HArDCore2D::NavierStokes Struct Reference

Class for the Navier-Stokes model. More...

#include <hho-ns.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< 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 IntegralWeight	ViscosityType
typedef Eigen::SparseMatrix< double >	SystemMatrixType
typedef std::function< VectorRd(const VectorRd &)>	MomentumForcingTermType
typedef std::function< double(const VectorRd &)>	CompressibilityForcingTermType
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 IntegralWeight	ViscosityType

Public Member Functions
	NavierStokes (const VHHOSpace &vhho_space, const GlobalDOFSpace &p_space, const BoundaryConditions &BC, bool use_threads, bool stokes=false, std::ostream &output=std::cout)
	Constructor.
void	assembleLinearisedSystem (const NavierStokesSolutions::IExactSolution *isolution, const Eigen::VectorXd &uph_old)
	Assemble the global 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	numNonSCDOFs () const
	Returns the number of DOFs after SC and with Lagrange multiplier, but before eliminating Dirichlet DOFs.
size_t	sizeSystem () const
	Returns the size of the final system with Lagrange multiplier, after application of SC and removal of Dirichlet BCs.
const VHHOSpace &	vhhospace () const
	Returns the velocity space.
const GlobalDOFSpace &	pspace () const
	Returns the pressure space.
const Mesh &	mesh () const
	Returns the mesh.
const SystemMatrixType &	systemMatrix () const
	Returns the linear system matrix.
SystemMatrixType &	systemMatrix ()
	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.
bool &	isStokes ()
	Returns the Stokes status.
Eigen::VectorXd	interpolate (const VelocityType &u, const PressureType &p, 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.
	NavierStokes (const VHHOSpace &vhho_space, const GlobalDOFSpace &p_space, const BoundaryConditions &BC, bool use_threads, bool stokes=false, std::ostream &output=std::cout)
	Constructor.
void	assembleLinearSystem (const MomentumForcingTermType &f, const CompressibilityForcingTermType &g, const ViscosityType &mu, const Eigen::VectorXd &u0, const Eigen::VectorXd &uold, const double &time_step)
	Assemble the global 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	numNonSCDOFs () const
	Returns the number of DOFs after SC and with Lagrange multiplier, but before eliminating Dirichlet DOFs.
size_t	sizeSystem () const
	Returns the size of the final system with Lagrange multiplier, after application of SC and removal of Dirichlet BCs.
const VHHOSpace &	vhhospace () const
	Returns the velocity space.
const GlobalDOFSpace &	pspace () const
	Returns the pressure space.
const Mesh &	mesh () const
	Returns the mesh.
const SystemMatrixType &	systemMatrix () const
	Returns the linear system matrix.
SystemMatrixType &	systemMatrix ()
	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.
bool &	isStokes ()
	Returns the Stokes status.
Eigen::VectorXd	interpolate (const VelocityType &u, const PressureType &p, 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.
Eigen::VectorXd	pressureVertexValues (const Eigen::VectorXd &p) const
	Create vertex values for the pressure (from the element values), for plotting.
void	writeToVtuFile (const Eigen::VectorXd &uph, const Eigen::VectorXd &upI, 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)
	Write solution to vut file.
Eigen::VectorXd	imposingBC (const VelocityType &u, const Eigen::VectorXd &uph) const
	impose boundary conditions
Eigen::VectorXd	newtonRaphson (LinearSolver< NavierStokes::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 ViscosityType &mu, const double &time_step)
	newton method

Detailed Description

Class for the Navier-Stokes model.

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 [1/2]

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

CompressibilityForcingTermType [2/2]

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

MomentumForcingTermType [1/2]

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

MomentumForcingTermType [2/2]

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

PressureGradientType [1/2]

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

PressureGradientType [2/2]

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

PressureType [1/2]

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

PressureType [2/2]

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

SystemMatrixType [1/2]

typedef Eigen::SparseMatrix<double> HArDCore2D::NavierStokes::SystemMatrixType

SystemMatrixType [2/2]

typedef Eigen::SparseMatrix<double> HArDCore2D::NavierStokes::SystemMatrixType

VelocityGradientType [1/2]

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

VelocityGradientType [2/2]

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

VelocityType [1/2]

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

VelocityType [2/2]

