Class for Navier-Stokes model. More...

#include <hho-nsa.hpp>

Public Types
typedef Eigen::SparseMatrix< double >	systemMatrixType

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

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

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

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

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

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

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

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

typedef IntegralWeight	ViscosityType

Public Member Functions
	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	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	assembleLinearDGSystem (const CompressibilityForcingTermType &h, const Eigen::VectorXd &uprho, const VolumicFractionType &rho, const double &time_step)
	DG ADVECTION SYSTEM.

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

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

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

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

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

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

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

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

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

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

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

size_t	sizeSystemDG () const

const VHHOSpace &	vhhospace () const
	Returns the velocity space.

const GlobalDOFSpace &	pspace () const
	Returns the pressure space.

const GlobalDOFSpace &	phispace () const
	Returns the pressure space.

const Mesh &	mesh () const
	Returns the mesh.

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

systemMatrixType &	systemMatrixHHO ()
	Returns the linear system matrix.

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

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

const double &	stabilizationParameter () const
	Returns the stabilization parameter (scaling)

double &	stabilizationParameter ()
	Returns the stabilization parameter.

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

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

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

systemMatrixType &	systemMatrixDG ()
	Returns the linear system matrix.

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

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

bool &	isStokes ()
	Returns the Stokes status.

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

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

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

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

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

double	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	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

Detailed Description

Class for Navier-Stokes model.

The global unknowns are in the following order:

Dirichlets dofs of the velocity (Dirichlet faces must be numbered first in the mesh)
Face and then element unknowns of the velocity
Element unknowns of the pressure
Lagrange multiplier The statically condenseds dofs for the velocity are the element unknowns of the velocity, and all dofs but the first one in each element for the pressure.

Member 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

Constructor & Destructor Documentation

◆ 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

Member 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

◆ 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

◆ 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

◆ 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()

bool & HArDCore2D::VarDensityNavierStokes::isStokes ( )

inline

Returns the Stokes status.

◆ mesh()

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

inline

Returns the mesh.

◆ 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.

◆ 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.

◆ 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.

◆ vhhospace()

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

inline

Returns the velocity space.

◆ 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.

The documentation for this struct was generated from the following files:

Schemes/HHO-ns/hho-nsa.hpp
Schemes/HHO-ns/hho-nsa.cpp

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ CompressibilityForcingTermType

◆ DensityForcingTermType

◆ MomentumForcingTermType

◆ PressureGradientType

◆ PressureType

◆ systemMatrixType

◆ VelocityGradientType

◆ VelocityType

◆ ViscosityType

◆ VolumicFractionType

Constructor & Destructor Documentation

◆ VarDensityNavierStokes()

Member Function Documentation

◆ assembleLinearDGSystem()

◆ assembleLinearHHOSystem()

◆ computeDGNorms()

◆ computeEnergyNorms()

◆ computePhysicalEnergies()

◆ computePressureL2Norm()

◆ dimPressure()

◆ dimVelocity()

◆ dimVolumicFraction()

◆ getUpwindDensity()

◆ imposingBC()

◆ interpolate()

◆ isStokes()

◆ mesh()

◆ newtonRaphson()

◆ nloc_sc_p()

◆ nloc_sc_u()

◆ numDirDOFs()

◆ numNonSCDOFs()

◆ numSCDOFs()

◆ numSCDOFs_p()

◆ numSCDOFs_u()

◆ phispace()

◆ pressureVertexValues()

◆ pspace()

◆ scMatrix()

◆ scVector()

◆ sizeSystemDG()

◆ sizeSystemHHO()

◆ stabilizationParameter() [1/2]

◆ stabilizationParameter() [2/2]

◆ systemMatrixDG() [1/2]

◆ systemMatrixDG() [2/2]

◆ systemMatrixHHO() [1/2]

◆ systemMatrixHHO() [2/2]

◆ systemVector() [1/2]

◆ systemVector() [2/2]

◆ systemVectorDG() [1/2]

◆ systemVectorDG() [2/2]

◆ vhhospace()

◆ volumicFractionVertexValues()

◆ writeFileHeader()

◆ writeTimeStepData()

◆ writeToVtuFile()