LinearFVDiffusion

Description

This kernel contributes to the system matrix and the right hand side of a system which is solved for a linear finite volume variable MooseVariableLinearFVReal. The contributions can be derived using the integral of the diffusion term in the following form:

where we used the divergence theorem to transform a volumetric integral over cell of a vector field to a sum of surface integrals over the faces of the cell. Furthermore, denotes a space dependent diffusion coefficient. With this, we can use the finite volume approximation for the face integrals in the following way:

where denotes the surface area. Vectors and are determined to respect , where is always parallel to the line connecting the current and neighbor cell centroids. We use the over-relaxed approach for the split of the normal vector, described in Moukalled et al. (2016) and Jasak (1996) in detail. As shown above, using these two vectors, the approximate form of the normal-gradient is typically split into two terms:

  • which describes a contribution that comes from a finite difference approximation of the gradient on orthogonal grids. Hence, it is referred to as an orthogonal contribution. For orthogonal meshes, is just where is the distance between the current and neighbor cell centroids. This term contributes a () to the diagonal and off-diagonal entries of the system matrix with different signs.

  • On non-orthogonal meshes, besides , the following correction term is needed: , where denotes the interpolated gradient at the face center computed using the cell gradients on the current and neighbor cells. This term is treated in an explicit manner meaning that it is added to the right hand side vector of the system.

For more information on the numerical representation of the diffusion term and the different techniques used for applying boundary conditions through this kernel, see Moukalled et al. (2016) and Jasak (1996).

The diffusion coefficient parameter ("diffusion_coeff") accepts anything that supports functor-based evaluations. For more information on functors in MOOSE, see Functor system.

warningwarning

When using non-zero flux boundary condition, only a single LinearFVFluxKernel may be used, as otherwise the boundary conditions may be applied multiple times. This warning applies to all LinearFVFluxKernel-derived classes.

Interpolating material coefficients

By default the diffusion coefficient functor is evaluated directly on each face. You can instead select an interpolation method through the "coeff_interp_method" parameter and an object declared in the [FVInterpolationMethods] block described in FVInterpolationMethod.

[FVInterpolationMethods<<<{"href": "../../syntax/FVInterpolationMethods/index.html"}>>>]
  [harm]
    type = FVHarmonicAverage<<<{"description": "Harmonic mean interpolation for finite-volume quantities using FaceInfo geometry weights.", "href": "../fvinterpolationmethods/FVHarmonicAverage.html"}>>>
  []
[]
(test/tests/linearfvkernels/diffusion/diffusion-1d.i)
[LinearFVKernels<<<{"href": "../../syntax/LinearFVKernels/index.html"}>>>]
  [diffusion]
    type = LinearFVDiffusion<<<{"description": "Represents the matrix and right hand side contributions of a diffusion term in a partial differential equation.", "href": "LinearFVDiffusion.html"}>>>
    variable<<<{"description": "The name of the variable whose linear system this object contributes to"}>>> = u
    diffusion_coeff<<<{"description": "The diffusion coefficient. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = coeff_pos_func
    coeff_interp_method<<<{"description": "Optional finite volume interpolation method used to compute a face-centered diffusion coefficient. If omitted, the functor is evaluated directly on the face."}>>> = harm
  []
[]
(test/tests/linearfvkernels/diffusion/diffusion-1d.i)

Example input syntax

The input file below shows a pure diffusion problem on a two-dimensional domain.

[LinearFVKernels<<<{"href": "../../syntax/LinearFVKernels/index.html"}>>>]
  [diffusion]
    type = LinearFVDiffusion<<<{"description": "Represents the matrix and right hand side contributions of a diffusion term in a partial differential equation.", "href": "LinearFVDiffusion.html"}>>>
    variable<<<{"description": "The name of the variable whose linear system this object contributes to"}>>> = u
    diffusion_coeff<<<{"description": "The diffusion coefficient. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = coeff_func
    use_nonorthogonal_correction<<<{"description": "If the nonorthogonal correction should be used when computing the normal gradient."}>>> = false
  []
  [source]
    type = LinearFVSource<<<{"description": "Represents the matrix and right hand side contributions of a solution-independent source term in a partial differential equation.", "href": "LinearFVSource.html"}>>>
    variable<<<{"description": "The name of the variable whose linear system this object contributes to"}>>> = u
    source_density<<<{"description": "The source density. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = source_func
  []
[]
(test/tests/linearfvkernels/diffusion/diffusion-2d.i)

Input Parameters

  • variableThe name of the variable whose linear system this object contributes to

    C++ Type:LinearVariableName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the variable whose linear system this object contributes to

Required Parameters

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

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

    Controllable:No

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

  • coeff_interp_methodOptional finite volume interpolation method used to compute a face-centered diffusion coefficient. If omitted, the functor is evaluated directly on the face.

    C++ Type:InterpolationMethodName

    Controllable:No

    Description:Optional finite volume interpolation method used to compute a face-centered diffusion coefficient. If omitted, the functor is evaluated directly on the face.

  • diffusion_coeff1The diffusion coefficient. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

    Default:1

    C++ Type:MooseFunctorName

    Unit:(no unit assumed)

    Controllable:No

    Description:The diffusion coefficient. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

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

    Default:False

    C++ Type:bool

    Controllable:No

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

  • use_nonorthogonal_correctionTrueIf the nonorthogonal correction should be used when computing the normal gradient.

    Default:True

    C++ Type:bool

    Controllable:No

    Description:If the nonorthogonal correction should be used when computing the normal gradient.

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>

    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>

    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>

    Controllable:No

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

  • matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Whether this object is only doing assembly to matrices (no vectors)

  • matrix_tagssystemThe tag for the matrices this Kernel should fill

    Default:system

    C++ Type:MultiMooseEnum

    Options:nontime, system

    Controllable:No

    Description:The tag for the matrices this Kernel should fill

  • vector_tagsrhsThe tag for the vectors this Kernel should fill

    Default:rhs

    C++ Type:MultiMooseEnum

    Options:rhs, time

    Controllable:No

    Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

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

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

    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

    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

    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

    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

    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

    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

    Controllable:No

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

Parallel Ghosting Parameters

Input Files

Child Objects

References

  1. Hrvoje Jasak. Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College London (University of London), 1996.[BibTeX]
  2. Fadl Moukalled, L Mangani, Marwan Darwish, and others. The finite volume method in computational fluid dynamics. Volume 6. Springer, 2016.[BibTeX]