokes::phispace ( ) const

inline

Returns the pressure space.

◆ pressure() [1/8]

double Linear::pressure	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressure() [2/8]

double Trigonometric::pressure	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressure() [3/8]

double CaiEtAl::pressure	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressure() [4/8]

double GuermondQuartapelle::pressure	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressure() [5/8]

double LidDrivenCavity::pressure	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressure() [6/8]

double RayleighTaylor::pressure	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressure() [7/8]

double DamBreak::pressure	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressure() [8/8]

virtual double HArDCore2D::NSASolutions::IExactSolution::pressure	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

pure virtual

Implemented in HArDCore2D::NSASolutions::Linear, HArDCore2D::NSASolutions::Trigonometric, HArDCore2D::NSASolutions::CaiEtAl, HArDCore2D::NSASolutions::GuermondQuartapelle, HArDCore2D::NSASolutions::LidDrivenCavity, HArDCore2D::NSASolutions::RayleighTaylor, and HArDCore2D::NSASolutions::DamBreak.

◆ pressureGradient() [1/8]

Eigen::Vector2d Linear::pressureGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressureGradient() [2/8]

Eigen::Vector2d Trigonometric::pressureGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressureGradient() [3/8]

Eigen::Vector2d CaiEtAl::pressureGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressureGradient() [4/8]

Eigen::Vector2d GuermondQuartapelle::pressureGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressureGradient() [5/8]

Eigen::Vector2d LidDrivenCavity::pressureGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressureGradient() [6/8]

Eigen::Vector2d RayleighTaylor::pressureGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressureGradient() [7/8]

Eigen::Vector2d DamBreak::pressureGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ pressureGradient() [8/8]

virtual Eigen::Vector2d HArDCore2D::NSASolutions::IExactSolution::pressureGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

pure virtual

Implemented in HArDCore2D::NSASolutions::Linear, HArDCore2D::NSASolutions::Trigonometric, HArDCore2D::NSASolutions::CaiEtAl, HArDCore2D::NSASolutions::GuermondQuartapelle, HArDCore2D::NSASolutions::LidDrivenCavity, HArDCore2D::NSASolutions::RayleighTaylor, and HArDCore2D::NSASolutions::DamBreak.

◆ pressureVertexValues()

Eigen::VectorXd VarDensityNavierStokes::pressureVertexValues ( const Eigen::VectorXd & p ) const

Create vertex values for the pressure (from the element values), for plotting.

Parameters

p	Vector of pressure DOFs

◆ pspace()

const GlobalDOFSpace & HArDCore2D::VarDensityNavierStokes::pspace ( ) const

inline

Returns the pressure space.

◆ RayleighTaylor()

RayleighTaylor::RayleighTaylor	(	const double &	rho_min,
		const double &	rho_max,
		const double &	Re,
		const double &	L,
		const double &	a,
		const double &	g
	)

◆ scMatrix()

const systemMatrixType & HArDCore2D::VarDensityNavierStokes::scMatrix ( ) const

inline

Returns the static condensation recovery operator.

◆ scVector()

Eigen::VectorXd & HArDCore2D::VarDensityNavierStokes::scVector ( )

inline

Returns the static condensation rhs.

◆ sizeSystemDG()

size_t HArDCore2D::VarDensityNavierStokes::sizeSystemDG ( ) const

inline

◆ sizeSystemHHO()

size_t HArDCore2D::VarDensityNavierStokes::sizeSystemHHO ( ) const

inline

Returns the size of the final system with Lagrange multiplier, after application of SC and removal of Dirichlet BCs.

◆ stabilizationParameter() [1/2]

double & HArDCore2D::VarDensityNavierStokes::stabilizationParameter ( )

inline

Returns the stabilization parameter.

◆ stabilizationParameter() [2/2]

const double & HArDCore2D::VarDensityNavierStokes::stabilizationParameter ( ) const

inline

Returns the stabilization parameter (scaling)

◆ systemMatrixDG() [1/2]

systemMatrixType & HArDCore2D::VarDensityNavierStokes::systemMatrixDG ( )

inline

Returns the linear system matrix.

◆ systemMatrixDG() [2/2]

const systemMatrixType & HArDCore2D::VarDensityNavierStokes::systemMatrixDG ( ) const

inline

Returns the linear system matrix.

◆ systemMatrixHHO() [1/2]

systemMatrixType & HArDCore2D::VarDensityNavierStokes::systemMatrixHHO ( )

inline

Returns the linear system matrix.

◆ systemMatrixHHO() [2/2]

const systemMatrixType & HArDCore2D::VarDensityNavierStokes::systemMatrixHHO ( ) const

inline

Returns the linear system matrix.

◆ systemVector() [1/2]

Eigen::VectorXd & HArDCore2D::VarDensityNavierStokes::systemVector ( )

inline

Returns the linear system right-hand side vector.

