VectorCoupledTimeDerivative

Time derivative Kernel that acts on a coupled vector variable. Weak form: $var element = document.getElementById("moose-equation-943bb2e6-a4f7-4078-a280-7839ff7f701f");katex.render("(\\vec{\\psi}_i, \\frac{\\partial \\vec{v_h}}{\\partial t})", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ .

Overview

The VectorCoupledTimeDerivative kernel is very similar to the VectorTimeDerivative kernel with the exception that the time derivative operator is applied to a coupled variable $var element = document.getElementById("moose-equation-89a2412c-a602-46a3-8bb8-d143224d0bbf");katex.render("\\vec{v}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ instead of the variable $var element = document.getElementById("moose-equation-b5b112d9-9a12-4882-93d8-749214f5ae3c");katex.render("\\vec{u}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ to whom's residual the VectorCoupledTimeDerivative kernel contributes. Consequently, the strong form on the the domain $var element = document.getElementById("moose-equation-58d49af9-f24a-47b7-80de-5f2997f12a75");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is

$(1)var element = document.getElementById("moose-equation-e92eadab-47c9-4c00-a086-4b7ffacaed21");katex.render("\\underbrace{\\frac{\\partial \\vec{v}}{\\partial t}}_{\\textrm{VectorCoupledTimeDerivative}} + \\sum_{i=1}^n \\beta_i = 0 \\in \\Omega ", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where the second term on the left hand side corresponds to the strong forms of other kernels. The VectorCoupledTimeDerivative weak form is then

$(2)var element = document.getElementById("moose-equation-4a42f318-b65c-46b6-b5c4-55c80c14bde8");katex.render("R_i(\\vec{u}_h) = \\bigg(\\vec{\\psi}_i, \\frac{\\partial \\vec{v}_h}{\\partial t}\\bigg) \\quad \\forall \\vec{\\psi}_i, ", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where the $var element = document.getElementById("moose-equation-fe7f3970-0ad1-41b1-b411-2cfeaaed80bd");katex.render("\\vec{\\psi}_i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are test functions and $var element = document.getElementById("moose-equation-0cc32b71-77ed-4233-815d-d4597cc9b6d7");katex.render("\\vec{u}_h", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the finite element solution of the weak formulation.

The Jacobian contribution is equal to $var element = document.getElementById("moose-equation-4eaf2d2d-f40a-4128-b889-da5ddceeed96");katex.render("\\frac{\\partial R_i(\\vec{u}_h)}{\\partial u_j} = (\\vec{\\psi}_i, a_v\\vec{\\phi}_j).", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-d42425e3-a8fe-4b9b-84a1-a6b3263de8a2");katex.render("a_v", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a constant that depends on the time stepping scheme; $var element = document.getElementById("moose-equation-e97f3244-e1c9-48e5-b11e-ddcadf416a10");katex.render("a_v", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is denoted by _dv_dot in the VectorCoupledTimeDerivative class.

Example Input File Syntax

[Kernels]
  [./time_u]
    type = VectorTimeDerivative
    variable = u
  [../]
  [./fn_u]
    type = VectorBodyForce
    variable = u
    function_x = 1
    function_y = 1
  [../]
  [./time_v]
    type = VectorCoupledTimeDerivative
    variable = v
    v = u
  [../]
  [./diff_v]
    type = VectorDiffusion
    variable = v
  [../]
[]

/opt/civet/build_0/moose/test/tests/kernels/coupled_time_derivative/vector_coupled_time_derivative_test.i

###########################################################
# This is a simple test of the VectorCoupledTimeDerivative kernel.
# The expected solution for the vector variable v is
# v_x(x) = 1/2 * (x^2 + x)
# v_y(x) = 1/2 * (x^2 + x)
###########################################################

[Mesh]
  type = GeneratedMesh
  nx = 5
  ny = 5
  dim = 2
[]

[Variables]
  [./u]
    family = LAGRANGE_VEC
  [../]
  [./v]
    family = LAGRANGE_VEC
  [../]
[]

[Kernels]
  [./time_u]
    type = VectorTimeDerivative
    variable = u
  [../]
  [./fn_u]
    type = VectorBodyForce
    variable = u
    function_x = 1
    function_y = 1
  [../]
  [./time_v]
    type = VectorCoupledTimeDerivative
    variable = v
    v = u
  [../]
  [./diff_v]
    type = VectorDiffusion
    variable = v
  [../]
[]

[BCs]
  [./left]
    type = VectorDirichletBC
    variable = v
    boundary = 'left'
    values = '0 0 0'
  [../]
  [./right]
    type = VectorDirichletBC
    variable = v
    boundary = 'right'
    values = '1 1 0'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

Input Parameters

vCoupled vector variable
C++ Type:std::vector
Options:
Description:Coupled vector variable
variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this Kernel operates on

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
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
Options:
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

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
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
Options:
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
Options:nontime system
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
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

test/tests/kernels/coupled_time_derivative/vector_coupled_time_derivative_test.i

test/tests/kernels/coupled_time_derivative/vector_coupled_time_derivative_test.i

###########################################################
# This is a simple test of the VectorCoupledTimeDerivative kernel.
# The expected solution for the vector variable v is
# v_x(x) = 1/2 * (x^2 + x)
# v_y(x) = 1/2 * (x^2 + x)
###########################################################

[Mesh]
  type = GeneratedMesh
  nx = 5
  ny = 5
  dim = 2
[]

[Variables]
  [./u]
    family = LAGRANGE_VEC
  [../]
  [./v]
    family = LAGRANGE_VEC
  [../]
[]

[Kernels]
  [./time_u]
    type = VectorTimeDerivative
    variable = u
  [../]
  [./fn_u]
    type = VectorBodyForce
    variable = u
    function_x = 1
    function_y = 1
  [../]
  [./time_v]
    type = VectorCoupledTimeDerivative
    variable = v
    v = u
  [../]
  [./diff_v]
    type = VectorDiffusion
    variable = v
  [../]
[]

[BCs]
  [./left]
    type = VectorDirichletBC
    variable = v
    boundary = 'left'
    values = '0 0 0'
  [../]
  [./right]
    type = VectorDirichletBC
    variable = v
    boundary = 'right'
    values = '1 1 0'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

Overview
Example Input File Syntax
Input Parameters
Input Files

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