HArDCore3D::NavierStokes Struct Reference

Class to assemble and solve a Navier-Stokes problem. More...

#include <sddr-navier-stokes.hpp>

Public Types
typedef Eigen::SparseMatrix< double >	SystemMatrixType
typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	ForcingTermType
typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	VelocityType
typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	VorticityType
typedef std::function< double(const Eigen::Vector3d &)>	PressureType
typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	PressureGradientType
typedef IntegralWeight	ViscosityType

Public Member Functions
	NavierStokes (const DDRCore &ddrcore, const BoundaryConditions &BC, bool use_threads, std::ostream &output=std::cout)
	Constructor.
Eigen::VectorXd	vectorDirBC (const VelocityType &u, const PressureType &p)
	Create a vector of Dirichlet boundary conditions.
void	computeLinearComponents (const ForcingTermType &f, const VelocityType &u, const VorticityType &omega, const double &reynolds)
	Create the linear part of the system ( curl-curl velocity matrix, vel-grad pressure matrix, and RHS). Needs to be called before assembleLinearSystem.
double	assembleLinearSystem (const Eigen::VectorXd &Xn, const double &reac)
	Assemble the global system at each Newton iteration, and returns the residual (norm of F(Xn)-b)
double	normGlobalRHS (const std::vector< Eigen::VectorXd > &locRHS)
	Computes the norm of a vector (in Xcurl-Xgrad space) from the element-wise contributions to that vector, excluding the Dirichlet components (only the UKN are taken into account in the norm)
Eigen::VectorXd	newtonIncrement (LinearSolver< SystemMatrixType > &solver, const double &navier_scaling, const double &relax, double &norm_dX)
	Solve the linear system and computes the Newton increment (taking into account relaxation)
std::vector< StokesNorms >	computeStokesNorms (const std::vector< Eigen::VectorXd > &list_dofs) const
	Compute the discrete L2 norms, for a family of Eigen::VectorXd representing velocities & pressures, of u, curl u, p and grad p.
std::pair< StokesNorms, StokesNorms >	computeContinuousErrorsNorms (const Eigen::VectorXd &v, const VelocityType &u, const VorticityType &curl_u, const PressureType &p, const PressureGradientType &grad_p) const
	Compute the continuous Hcurl errors in u and Hgrad error in p (1st component), and same with continuous norms (second component)
double	computeFlux (const Eigen::VectorXd &u, const Hull &surface) const
	Compute the flux (based on the polynomial reconstructions) for a discrete velocity across a flat convex hull.
size_t	nDOFs_up () const
	Number of DOFs for velocity and pressure.
size_t	nDOFs_dir_edge_u () const
	Number of DOFs on Dirichlet edges for the velocity.
size_t	nDOFs_dir_face_u () const
	Number of DOFs on Dirichlet faces for the velocity.
size_t	nDOFs_dir_u () const
	Total number of Dirichlet DOFs for the velocity.
size_t	nDOFs_dir_vertex_p () const
	Number of DOFs on Dirichlet vertices for the pressure.
size_t	nDOFs_dir_edge_p () const
	Number of DOFs on Dirichlet edges for the pressure.
size_t	nDOFs_dir_face_p () const
	Number of DOFs on Dirichlet faces for the pressure.
size_t	nDOFs_dir_p () const
	Total number of Dirichlet DOFs for the pressure.
size_t	nSCUKN_u () const
	Number of statically condensed unknowns (velocity)
size_t	nSCUKN_p () const
	Number of statically condensed unknowns (pressure)
size_t	nSCUKN () const
	Number of statically condensed unknowns (both velocity and pressure)
size_t	nUKN_u () const
	Number of velocity unknowns (statically condensed and global, but no Dirichlet)
size_t	nUKN_p () const
	Number of pressure unknowns (statically condensed and global)
size_t	nUKN_lambda () const
	Number of Lagrange multiplier unknowns (1 if BC=N to impose \int p=0, 0 otherwise)
size_t	nUKN_uplambda () const
	Number of unknowns (velocity-pressure-Lagrange multiplier, including statically condensed and globally coupled unknowns)
size_t	nGLUKN_u () const
	Number of globally coupled unknowns for the velocity (statically condensed unknowns removed)
size_t	nGLUKN_p () const
	Number of globally coupled unknowns for the pressure (statically condensed unknowns removed)
size_t	nGLUKN () const
	Number of globally coupled unknowns for velocity, pressure, Lagrange multiplier.
const SXGrad &	sxGrad () const
	Returns the space SXGrad.
const SXCurl &	sxCurl () const
	Returns the space SXCurl.
const SXDiv &	sxDiv () const
	Returns the space XDiv.
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 SystemMatrixType &	scMatrix () const
	Returns the static condensation recovery operator.
Eigen::VectorXd &	scVector ()
	Returns the static condensation rhs.
std::vector< Eigen::VectorXd > &	rhsSourceNaturalBC ()
	Returns local RHS for Stokes problem (useful to compute relative residual)
const double &	stabilizationParameter () const
	Returns the stabilization parameter.
double &	stabilizationParameter ()
	Returns the stabilization parameter.
const bool &	iterativeSolver () const
	Returns the selection of iterative solver.
bool &	iterativeSolver ()
	Returns the selection of iterative solver.
double &	Reynolds ()
	Returns the reynolds number.

