- variableThe name of the variable whose linear system this object contributes to
C++ Type:LinearVariableName
Controllable:No
Description:The name of the variable whose linear system this object contributes to
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.
Example input syntax
The input file below shows a pure diffusion problem on a two-dimensional domain.
[LinearFVKernels]
[diffusion]
type = LinearFVDiffusion
variable = u
diffusion_coeff = coeff_func
use_nonorthogonal_correction = false
[]
[source]
type = LinearFVSource
variable = u
source_density = source_func
[]
[]
Input 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
- diffusion_coeff1The diffusion coefficient. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
Default:1
C++ Type:MooseFunctorName
Controllable:No
Description:The diffusion coefficient. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.
- 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_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
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
Controllable:No
Description:The tag for the vectors this Kernel should fill
Tagging 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
References
- 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]
- Fadl Moukalled, L Mangani, Marwan Darwish, and others.
The finite volume method in computational fluid dynamics.
Volume 6.
Springer, 2016.[BibTeX]