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3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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Test for the 1-D Navier-Stokes model with an analytical solution. More...
#include <test/freeflow/navierstokes/channel/1d/problem.hh>
Test for the 1-D Navier-Stokes model with an analytical solution.
The 1-D analytic solution is given by
\[ p = 2 - 2 \cdot x \]
\[ v_\text{x} = 2 \cdot x^3 \]
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Public Member Functions | |
| NavierStokesAnalyticProblem (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 typename GridGeometry::LocalView &fvGeometry, const typename GridGeometry::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... | |
| const DimVector | v (const DimVector &globalPos) const |
| The velocity. More... | |
| const DimMatrix | dvdx (const DimVector &globalPos) const |
| The velocity gradient. More... | |
| const DimMatrix | dv2dx (const DimVector &globalPos) const |
| The gradient of the velocity squared (using product rule -> nothing to do here) More... | |
| const DimMatrix | dvdx2 (const DimVector &globalPos) const |
| The gradient of the velocity gradient. More... | |
| const Scalar | p (const DimVector &globalPos) const |
| The pressure. More... | |
| const DimVector | dpdx (const DimVector &globalPos) const |
| The pressure gradient. 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... | |
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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.
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Returns the analytical solution of the problem at a given position.
| globalPos | The global position |
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inlineinherited |
Applys the initial face solution (velocities on the faces). Specialization for staggered grid discretization.
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inlineinherited |
helper function to evaluate the slip velocity on the boundary when the Beavers-Joseph condition is used
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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.
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inlineinherited |
helper function to evaluate the slip velocity on the boundary when the Beavers-Joseph-Saffman condition is used
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Specifies which kind of boundary condition should be used for which equation on a given boundary control volume.
| globalPos | The position of the center of the finite volume |
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Returns Dirichlet boundary values at a given position.
| globalPos | The global position |
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The pressure gradient.
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The gradient of the velocity squared (using product rule -> nothing to do here)
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The velocity gradient.
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The gradient of the velocity gradient.
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Returns whether interia terms should be considered.
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Returns the analytical solution for the pressure.
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Returns the analytical solution for the velocity.
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Returns the analytical solution for the velocity at the faces.
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Returns the acceleration due to gravity.
If the Problem.EnableGravity parameter is true, this means \(\boldsymbol{g} = ( 0,\dots,\ -9.81)^T \), else \(\boldsymbol{g} = ( 0,\dots, 0)^T \)
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Evaluates the initial value for a control volume.
| globalPos | The global position |
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Returns whether a fixed Dirichlet value shall be used at a given cell.
| element | The finite element |
| fvGeometry | The finite-volume geometry |
| scv | The sub control volume |
| pvIdx | The primary variable index in the solution vector |
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The pressure.
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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.
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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].
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Convenience function for staggered grid implementation.
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Returns the sources within the domain.
| globalPos | The global position |
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Returns the temperature within the domain in [K].
This problem assumes a temperature of 10 degrees Celsius.
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Returns the temperature \(\mathrm{[K]}\) at a given global position.
This is not specific to the discretization. By default it just calls temperature().
| globalPos | The position in global coordinates where the temperature should be specified. |
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The velocity.
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Returns the velocity in the porous medium (which is 0 by default according to Saffmann).
1.9.3