PINSFVMomentumFrictionCorrection

Computes a correction term to avoid oscillations from average pressure interpolation in regions of high changes in friction coefficients.

Since the friction corrector in the pressure interpolation scheme is not explained elsewhere, we provide a complete explanation in this document.

Pressure interpolation at the interfaces

Assume de\vec{d}_e to be the vector position of the center node of the current cell, dn\vec{d}_n to be the center node of the neighbor cell, dne=dnde\vec{d}_{ne} = \vec{d}_n - \vec{d}_e to be the distance vector between both cells, and dn,int=dndne\vec{d}_{n,int} = \vec{d}_n - \vec{d}_{ne} and de,int=dedne\vec{d}_{e,int} = \vec{d}_e - \vec{d}_{ne} the distance vectors to the interface. Assuming that the pressure for the collocated node at the current and neighbor cells are pep_e and pnp_n, respectively, the pressure at the interface can be computed as follows:

pne=f(dn,int)pn+g(de,int)pe,p_ne = f(\vec{d}_{n,int}) p_n + g(\vec{d}_{e,int}) p_e \,,

where ff and gg are some generic functions. In MOOSE finite volume, and in cell-centered finite volume methods generally, cell-centered fields are often interpolated to faces using arithmetic means, i.e., f(dn,int)=de,intdnef(\vec{d}_{n,int}) = \frac{|\vec{d}_{e,int}|}{|\vec{d}_{ne}|} and f(de,int)=dn,intdne=1de,intdnef(\vec{d}_{e,int}) = \frac{|\vec{d}_{n,int}|}{|\vec{d}_{ne}|} = 1 - \frac{|\vec{d}_{e,int}|}{|\vec{d}_{ne}|}, which yields:

p~ne=de,intdnepn+dn,intdnepe.\tilde{p}_{ne} = \frac{|\vec{d}_{e,int}|}{|\vec{d}_{ne}|} p_n + \frac{|\vec{d}_{n,int}|}{|\vec{d}_{ne}|} p_e \,.

This interpolation is exact as long as there is no variation in the pressure gradient between the current and neighbor cells. Otherwise, it introduces an interpolation error proportional to the difference in the gradients for the current and neighbor cells and the distance between cells. Large differences in pressure gradient can happen for instance in sharp porous media, due to differences in friction loss and/or effective flow area.

Correction of the interpolated pressure at the interfaces

The pressure correction interpolation is based on the introduction of a correction term provided by considering the upwind and downwind linear interpolation at the cell faces.

Upwinding the pressure from the current cell to the interface yields:

pneu=pe+αcpede,int,p_{ne}^u = p_e + \alpha_c \nabla{p}_e \vec{d}_{e,int} \,,

where αcR+\alpha_c \in \mathbb{R}^+ is a factor that defines the advection character in the pressure interpolation.

Similarly, approximating the pressure at the interface by down-winding from the neighbor yields:

pned=pnαcpndn,int.p_{ne}^d = p_n - \alpha_c \nabla{p}_n \vec{d}_{n,int} \,.

Now we define the interface pressure as the arithmetic means of the upwind and downwind pressures to yield:

pne=de,intdnepned+dn,intdnepneu=de,intdnepn+dn,intdnepeαcde,intdnepndn,int+αcdn,intdnepede,int=p~neαcde,intdnepndn,int+αcdn,intdnepede,intp_{ne} = \frac{|\vec{d}_{e,int}|}{|\vec{d}_{ne}|} p_{ne}^d + \frac{|\vec{d}_{n,int}|}{|\vec{d}_{ne}|} p_{ne}^u = \frac{|\vec{d}_{e,int}|}{|\vec{d}_{ne}|} p_n + \frac{|\vec{d}_{n,int}|}{|\vec{d}_{ne}|} p_e - \alpha_c \frac{|\vec{d}_{e,int}|}{|\vec{d}_{ne}|} \nabla{p}_n \vec{d}_{n,int} + \alpha_c \frac{|\vec{d}_{n,int}|}{|\vec{d}_{ne}|} \nabla{p}_e \vec{d}_{e,int} = \tilde{p}_{ne} - \alpha_c \frac{|\vec{d}_{e,int}|}{|\vec{d}_{ne}|} \nabla{p}_n \vec{d}_{n,int} + \alpha_c \frac{|\vec{d}_{n,int}|}{|\vec{d}_{ne}|} \nabla{p}_e \vec{d}_{e,int}