◆ systemVector() [2/2]

const Eigen::VectorXd & HArDCore2D::VarDensityNavierStokes::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

◆ systemVectorDG() [1/2]

Eigen::VectorXd & HArDCore2D::VarDensityNavierStokes::systemVectorDG ( )

inline

Returns the linear system right-hand side vector.

◆ systemVectorDG() [2/2]

const Eigen::VectorXd & HArDCore2D::VarDensityNavierStokes::systemVectorDG ( ) const

inline

Returns the linear system right-hand side vector.

◆ Trigonometric()

Trigonometric::Trigonometric ( const int & stokes )

◆ VarDensityNavierStokes()

VarDensityNavierStokes::VarDensityNavierStokes	(	const VHHOSpace &	vhho_space,
		const GlobalDOFSpace &	p_space,
		const GlobalDOFSpace &	phi_space,
		const BoundaryConditions &	BC,
		bool	use_threads,
		bool	stokes = `false`,
		std::ostream &	output = `std::cout`
	)

Constructor.

Parameters

vhho_space	Velocity space and operators
p_space	Space for the pressure
phi_space	Space for the volumic fraction
BC	Boundary conditions
use_threads	True for parallel execution, false for sequential execution
stokes	True if we want to assemble the Stokes system without convective terms
output	Output stream to print status messages

◆ velocity() [1/8]

Eigen::Vector2d Linear::velocity	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocity() [2/8]

Eigen::Vector2d Trigonometric::velocity	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocity() [3/8]

Eigen::Vector2d CaiEtAl::velocity	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocity() [4/8]

Eigen::Vector2d GuermondQuartapelle::velocity	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocity() [5/8]

Eigen::Vector2d LidDrivenCavity::velocity	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocity() [6/8]

Eigen::Vector2d RayleighTaylor::velocity	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocity() [7/8]

Eigen::Vector2d DamBreak::velocity	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocity() [8/8]

virtual Eigen::Vector2d HArDCore2D::NSASolutions::IExactSolution::velocity	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

pure virtual

Implemented in HArDCore2D::NSASolutions::Linear, HArDCore2D::NSASolutions::Trigonometric, HArDCore2D::NSASolutions::CaiEtAl, HArDCore2D::NSASolutions::GuermondQuartapelle, HArDCore2D::NSASolutions::LidDrivenCavity, HArDCore2D::NSASolutions::RayleighTaylor, and HArDCore2D::NSASolutions::DamBreak.

◆ velocityGradient() [1/8]

Eigen::Matrix2d Linear::velocityGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocityGradient() [2/8]

Eigen::Matrix2d Trigonometric::velocityGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocityGradient() [3/8]

Eigen::Matrix2d CaiEtAl::velocityGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocityGradient() [4/8]

Eigen::Matrix2d GuermondQuartapelle::velocityGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocityGradient() [5/8]

Eigen::Matrix2d LidDrivenCavity::velocityGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocityGradient() [6/8]

Eigen::Matrix2d RayleighTaylor::velocityGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocityGradient() [7/8]

Eigen::Matrix2d DamBreak::velocityGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ velocityGradient() [8/8]

virtual Eigen::Matrix2d HArDCore2D::NSASolutions::IExactSolution::velocityGradient	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

pure virtual

Implemented in HArDCore2D::NSASolutions::Linear, HArDCore2D::NSASolutions::Trigonometric, HArDCore2D::NSASolutions::CaiEtAl, HArDCore2D::NSASolutions::GuermondQuartapelle, HArDCore2D::NSASolutions::LidDrivenCavity, HArDCore2D::NSASolutions::RayleighTaylor, and HArDCore2D::NSASolutions::DamBreak.

◆ vhhospace()

const VHHOSpace & HArDCore2D::VarDensityNavierStokes::vhhospace ( ) const

inline

Returns the velocity space.

◆ viscosity()

double HArDCore2D::NSASolutions::IExactSolution::viscosity ( ) const

inline

Return the viscosity.

◆ volumicFraction() [1/8]

double Linear::volumicFraction	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ volumicFraction() [2/8]

double Trigonometric::volumicFraction	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ volumicFraction() [3/8]

double CaiEtAl::volumicFraction	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ volumicFraction() [4/8]

double GuermondQuartapelle::volumicFraction	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ volumicFraction() [5/8]

double LidDrivenCavity::volumicFraction	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ volumicFraction() [6/8]

double RayleighTaylor::volumicFraction	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ volumicFraction() [7/8]

double DamBreak::volumicFraction	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

virtual

Implements HArDCore2D::NSASolutions::IExactSolution.

◆ volumicFraction() [8/8]

virtual double HArDCore2D::NSASolutions::IExactSolution::volumicFraction	(	const Eigen::Vector2d &	x,
		const double &	t = `0`
	)		const

pure virtual

Implemented in HArDCore2D::NSASolutions::Linear, HArDCore2D::NSASolutions::Trigonometric, HArDCore2D::NSASolutions::CaiEtAl, HArDCore2D::NSASolutions::GuermondQuartapelle, HArDCore2D::NSASolutions::LidDrivenCavity, HArDCore2D::NSASolutions::RayleighTaylor, and HArDCore2D::NSASolutions::DamBreak.

