LinearFVTimeDerivative

Description

This kernel represents a time derivative term in a partial differential equation discretized using the finite volume method:

var element = document.getElementById("moose-equation-da56193a-c94c-42d5-beb1-0ccb17394c7e");katex.render("\\int\\limits_{V_C} \\frac{\\partial cu}{\\partial t} dV \\approx \\left(\\frac{\\partial cu}{\\partial t}\\right)_C V_C~,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-208dc31a-79ce-4c5c-9b42-6fc03218c209");katex.render("\\left(\\frac{\\partial cu}{\\partial t}\\right)_C", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-ee22a4b2-cfd2-4530-9c92-c2be91dcc5da");katex.render("V_C", element, {displayMode:false,throwOnError:false});$ are the time derivative of the field value at the cell center and the cell volume, respectively. Note that we added a multiplier, $var element = document.getElementById("moose-equation-35aecd56-34db-4638-9d19-6ca0365b2b83");katex.render("c", element, {displayMode:false,throwOnError:false});$ which often represents a material property. A good example for the multiplier can be the density in the momentum equation in the Navier Stokes equation. This can be defined through parameter "factor" that accepts anything that supports functor-based evaluations. For more information on functors in MOOSE, see Functor system. This kernel adds to the matrix diagonal and right hand side of a linear system and the contributions depend on the method chosen for time integration. For more information on available methods, see the TimeIntegrators page. For example, with an implicit Euler scheme the contribution to the right hand side becomes:

var element = document.getElementById("moose-equation-cb4d1337-effa-41ca-81ea-93be03bfab2b");katex.render("\\frac{c_C}{\\Delta t}V_C,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-ee3bf101-dcbd-4261-ae59-97394529dd17");katex.render("\\Delta t", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-e853a536-8fbd-4b72-adf6-e1999243d1b0");katex.render("c_C", element, {displayMode:false,throwOnError:false});$ are the time step size and multiplier at the cell center, respectively. With these, the contribution to the right hand side becomes:

var element = document.getElementById("moose-equation-fc8169c9-4965-4790-8930-e9f93e356050");katex.render("\\frac{c_C u_{old,C}}{\\Delta t}V_C,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-70c76cbb-d037-46e3-a520-68f89ceddd10");katex.render("u_{old,C}", element, {displayMode:false,throwOnError:false});$ represents the solution at the previous time step.

Example Syntax

The case below demonstrates the use of LinearFVTimeDerivative used in a simple linear time-dependent diffusion problem:

[LinearFVKernels]
  [ie]
    type = LinearFVTimeDerivative
    variable = u
  []
  [diff]
    type = LinearFVDiffusion
    variable = u
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = forcing_fn
  []
[]

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>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
factor1A multiplier on the variable within the time derivative. 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
Unit:(no unit assumed)
Controllable:No
Description:A multiplier on the variable within the time derivative. A functor is any of the following: a variable, a functor material property, a function, a post-processor, or a number.

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/time_integrators/implicit-euler/ie-linearfv.i)

###########################################################
# This is a simple test with a time-dependent problem
# demonstrating the use of the TimeIntegrator system.
#
# Testing a solution that is second order in space
# and first order in time
#
# @Requirement F1.30
###########################################################

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 10
  ny = 10
[]

[Problem]
  linear_sys_names = 'u_sys'
[]

[Variables]
  [u]
    type = MooseLinearVariableFVReal
    solver_sys = 'u_sys'
    initial_condition = 0.0
  []
[]

[Functions]
  [forcing_fn]
    type = ParsedFunction
    expression = ((x*x)+(y*y))-(4*t)
  []
  [exact_fn]
    type = ParsedFunction
    expression = t*((x*x)+(y*y))
  []
[]

[LinearFVKernels]
  [ie]
    type = LinearFVTimeDerivative
    variable = u
  []
  [diff]
    type = LinearFVDiffusion
    variable = u
  []
  [source]
    type = LinearFVSource
    variable = u
    source_density = forcing_fn
  []
[]

[LinearFVBCs]
  [all]
    type = LinearFVAdvectionDiffusionFunctorDirichletBC
    variable = u
    boundary = '0 1 2 3'
    functor = exact_fn
  []
[]

[Postprocessors]
  [l2_err]
    type = ElementL2Error
    variable = u
    function = exact_fn
  []
[]

[Executioner]
  type = Transient

  system_names = u_sys
  l_tol = 1e-10

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'

  # Test of the TimeIntegrator System
  scheme = 'implicit-euler'

  start_time = 0.0
  num_steps = 5
  dt = 0.25
[]

[Outputs]
  exodus = true
[]

Description
Example Syntax
Input Parameters