Next, we approximate the pressure gradients by the body forces as peFe\nabla{p}_e \approx \vec{F}_e and pnFn\nabla{p}_n \approx \vec{F}_n, i.e., we neglect the effects of flow acceleration and inertia on the pressure correction. This yields the following interpolation field for the pressure at the interfaces:

pne=p~ne+αcdne(Fede,intdn,intFndn,intde,int)p_{ne} = \tilde{p}_{ne} + \frac{\alpha_c}{|\vec{d}_{ne}|} (\vec{F}_e \vec{d}_{e,int} |\vec{d}_{n,int}| - \vec{F}_n \vec{d}_{n,int} |\vec{d}_{e,int}|)

Setting the parameter αc\alpha_c

During finite-volume integration, we will sum over the control volume the fluxes at the faces. For the correction in the pressure interpolation this yields:

intαcdne(Fede,intdn,intFndn,intde,int),\sum_{int} \frac{\alpha_c}{|\vec{d}_{ne}|} (\vec{F}_e \vec{d}_{e,int} |\vec{d}_{n,int}| - \vec{F}_n \vec{d}_{n,int} |\vec{d}_{e,int}|) \,,

which defines a diffusion term of the form:

(αcde,intdn,int)F.\nabla \cdot (\alpha_c \vec{d}_{e,int} |\vec{d}_{n,int}|) \nabla \vec{F} \,.

When increasing the value of the advection parameter αc\alpha_c, oscillations are reduced as the arithmetic means interpolation error becomes less significant with respect to the advection interpolation. However, note that in a sharp porous media, the term F\vec{F} may be sharp and discontinuous. Hence, increasing the value of the advection parameter adds stiffness to the problem, which deteriorates the performance of iterative solvers. In practice, a value of alphac10alpha_c \approx 10 have shown good performance in reducing porous-media-driven oscillations without causing convergence issues

Input Parameters

  • momentum_componentThe component of the momentum equation that this kernel applies to.

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:x, y, z

    Controllable:No

    Description:The component of the momentum equation that this kernel applies to.

  • rhie_chow_user_objectThe rhie-chow user-object

    C++ Type:UserObjectName

    Unit:(no unit assumed)

    Controllable:No

    Description:The rhie-chow user-object

  • rhoThe density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

    C++ Type:MooseFunctorName

    Unit:(no unit assumed)

    Controllable:No

    Description:The density. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

  • variableThe name of the variable that this residual object operates on

    C++ Type:NonlinearVariableName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the variable that this residual object operates on

Required Parameters

  • Darcy_nameName of the Darcy coefficients property. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

    C++ Type:MooseFunctorName

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the Darcy coefficients property. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

  • Forchheimer_nameName of the Forchheimer coefficients property. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

    C++ Type:MooseFunctorName

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the Forchheimer coefficients property. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • consistent_scaling1Smoothing scaling parameter to control collocated mesh oscillations

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Smoothing scaling parameter to control collocated mesh oscillations

  • mumuThe dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

    Default:mu

    C++ Type:MooseFunctorName

    Unit:(no unit assumed)

    Controllable:No

    Description:The dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

  • speedThe norm of the interstitial velocity. This is required for Forchheimer calculations. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

    C++ Type:MooseFunctorName

    Unit:(no unit assumed)

    Controllable:No

    Description:The norm of the interstitial velocity. This is required for Forchheimer calculations. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

  • absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution

  • extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The extra tags for the matrices this Kernel should fill

  • extra_vector_tagsThe extra tags for the vectors this Kernel should fill

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The extra tags for the vectors this Kernel should fill

  • matrix_tagssystemThe tag for the matrices this Kernel should fill

    Default:system

    C++ Type:MultiMooseEnum

    Unit:(no unit assumed)

    Options:nontime, system

    Controllable:No

    Description:The tag for the matrices this Kernel should fill

  • vector_tagsnontimeThe tag for the vectors this Kernel should fill

    Default:nontime

    C++ Type:MultiMooseEnum

    Unit:(no unit assumed)

    Options:nontime, time

    Controllable:No

    Description:The tag for the vectors this Kernel should fill

Tagging Parameters

  • boundaries_to_avoidThe set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.

    C++ Type:std::vector<BoundaryName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.

  • boundaries_to_forceThe set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.

    C++ Type:std::vector<BoundaryName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.

  • force_boundary_executionFalseWhether to force execution of this object on all external boundaries.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether to force execution of this object on all external boundaries.

Boundary Execution Modification Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Determines whether this object is calculated using an implicit or explicit form

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The seed for the master random number generator

  • use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

  • ghost_layers1The number of layers of elements to ghost.

    Default:1

    C++ Type:unsigned short

    Unit:(no unit assumed)

    Controllable:No

    Description:The number of layers of elements to ghost.

  • use_point_neighborsFalseWhether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

Parallel Ghosting Parameters