Test problem for the staggered grid (Kovasznay 1948, [38]) More...

#include <test/freeflow/navierstokes/kovasznay/problem.hh>

Inheritance diagram for Dumux::KovasznayTestProblem< TypeTag >:

Description

template<class TypeTag>
class Dumux::KovasznayTestProblem< TypeTag >

Test problem for the staggered grid (Kovasznay 1948, [38])

A two-dimensional Navier-Stokes flow with a periodicity in one direction is considered. The set-up represents a wake behind a two-dimensional grid and is chosen in a way such that an exact solution is available.

Public Member Functions
	KovasznayTestProblem (std::shared_ptr< const GridGeometry > gridGeometry)

Scalar	temperatureAtPos (const GlobalPosition &globalPos) const
	Returns the temperature \(\mathrm{[K]}\) at a given global position. More...

const GravityVector &	gravity () const
	Returns the acceleration due to gravity. More...

bool	enableInertiaTerms () const
	Returns whether interia terms should be considered. More...

template<class SolutionVector , class G = GridGeometry>
std::enable_if< G::discMethod==DiscretizationMethod::staggered, void >::type	applyInitialFaceSolution (SolutionVector &sol, const SubControlVolumeFace &scvf, const PrimaryVariables &initSol) const
	Applys the initial face solution (velocities on the faces). Specialization for staggered grid discretization. More...

Scalar	pseudo3DWallFriction (const Scalar velocity, const Scalar viscosity, const Scalar height, const Scalar factor=8.0) const
	An additional drag term can be included as source term for the momentum balance to mimic 3D flow behavior in 2D: More...

template<class ElementVolumeVariables , class ElementFaceVariables , class G = GridGeometry>
std::enable_if< G::discMethod==DiscretizationMethod::staggered, Scalar >::type	pseudo3DWallFriction (const SubControlVolumeFace &scvf, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars, const Scalar height, const Scalar factor=8.0) const
	Convenience function for staggered grid implementation. More...

Scalar	permeability (const Element &element, const SubControlVolumeFace &scvf) const
	Returns the intrinsic permeability of required as input parameter for the Beavers-Joseph-Saffman boundary condition. More...

Scalar	alphaBJ (const SubControlVolumeFace &scvf) const
	Returns the alpha value required as input parameter for the Beavers-Joseph-Saffman boundary condition. More...

Scalar	betaBJ (const Element &element, const SubControlVolumeFace &scvf) const
	Returns the alpha value required as input parameter for the Beavers-Joseph-Saffman boundary condition. More...

Scalar	velocityPorousMedium (const Element &element, const SubControlVolumeFace &scvf) const
	Returns the velocity in the porous medium (which is 0 by default according to Saffmann). More...

const Scalar	bjsVelocity (const Element &element, const SubControlVolume &scv, const SubControlVolumeFace &faceOnPorousBoundary, const Scalar velocitySelf) const
	helper function to evaluate the slip velocity on the boundary when the Beavers-Joseph-Saffman condition is used More...

const Scalar	beaversJosephVelocity (const Element &element, const SubControlVolume &scv, const SubControlVolumeFace &faceOnPorousBoundary, const Scalar velocitySelf, const Scalar tangentialVelocityGradient) const
	helper function to evaluate the slip velocity on the boundary when the Beavers-Joseph condition is used More...

Problem parameters
bool	shouldWriteRestartFile () const

void	printL2Error (const SolutionVector &curSol) const

Scalar	temperature () const
	Returns the temperature within the domain in [K]. More...

NumEqVector	sourceAtPos (const GlobalPosition &globalPos) const
	Returns the sources within the domain. More...

Boundary conditions
BoundaryTypes	boundaryTypesAtPos (const GlobalPosition &globalPos) const
	Specifies which kind of boundary condition should be used for which equation on a given boundary control volume. More...

bool	isDirichletCell (const Element &element, const FVElementGeometry &fvGeometry, const SubControlVolume &scv, int pvIdx) const
	Returns whether a fixed Dirichlet value shall be used at a given cell. More...

PrimaryVariables	dirichletAtPos (const GlobalPosition &globalPos) const
	Returns Dirichlet boundary values at a given position. More...

PrimaryVariables	analyticalSolution (const GlobalPosition &globalPos) const
	Returns the analytical solution of the problem at a given position. More...

Volume terms
PrimaryVariables	initialAtPos (const GlobalPosition &globalPos) const
	Evaluates the initial value for a control volume. More...

auto &	getAnalyticalPressureSolution () const
	Returns the analytical solution for the pressure. More...

auto &	getAnalyticalVelocitySolution () const
	Returns the analytical solution for the velocity. More...

auto &	getAnalyticalVelocitySolutionOnFace () const
	Returns the analytical solution for the velocity at the faces. More...