Detailed Description

Class to assemble and solve a Navier-Stokes problem.

Member Typedef Documentation

ForcingTermType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::NavierStokes::ForcingTermType

PressureGradientType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::NavierStokes::PressureGradientType

PressureType

typedef std::function<double(const Eigen::Vector3d &)> HArDCore3D::NavierStokes::PressureType

SystemMatrixType

typedef Eigen::SparseMatrix<double> HArDCore3D::NavierStokes::SystemMatrixType

VelocityType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::NavierStokes::VelocityType

ViscosityType

typedef IntegralWeight HArDCore3D::NavierStokes::ViscosityType

VorticityType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::NavierStokes::VorticityType

Constructor & Destructor Documentation

NavierStokes()

NavierStokes::NavierStokes	(	const DDRCore &	ddrcore,
		const BoundaryConditions &	BC,
		bool	use_threads,
		std::ostream &	output = std::cout
	)

Constructor.

Parameters

ddrcore	Core for the DDR space sequence
BC	Type of BC
use_threads	True for parallel execution, false for sequential execution
output	Output stream to print status messages

Member Function Documentation

assembleLinearSystem()

double NavierStokes::assembleLinearSystem	(	const Eigen::VectorXd &	Xn,
		const double &	reac
	)

Assemble the global system at each Newton iteration, and returns the residual (norm of F(Xn)-b)

Parameters

Xn	State in the Newton iteration
reac	Coefficient of mass matrix for pseudo-temporal iterations

computeContinuousErrorsNorms()

std::pair< StokesNorms, StokesNorms > NavierStokes::computeContinuousErrorsNorms	(	const Eigen::VectorXd &	v,
		const VelocityType &	u,
		const VorticityType &	curl_u,
		const PressureType &	p,
		const PressureGradientType &	grad_p
	)		const

Compute the continuous Hcurl errors in u and Hgrad error in p (1st component), and same with continuous norms (second component)

Parameters

v	The vector, contains both velocity and pressure
u	Continuous velocity
curl_u	Curl of continuous velocity
p	Continuous pressure
grad_p	Grad of continuous pressure

computeFlux()

double NavierStokes::computeFlux	(	const Eigen::VectorXd &	u,
		const Hull &	surface
	)		const

Compute the flux (based on the polynomial reconstructions) for a discrete velocity across a flat convex hull.