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

ViscosityType [1/2]

typedef IntegralWeight HArDCore2D::NavierStokes::ViscosityType

ViscosityType [2/2]

typedef IntegralWeight HArDCore2D::NavierStokes::ViscosityType

Constructor & Destructor Documentation

NavierStokes() [1/2]

NavierStokes::NavierStokes	(	const VHHOSpace &	vhho_space,
		const GlobalDOFSpace &	p_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
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

NavierStokes() [2/2]

HArDCore2D::NavierStokes::NavierStokes	(	const VHHOSpace &	vhho_space,
		const GlobalDOFSpace &	p_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
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

assembleLinearisedSystem()

void NavierStokes::assembleLinearisedSystem	(	const NavierStokesSolutions::IExactSolution *	isolution,
		const Eigen::VectorXd &	uph_old
	)

Assemble the global system

Parameters

isolution	Solution data
uph_old	Velocity at the previous iteration

assembleLinearSystem()

void NavierStokes::assembleLinearSystem	(	const MomentumForcingTermType &	f,
		const CompressibilityForcingTermType &	g,
		const ViscosityType &	mu,
		const Eigen::VectorXd &	u0,
		const Eigen::VectorXd &	uold,
		const double &	time_step
	)

Assemble the global system

Parameters

f	Forcing term
g	Forcing term for the divergence equation
mu	Viscosity

computeEnergyNorms() [1/2]

std::vector< double > NavierStokes::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

computeEnergyNorms() [2/2]

std::vector< double > HArDCore2D::NavierStokes::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

dimPressure() [1/2]

size_t HArDCore2D::NavierStokes::dimPressure ( ) const

inline

Returns the dimension of pressure space.

dimPressure() [2/2]

size_t HArDCore2D::NavierStokes::dimPressure ( ) const

inline

Returns the dimension of pressure space.

dimVelocity() [1/2]

size_t HArDCore2D::NavierStokes::dimVelocity ( ) const

inline

Returns the dimension of velocity space.

dimVelocity() [2/2]

size_t HArDCore2D::NavierStokes::dimVelocity ( ) const

inline

Returns the dimension of velocity space.

imposingBC()

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

impose boundary conditions

interpolate() [1/2]

Eigen::VectorXd NavierStokes::interpolate	(	const VelocityType &	u,
		const PressureType &	p,
		const int	doe_cell = -1,
		const int	doe_face = -1
	)		const

Interpolates velocity and pressure.

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.

interpolate() [2/2]

Eigen::VectorXd HArDCore2D::NavierStokes::interpolate	(	const VelocityType &	u,
		const PressureType &	p,
		const int	doe_cell = -1,
		const int	doe_face = -1
	)		const

Interpolates velocity and pressure.

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::NavierStokes::isStokes ( )

inline

Returns the Stokes status.

isStokes() [2/2]

bool & HArDCore2D::NavierStokes::isStokes ( )

inline

Returns the Stokes status.

mesh() [1/2]

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

inline

Returns the mesh.

mesh() [2/2]

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

inline

Returns the mesh.

newtonRaphson()

Eigen::VectorXd NavierStokes::newtonRaphson	(	LinearSolver< NavierStokes::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 ViscosityType &	mu,
		const double &	time_step
	)

newton method

initializing parameters

nloc_sc_p() [1/2]

size_t HArDCore2D::NavierStokes::nloc_sc_p ( ) const

inline

Returns the local number of pressure statically condensed DOFs.

nloc_sc_p() [2/2]

size_t HArDCore2D::NavierStokes::nloc_sc_p ( ) const

inline

Returns the local number of pressure statically condensed DOFs.

nloc_sc_u() [1/2]

size_t HArDCore2D::NavierStokes::nloc_sc_u ( ) const

inline

Returns the local number of velocity statically condensed DOFs.

nloc_sc_u() [2/2]

size_t HArDCore2D::NavierStokes::nloc_sc_u ( ) const

inline

Returns the local number of velocity statically condensed DOFs.

numDirDOFs() [1/2]

size_t HArDCore2D::NavierStokes::numDirDOFs ( ) const

inline

Returns the number of Dirichlet DOFs.

numDirDOFs() [2/2]

size_t HArDCore2D::NavierStokes::numDirDOFs ( ) const

inline

Returns the number of Dirichlet DOFs.