Constructor & Destructor Documentation

◆ KovasznayTestProblem()

template<class TypeTag >

Dumux::KovasznayTestProblem< TypeTag >::KovasznayTestProblem ( std::shared_ptr< const GridGeometry > gridGeometry )

inline

Member Function Documentation

◆ alphaBJ()

template<class TypeTag >

Scalar Dumux::NavierStokesProblem< TypeTag >::alphaBJ ( const SubControlVolumeFace & scvf ) const

inlineinherited

Returns the alpha value required as input parameter for the Beavers-Joseph-Saffman boundary condition.

This member function must be overloaded in the problem implementation, if the BJS boundary condition is used.

◆ analyticalSolution()

template<class TypeTag >

PrimaryVariables Dumux::KovasznayTestProblem< TypeTag >::analyticalSolution ( const GlobalPosition & globalPos ) const

inline

Returns the analytical solution of the problem at a given position.

Parameters

globalPos The global position

◆ applyInitialFaceSolution()

template<class TypeTag >

template<class SolutionVector , class G = GridGeometry>

std::enable_if< G::discMethod==DiscretizationMethod::staggered, void >::type Dumux::NavierStokesProblem< TypeTag >::applyInitialFaceSolution	(	SolutionVector &	sol,
		const SubControlVolumeFace &	scvf,
		const PrimaryVariables &	initSol
	)		const

inlineinherited

Applys the initial face solution (velocities on the faces). Specialization for staggered grid discretization.

◆ beaversJosephVelocity()

template<class TypeTag >

const Scalar Dumux::NavierStokesProblem< TypeTag >::beaversJosephVelocity	(	const Element &	element,
		const SubControlVolume &	scv,
		const SubControlVolumeFace &	faceOnPorousBoundary,
		const Scalar	velocitySelf,
		const Scalar	tangentialVelocityGradient
	)		const

inlineinherited

helper function to evaluate the slip velocity on the boundary when the Beavers-Joseph condition is used

◆ betaBJ()

template<class TypeTag >

Scalar Dumux::NavierStokesProblem< TypeTag >::betaBJ	(	const Element &	element,
		const SubControlVolumeFace &	scvf
	)		const

inlineinherited

Returns the alpha value required as input parameter for the Beavers-Joseph-Saffman boundary condition.

This member function must be overloaded in the problem implementation, if the BJS boundary condition is used.

◆ bjsVelocity()

template<class TypeTag >

const Scalar Dumux::NavierStokesProblem< TypeTag >::bjsVelocity	(	const Element &	element,
		const SubControlVolume &	scv,
		const SubControlVolumeFace &	faceOnPorousBoundary,
		const Scalar	velocitySelf
	)		const

inlineinherited

helper function to evaluate the slip velocity on the boundary when the Beavers-Joseph-Saffman condition is used

Deprecated:: "Use beaversJosephVelocity(element, scv, faceOnPorousBoundary, velocitySelf, tangentialVelocityGradient) instead"

◆ boundaryTypesAtPos()

template<class TypeTag >

BoundaryTypes Dumux::KovasznayTestProblem< TypeTag >::boundaryTypesAtPos ( const GlobalPosition & globalPos ) const

inline

Specifies which kind of boundary condition should be used for which equation on a given boundary control volume.

Parameters

globalPos The position of the center of the finite volume

◆ dirichletAtPos()

template<class TypeTag >

PrimaryVariables Dumux::KovasznayTestProblem< TypeTag >::dirichletAtPos ( const GlobalPosition & globalPos ) const

inline

Returns Dirichlet boundary values at a given position.

Parameters

globalPos The global position

◆ enableInertiaTerms()

template<class TypeTag >

bool Dumux::NavierStokesProblem< TypeTag >::enableInertiaTerms ( ) const

inlineinherited

Returns whether interia terms should be considered.

◆ getAnalyticalPressureSolution()

template<class TypeTag >

auto & Dumux::KovasznayTestProblem< TypeTag >::getAnalyticalPressureSolution ( ) const

inline

Returns the analytical solution for the pressure.

◆ getAnalyticalVelocitySolution()

template<class TypeTag >

auto & Dumux::KovasznayTestProblem< TypeTag >::getAnalyticalVelocitySolution ( ) const

inline

Returns the analytical solution for the velocity.

◆ getAnalyticalVelocitySolutionOnFace()

template<class TypeTag >

auto & Dumux::KovasznayTestProblem< TypeTag >::getAnalyticalVelocitySolutionOnFace ( ) const

inline

Returns the analytical solution for the velocity at the faces.

◆ gravity()

template<class TypeTag >

const GravityVector & Dumux::NavierStokesProblem< TypeTag >::gravity ( ) const

inlineinherited

Returns the acceleration due to gravity.

If the Problem.EnableGravity parameter is true, this means \(\boldsymbol{g} = ( 0,\dots,\ -9.81)^T \), else \(\boldsymbol{g} = ( 0,\dots, 0)^T \)

◆ initialAtPos()

template<class TypeTag >

PrimaryVariables Dumux::KovasznayTestProblem< TypeTag >::initialAtPos ( const GlobalPosition & globalPos ) const

inline

Evaluates the initial value for a control volume.