Parameters

u	Discrete vector (in Xcurl) of the velocity
surface	Surface, described as a convex hull, across which the flux is computed

computeLinearComponents()

void NavierStokes::computeLinearComponents	(	const ForcingTermType &	f,
		const VelocityType &	u,
		const VorticityType &	omega,
		const double &	reynolds
	)

Create the linear part of the system ( curl-curl velocity matrix, vel-grad pressure matrix, and RHS). Needs to be called before assembleLinearSystem.

Parameters

f	Forcing term
u	Boundary condition on velocity
omega	Boundary condition on vorticity
reynolds	Reynolds number for BC on vorticity

computeStokesNorms()

std::vector< StokesNorms > NavierStokes::computeStokesNorms

(

const std::vector< Eigen::VectorXd > &

list_dofs

)

const

Compute the discrete L2 norms, for a family of Eigen::VectorXd representing velocities & pressures, of u, curl u, p and grad p.

Parameters

list_dofs

List of vectors representing velocities and pressures

iterativeSolver() [1/2]

bool & HArDCore3D::NavierStokes::iterativeSolver ( )

inline

Returns the selection of iterative solver.

iterativeSolver() [2/2]

const bool & HArDCore3D::NavierStokes::iterativeSolver ( ) const

inline

Returns the selection of iterative solver.

nDOFs_dir_edge_p()

size_t HArDCore3D::NavierStokes::nDOFs_dir_edge_p ( ) const

inline

Number of DOFs on Dirichlet edges for the pressure.

nDOFs_dir_edge_u()

size_t HArDCore3D::NavierStokes::nDOFs_dir_edge_u ( ) const

inline

Number of DOFs on Dirichlet edges for the velocity.

nDOFs_dir_face_p()

size_t HArDCore3D::NavierStokes::nDOFs_dir_face_p ( ) const

inline

Number of DOFs on Dirichlet faces for the pressure.

nDOFs_dir_face_u()

size_t HArDCore3D::NavierStokes::nDOFs_dir_face_u ( ) const

inline

Number of DOFs on Dirichlet faces for the velocity.

nDOFs_dir_p()

size_t HArDCore3D::NavierStokes::nDOFs_dir_p ( ) const

inline

Total number of Dirichlet DOFs for the pressure.

nDOFs_dir_u()

size_t HArDCore3D::NavierStokes::nDOFs_dir_u ( ) const

inline

Total number of Dirichlet DOFs for the velocity.

nDOFs_dir_vertex_p()

size_t HArDCore3D::NavierStokes::nDOFs_dir_vertex_p ( ) const

inline

Number of DOFs on Dirichlet vertices for the pressure.

nDOFs_up()

size_t HArDCore3D::NavierStokes::nDOFs_up ( ) const

inline

Number of DOFs for velocity and pressure.

newtonIncrement()

Eigen::VectorXd NavierStokes::newtonIncrement	(	LinearSolver< SystemMatrixType > &	solver,
		const double &	navier_scaling,
		const double &	relax,
		double &	norm_dX
	)

Solve the linear system and computes the Newton increment (taking into account relaxation)

Parameters

solver	Linear solver to use
navier_scaling	Scaling of the Navier term
relax	Relaxation parameter
norm_dX	Norm of the increment dX (before applying relaxation)

nGLUKN()

size_t HArDCore3D::NavierStokes::nGLUKN ( ) const

inline

Number of globally coupled unknowns for velocity, pressure, Lagrange multiplier.

nGLUKN_p()

size_t HArDCore3D::NavierStokes::nGLUKN_p ( ) const

inline

Number of globally coupled unknowns for the pressure (statically condensed unknowns removed)

nGLUKN_u()

size_t HArDCore3D::NavierStokes::nGLUKN_u ( ) const

inline

Number of globally coupled unknowns for the velocity (statically condensed unknowns removed)

normGlobalRHS()

double NavierStokes::normGlobalRHS

(

const std::vector< Eigen::VectorXd > &

locRHS

)

