Test problem for the one-phase (Navier-) Stokes model in a 3D or pseudo 3D channel. More...

#include <test/freeflow/navierstokes/channel/3d/problem.hh>

Inheritance diagram for Dumux::ThreeDChannelTestProblem< TypeTag >:

Description

template<class TypeTag>
class Dumux::ThreeDChannelTestProblem< TypeTag >

Test problem for the one-phase (Navier-) Stokes model in a 3D or pseudo 3D channel.

Flow from left to right in a three-dimensional channel is considered. At the inlet (left) and outlet (right) fixed values for pressure are set. The channel is confined by solid walls at all other sides of the domain which corresponds to no-slip/no-flow conditions. The value of an analytical solution for the given flow configuration is furthermore provided. For sake of efficiency, the 3D problem can be reduced to a two-dimensional one by including an additional wall friction term to the momentum balance (Flekkoy et al., 1995 [25]).

Public Member Functions
	ThreeDChannelTestProblem (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
Scalar	temperature () const
	Returns the temperature within the domain in [K]. More...

template<class ElementVolumeVariables , class ElementFaceVariables >
NumEqVector	source (const Element &element, const FVElementGeometry &fvGeometry, const ElementVolumeVariables &elemVolVars, const ElementFaceVariables &elemFaceVars, const SubControlVolumeFace &scvf) const

Scalar	extrusionFactorAtPos (const GlobalPosition &pos) const

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...

PrimaryVariables	dirichletAtPos (const GlobalPosition &globalPos) const
	Evaluates the boundary conditions for a Dirichlet control volume. More...

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

Scalar	analyticalFlux () const
	Returns the analytical solution for the flux through the rectangular channel. More...

Constructor & Destructor Documentation

◆ ThreeDChannelTestProblem()

template<class TypeTag >

Dumux::ThreeDChannelTestProblem< TypeTag >::ThreeDChannelTestProblem ( 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.

◆ analyticalFlux()

template<class TypeTag >

Scalar Dumux::ThreeDChannelTestProblem< TypeTag >::analyticalFlux ( ) const

inline

Returns the analytical solution for the flux through the rectangular channel.

◆ 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::ThreeDChannelTestProblem< 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::ThreeDChannelTestProblem< TypeTag >::dirichletAtPos ( const GlobalPosition & globalPos ) const

inline

Evaluates the boundary conditions for a Dirichlet control volume.

Parameters

globalPos The center of the finite volume which ought to be set.

◆ enableInertiaTerms()

template<class TypeTag >

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

inlineinherited

Returns whether interia terms should be considered.

◆ extrusionFactorAtPos()

template<class TypeTag >

Scalar Dumux::ThreeDChannelTestProblem< TypeTag >::extrusionFactorAtPos ( const GlobalPosition & pos ) const

inline

◆ 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::ThreeDChannelTestProblem< TypeTag >::initialAtPos ( const GlobalPosition & globalPos ) const

inline

Evaluates the initial value for a control volume.

Parameters

globalPos The global position

◆ 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.

◆ 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.

◆ source()

template<class TypeTag >

template<class ElementVolumeVariables , class ElementFaceVariables >

NumEqVector Dumux::ThreeDChannelTestProblem< TypeTag >::source	(	const Element &	element,
		const FVElementGeometry &	fvGeometry,
		const ElementVolumeVariables &	elemVolVars,
		const ElementFaceVariables &	elemFaceVars,
		const SubControlVolumeFace &	scvf
	)		const

inline

◆ temperature()

template<class TypeTag >

Scalar Dumux::ThreeDChannelTestProblem< 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/channel/3d/problem.hh

Description

Public Member Functions

Boundary conditions

Constructor & Destructor Documentation

◆ ThreeDChannelTestProblem()

Member Function Documentation

◆ alphaBJ()

◆ analyticalFlux()

◆ applyInitialFaceSolution()

◆ beaversJosephVelocity()

◆ betaBJ()

◆ bjsVelocity()

◆ boundaryTypesAtPos()

◆ dirichletAtPos()

◆ enableInertiaTerms()

◆ extrusionFactorAtPos()

◆ gravity()

◆ initialAtPos()

◆ permeability()

◆ pseudo3DWallFriction() [1/2]

◆ pseudo3DWallFriction() [2/2]

◆ source()

◆ temperature()

◆ temperatureAtPos()

◆ velocityPorousMedium()