Parameters

globalPos The global position

◆ isDirichletCell()

template<class TypeTag >

bool Dumux::KovasznayTestProblem< TypeTag >::isDirichletCell	(	const Element &	element,
		const FVElementGeometry &	fvGeometry,
		const SubControlVolume &	scv,
		int	pvIdx
	)		const

inline

Returns whether a fixed Dirichlet value shall be used at a given cell.

Parameters

element	The finite element
fvGeometry	The finite-volume geometry
scv	The sub control volume
pvIdx	The primary variable index in the solution vector

◆ permeability()

template<class TypeTag >

Scalar Dumux::NavierStokesProblem< TypeTag >::permeability	(	const Element &	element,
		const SubControlVolumeFace &	scvf
	)		const

inlineinherited

Returns the intrinsic permeability of required as input parameter for the Beavers-Joseph-Saffman boundary condition.

This member function must be overloaded in the problem implementation, if the BJS boundary condition is used.

◆ printL2Error()

template<class TypeTag >

void Dumux::KovasznayTestProblem< TypeTag >::printL2Error ( const SolutionVector & curSol ) const

inline

◆ pseudo3DWallFriction() [1/2]

template<class TypeTag >

Scalar Dumux::NavierStokesProblem< TypeTag >::pseudo3DWallFriction	(	const Scalar	velocity,
		const Scalar	viscosity,
		const Scalar	height,
		const Scalar	factor = `8.0`
	)		const

inlineinherited

An additional drag term can be included as source term for the momentum balance to mimic 3D flow behavior in 2D:

\[ f_{drag} = -(8 \mu / h^2)v \]

Here, \(h\) corresponds to the extruded height that is bounded by the imaginary walls. See Flekkoy et al. (1995) [25]
A value of 8.0 is used as a default factor, corresponding to the velocity profile at the center plane of the virtual height (maximum velocity). Setting this value to 12.0 corresponds to an depth-averaged velocity (Venturoli and Boek, 2006) [74].

◆ pseudo3DWallFriction() [2/2]

template<class TypeTag >

template<class ElementVolumeVariables , class ElementFaceVariables , class G = GridGeometry>

std::enable_if< G::discMethod==DiscretizationMethod::staggered, Scalar >::type Dumux::NavierStokesProblem< TypeTag >::pseudo3DWallFriction	(	const SubControlVolumeFace &	scvf,
		const ElementVolumeVariables &	elemVolVars,
		const ElementFaceVariables &	elemFaceVars,
		const Scalar	height,
		const Scalar	factor = `8.0`
	)		const

inlineinherited

Convenience function for staggered grid implementation.

◆ shouldWriteRestartFile()

template<class TypeTag >

bool Dumux::KovasznayTestProblem< TypeTag >::shouldWriteRestartFile ( ) const

inline

◆ sourceAtPos()

template<class TypeTag >

NumEqVector Dumux::KovasznayTestProblem< TypeTag >::sourceAtPos ( const GlobalPosition & globalPos ) const

inline

Returns the sources within the domain.

Parameters

globalPos The global position

◆ temperature()

template<class TypeTag >

Scalar Dumux::KovasznayTestProblem< TypeTag >::temperature ( ) const

inline

Returns the temperature within the domain in [K].

This problem assumes a temperature of 10 degrees Celsius.

◆ temperatureAtPos()

template<class TypeTag >

Scalar Dumux::NavierStokesProblem< TypeTag >::temperatureAtPos ( const GlobalPosition & globalPos ) const

inlineinherited

Returns the temperature \(\mathrm{[K]}\) at a given global position.

This is not specific to the discretization. By default it just calls temperature().

Parameters

globalPos The position in global coordinates where the temperature should be specified.

◆ velocityPorousMedium()

template<class TypeTag >

Scalar Dumux::NavierStokesProblem< TypeTag >::velocityPorousMedium	(	const Element &	element,
		const SubControlVolumeFace &	scvf
	)		const

inlineinherited

Returns the velocity in the porous medium (which is 0 by default according to Saffmann).

The documentation for this class was generated from the following file:

test/freeflow/navierstokes/kovasznay/problem.hh

Description

Public Member Functions

Volume terms

Constructor & Destructor Documentation

◆ KovasznayTestProblem()

Member Function Documentation

◆ alphaBJ()

◆ analyticalSolution()

◆ applyInitialFaceSolution()

◆ beaversJosephVelocity()

◆ betaBJ()

◆ bjsVelocity()

◆ boundaryTypesAtPos()

◆ dirichletAtPos()

◆ enableInertiaTerms()

◆ getAnalyticalPressureSolution()

◆ getAnalyticalVelocitySolution()

◆ getAnalyticalVelocitySolutionOnFace()

◆ gravity()

◆ initialAtPos()

◆ isDirichletCell()

◆ permeability()

◆ printL2Error()

◆ pseudo3DWallFriction() [1/2]

◆ pseudo3DWallFriction() [2/2]

◆ shouldWriteRestartFile()

◆ sourceAtPos()

◆ temperature()

◆ temperatureAtPos()

◆ velocityPorousMedium()