numNonSCDOFs() [1/2]

size_t HArDCore2D::NavierStokes::numNonSCDOFs ( ) const

inline

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

numNonSCDOFs() [2/2]

size_t HArDCore2D::NavierStokes::numNonSCDOFs ( ) const

inline

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

numSCDOFs() [1/2]

size_t HArDCore2D::NavierStokes::numSCDOFs ( ) const

inline

Returns the number of statically condensed DOFs.

numSCDOFs() [2/2]

size_t HArDCore2D::NavierStokes::numSCDOFs ( ) const

inline

Returns the number of statically condensed DOFs.

numSCDOFs_p() [1/2]

size_t HArDCore2D::NavierStokes::numSCDOFs_p ( ) const

inline

Returns the number of pressure statically condensed DOFs.

numSCDOFs_p() [2/2]

size_t HArDCore2D::NavierStokes::numSCDOFs_p ( ) const

inline

Returns the number of pressure statically condensed DOFs.

numSCDOFs_u() [1/2]

size_t HArDCore2D::NavierStokes::numSCDOFs_u ( ) const

inline

Returns the number of velocity statically condensed DOFs.

numSCDOFs_u() [2/2]

size_t HArDCore2D::NavierStokes::numSCDOFs_u ( ) const

inline

Returns the number of velocity statically condensed DOFs.

pressureVertexValues()

Eigen::VectorXd NavierStokes::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() [1/2]

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

inline

Returns the pressure space.

pspace() [2/2]

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

inline

Returns the pressure space.

scMatrix() [1/2]

const SystemMatrixType & HArDCore2D::NavierStokes::scMatrix ( ) const

inline

Returns the static condensation recovery operator.

scMatrix() [2/2]

const SystemMatrixType & HArDCore2D::NavierStokes::scMatrix ( ) const

inline

Returns the static condensation recovery operator.

scVector() [1/2]

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

inline

Returns the static condensation rhs.

scVector() [2/2]

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

inline

Returns the static condensation rhs.

sizeSystem() [1/2]

size_t HArDCore2D::NavierStokes::sizeSystem ( ) const

inline

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

sizeSystem() [2/2]

size_t HArDCore2D::NavierStokes::sizeSystem ( ) const

inline

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

stabilizationParameter() [1/4]

double & HArDCore2D::NavierStokes::stabilizationParameter ( )

inline

Returns the stabilization parameter.

stabilizationParameter() [2/4]

double & HArDCore2D::NavierStokes::stabilizationParameter ( )

inline

Returns the stabilization parameter.

stabilizationParameter() [3/4]

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

inline

Returns the stabilization parameter (scaling)

stabilizationParameter() [4/4]

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

inline

Returns the stabilization parameter (scaling)

systemMatrix() [1/4]

SystemMatrixType & HArDCore2D::NavierStokes::systemMatrix ( )

inline

Returns the linear system matrix.

systemMatrix() [2/4]

SystemMatrixType & HArDCore2D::NavierStokes::systemMatrix ( )

inline

Returns the linear system matrix.

systemMatrix() [3/4]

const SystemMatrixType & HArDCore2D::NavierStokes::systemMatrix ( ) const

inline

Returns the linear system matrix.

systemMatrix() [4/4]

const SystemMatrixType & HArDCore2D::NavierStokes::systemMatrix ( ) const

inline

Returns the linear system matrix.

systemVector() [1/4]

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

inline

Returns the linear system right-hand side vector.

systemVector() [2/4]

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

inline

Returns the linear system right-hand side vector.

systemVector() [3/4]

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

inline

Returns the linear system right-hand side vector.

systemVector() [4/4]

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

inline

Returns the linear system right-hand side vector.

vhhospace() [1/2]

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

inline

Returns the velocity space.

vhhospace() [2/2]

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

inline

Returns the velocity space.

writeToVtuFile()

void NavierStokes::writeToVtuFile	(	const Eigen::VectorXd &	uph,
		const Eigen::VectorXd &	upI,
		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
	)

Write solution to vut file.

Write solution to vtu file.

---

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

• Schemes/HHO-ns/hho-ns.hpp
• Schemes/HHO-ns/hho-uns.hpp
• Schemes/HHO-ns/hho-ns.cpp
• Schemes/HHO-ns/hho-uns.cpp