LinearFVAdvection

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 discretized term of the advection term:

var element = document.getElementById("moose-equation-270ef22c-9b4e-41a8-b8a3-5e081cbbc597");katex.render("\\int_{V_C} \\nabla \\cdot (u \\vec{v}) dV = \\sum_f\\int\\limits_{S_f} u \\vec{v}\\cdot \\vec{n} dS \\approx \\sum_f u_f\\vec{v}\\cdot \\vec{n}_f|S_f|,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-41e3a1c3-3622-4715-889e-e677eac377d2");katex.render("V_C", element, {displayMode:false,throwOnError:false});$ is a cell in the mesh, while $var element = document.getElementById("moose-equation-9c123ccd-8aec-4f99-a215-1e9cb9bf5177");katex.render("\\vec{v}", element, {displayMode:false,throwOnError:false});$ is a pre-defined constant advecting velocity that can be supplied through the "velocity" parameter. The face value of the variable $var element = document.getElementById("moose-equation-22b8d664-583d-4ca4-914e-6f94d4423af8");katex.render("u_f", element, {displayMode:false,throwOnError:false});$ is computed using the user-selected interpolation technique that can be supplied through the "advected_interp_method" parameter.

In the simplest case, using a linear interpolation method and an internal face for the integration, we get the following matrix contribution to the degree of freedom corresponding to the variable on $var element = document.getElementById("moose-equation-bd760a3f-9c38-42c9-b6a5-96edd0f4e0d3");katex.render("V_C", element, {displayMode:false,throwOnError:false});$ :

var element = document.getElementById("moose-equation-639d983a-9539-4e1c-a74d-58a43119f15b");katex.render("\\vec{v} \\cdot \\vec{n}_f |S_f| g_{C,f},", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-10fc2e43-910f-4895-befb-24519904d89c");katex.render("g_C", element, {displayMode:false,throwOnError:false});$ is the geometric interpolation weight for the interpolation. Similarly, the same term contributes to the degree of freedom on the other side of the face with:

var element = document.getElementById("moose-equation-c49fc135-389f-4a21-bb6c-668cebd98793");katex.render("\\vec{v} \\cdot \\vec{n}_f |S_f| (1-g_{C,f}).", element, {displayMode:true,throwOnError:false});

Example input syntax

This example describes a pure advection problem with a source term on a 2D mesh.

[LinearFVKernels]
  [advection]
    type = LinearFVAdvection
    variable = u
    velocity = "0.5 0 0"
    advected_interp_method = upwind
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_func
  []
[]

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
velocityConstant advection velocity
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:Constant advection velocity

Required Parameters

advected_interp_methodupwindThe interpolation to use for the advected quantity. Options are 'upwind', 'average', 'sou' (for second-order upwind), 'min_mod', 'vanLeer', 'quick', 'venkatakrishnan', and 'skewness-corrected' with the default being 'upwind'.
Default:upwind
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:average, upwind, sou, min_mod, vanLeer, quick, venkatakrishnan, skewness-corrected
Controllable:No
Description:The interpolation to use for the advected quantity. Options are 'upwind', 'average', 'sou' (for second-order upwind), 'min_mod', 'vanLeer', 'quick', 'venkatakrishnan', and 'skewness-corrected' with the default being 'upwind'.
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
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.

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_tagsrhsThe tag for the vectors this Kernel should fill
Default:rhs
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:rhs, time
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>
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

(moose/test/tests/linearfvkernels/advection/advection-2d.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny= 1
    ymax = 0.5
  []
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    initial_condition = 1.0
  []
[]

[LinearFVKernels]
  [advection]
    type = LinearFVAdvection
    variable = u
    velocity = "0.5 0 0"
    advected_interp_method = upwind
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = source_func
  []
[]

[LinearFVBCs]
  [inflow]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = "left top bottom"
    functor = analytic_solution
  []
  [outflow]
    type = LinearFVAdvectionDiffusionOutflowBC
    variable = u
    boundary = "right"
    use_two_term_expansion = false
  []
[]

[Functions]
  [source_func]
    type = ParsedFunction
    expression = '0.5*pi*sin(2*y*pi)*cos(x*pi)'
  []
  [analytic_solution]
    type = ParsedFunction
    expression = 'sin(x*pi)*sin(2*y*pi) + 1.5'
  []
[]

[Postprocessors]
  [error]
    type = ElementL2FunctorError
    approximate = u
    exact = analytic_solution
    execute_on = FINAL
  []
  [h]
    type = AverageElementSize
    execute_on = FINAL
  []
[]

[Convergence]
  [linear]
    type = IterationCountConvergence
    max_iterations = 1
    converge_at_max_iterations = true
  []
[]

[Executioner]
  type = Steady
  system_names = u_sys
  l_abs_tol = 1e-10
  multi_system_fixed_point=true
  multi_system_fixed_point_convergence=linear
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       NONZERO               1e-10'
[]

[Outputs]
  [csv]
    type = CSV
    execute_on = FINAL
  []
[]

Description
Example input syntax
Input Parameters