Computes the norm of a vector (in Xcurl-Xgrad space) from the element-wise contributions to that vector, excluding the Dirichlet components (only the UKN are taken into account in the norm)

Parameters

locRHS

List of local contributions

nSCUKN()

size_t HArDCore3D::NavierStokes::nSCUKN ( ) const

inline

Number of statically condensed unknowns (both velocity and pressure)

nSCUKN_p()

size_t HArDCore3D::NavierStokes::nSCUKN_p ( ) const

inline

Number of statically condensed unknowns (pressure)

nSCUKN_u()

size_t HArDCore3D::NavierStokes::nSCUKN_u ( ) const

inline

Number of statically condensed unknowns (velocity)

nUKN_lambda()

size_t HArDCore3D::NavierStokes::nUKN_lambda ( ) const

inline

Number of Lagrange multiplier unknowns (1 if BC=N to impose \int p=0, 0 otherwise)

nUKN_p()

size_t HArDCore3D::NavierStokes::nUKN_p ( ) const

inline

Number of pressure unknowns (statically condensed and global)

nUKN_u()

size_t HArDCore3D::NavierStokes::nUKN_u ( ) const

inline

Number of velocity unknowns (statically condensed and global, but no Dirichlet)

nUKN_uplambda()

size_t HArDCore3D::NavierStokes::nUKN_uplambda ( ) const

inline

Number of unknowns (velocity-pressure-Lagrange multiplier, including statically condensed and globally coupled unknowns)

Reynolds()

double & HArDCore3D::NavierStokes::Reynolds ( )

inline

Returns the reynolds number.

rhsSourceNaturalBC()

std::vector< Eigen::VectorXd > & HArDCore3D::NavierStokes::rhsSourceNaturalBC ( )

inline

Returns local RHS for Stokes problem (useful to compute relative residual)

scMatrix()

const SystemMatrixType & HArDCore3D::NavierStokes::scMatrix ( ) const

inline

Returns the static condensation recovery operator.

scVector()

Eigen::VectorXd & HArDCore3D::NavierStokes::scVector ( )

inline

Returns the static condensation rhs.

stabilizationParameter() [1/2]

double & HArDCore3D::NavierStokes::stabilizationParameter ( )

inline

Returns the stabilization parameter.

stabilizationParameter() [2/2]

const double & HArDCore3D::NavierStokes::stabilizationParameter ( ) const

inline

Returns the stabilization parameter.

sxCurl()

const SXCurl & HArDCore3D::NavierStokes::sxCurl ( ) const

inline

Returns the space SXCurl.

sxDiv()

const SXDiv & HArDCore3D::NavierStokes::sxDiv ( ) const

inline

Returns the space XDiv.

sxGrad()

const SXGrad & HArDCore3D::NavierStokes::sxGrad ( ) const

inline

Returns the space SXGrad.

systemMatrix() [1/2]

SystemMatrixType & HArDCore3D::NavierStokes::systemMatrix ( )

inline

Returns the linear system matrix.

systemMatrix() [2/2]

const SystemMatrixType & HArDCore3D::NavierStokes::systemMatrix ( ) const

inline

Returns the linear system matrix.

systemVector() [1/2]

Eigen::VectorXd & HArDCore3D::NavierStokes::systemVector ( )

inline

Returns the linear system right-hand side vector.

systemVector() [2/2]

const Eigen::VectorXd & HArDCore3D::NavierStokes::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

vectorDirBC()

Eigen::VectorXd NavierStokes::vectorDirBC	(	const VelocityType &	u,
		const PressureType &	p
	)

Create a vector of Dirichlet boundary conditions.

The vector has dimension velocity-pressure and zero everywhere except for Dirichlet DOFs on the velocity and pressure

Parameters

u	BC on velocity
p	BC on pressure

---

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

• Schemes/DDR-navier-stokes/sddr-navier-stokes.hpp
• Schemes/DDR-navier-stokes/sddr-navier-stokes.cpp