◆ volumicFractionVertexValues()

Eigen::VectorXd VarDensityNavierStokes::volumicFractionVertexValues ( const Eigen::VectorXd & phi ) const

Create vertex values for volumic fraction.

Creating vertex values for volumic fraction.

Parameters

phi	Vector of volumic fraction DOFs

◆ writeFileHeader()

void VarDensityNavierStokes::writeFileHeader	(	const std::string &	filename,
		const std::string &	solution_name,
		const int &	solution_number,
		const std::string &	mesh_name,
		const size_t &	degree,
		const std::unique_ptr< Mesh > &	mesh_ptr,
		const double &	viscosity
	)		const

Writing file header with simulation metadata.

◆ writeTimeStepData()

void VarDensityNavierStokes::writeTimeStepData	(	const std::string &	filename,
		const int &	time_it,
		const double &	time,
		const double &	dt,
		const double &	L2_u_err,
		const double &	H1_u_err,
		const double &	Energy_err,
		const double &	L2_rho_err,
		const double &	cf_rho_err,
		const double &	upw_rho_err,
		const double &	E_kinetic,
		const double &	E_potential,
		const double &	E_dissipation
	)		const

Writing data to txt file.

◆ writeToVtuFile()

void VarDensityNavierStokes::writeToVtuFile	(	const Eigen::VectorXd &	upphi,
		const Eigen::VectorXd &	upphiI,
		const std::unique_ptr< Mesh > &	mesh_ptr,
		const std::string &	solution_name,
		const std::string &	mesh_name,
		const size_t &	degree,
		const int &	time_it,
		const double &	reynolds,
		const std::vector< std::string > &	plot_variables,
		const std::string &	output_path
	)

Write solution to vut file.

Writing solution to vtu file.

◆ ~IExactSolution()

IExactSolution::~IExactSolution ( )

virtual

Variable Documentation

◆ m_is_stokes

bool HArDCore2D::NSASolutions::IExactSolution::m_is_stokes

protected

◆ m_name

std::string HArDCore2D::NSASolutions::IExactSolution::m_name

protected

◆ m_viscosity

double HArDCore2D::NSASolutions::IExactSolution::m_viscosity

protected

◆ s_L

double HArDCore2D::NSASolutions::RayleighTaylor::s_L = 0.0

static

Namespaces

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ CompressibilityForcingTermType

◆ DensityForcingTermType

◆ MomentumForcingTermType

◆ PressureGradientType

◆ PressureType

◆ systemMatrixType

◆ VelocityGradientType

◆ VelocityType

◆ ViscosityType

◆ VolumicFractionType

Function Documentation

◆ assembleLinearDGSystem()

◆ assembleLinearHHOSystem()

◆ CaiEtAl()

◆ compressibilityForcingTerm() [1/8]

◆ compressibilityForcingTerm() [2/8]

◆ compressibilityForcingTerm() [3/8]

◆ compressibilityForcingTerm() [4/8]

◆ compressibilityForcingTerm() [5/8]

◆ compressibilityForcingTerm() [6/8]

◆ compressibilityForcingTerm() [7/8]

◆ compressibilityForcingTerm() [8/8]

◆ computeDGNorms()

◆ computeEnergyNorms()

◆ computePhysicalEnergies()

◆ computePressureL2Norm()

◆ DamBreak()

◆ densityForcingTerm() [1/8]

◆ densityForcingTerm() [2/8]

◆ densityForcingTerm() [3/8]

◆ densityForcingTerm() [4/8]

◆ densityForcingTerm() [5/8]

◆ densityForcingTerm() [6/8]

◆ densityForcingTerm() [7/8]

◆ densityForcingTerm() [8/8]

◆ dimPressure()

◆ dimVelocity()

◆ dimVolumicFraction()

◆ getUpwindDensity()

◆ GuermondQuartapelle()

◆ IExactSolution()

◆ imposingBC()

◆ interpolate()

◆ isStokes() [1/2]

◆ isStokes() [2/2]

◆ LidDrivenCavity()

◆ Linear()

◆ mesh()

◆ momentumForcingTerm() [1/8]

◆ momentumForcingTerm() [2/8]

◆ momentumForcingTerm() [3/8]

◆ momentumForcingTerm() [4/8]

◆ momentumForcingTerm() [5/8]

◆ momentumForcingTerm() [6/8]

◆ momentumForcingTerm() [7/8]

◆ momentumForcingTerm() [8/8]

◆ name()

◆ newtonRaphson()

◆ nloc_sc_p()

◆ nloc_sc_u()

◆ numDirDOFs()

◆ numNonSCDOFs()

◆ numSCDOFs()

◆ numSCDOFs_p()

◆ numSCDOFs_u()

◆ phispace()

◆ pressure() [1/8]

◆ pressure() [2/8]

◆ pressure() [3/8]

◆ pressure() [4/8]

◆ pressure() [5/8]

◆ pressure() [6/8]

◆ pressure() [7/8]