VariableTimeIntegrationAux

Integrates a field variable in time.

The integration over time is lead over every quadrature point.

Example syntax

In this example, the VariableTimeIntegrationAux computes the time integral of variable u with a first, second and third order scheme respectively.

[AuxKernels]
  [./MidpointTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_midpoint
    order = 1
  [../]
  [./TrapazoidalTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_trapazoid
    order = 2
  [../]
  [./SimpsonsTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_simpson
    order = 3
  [../]
[]

Input Parameters

variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object applies to
variable_to_integrateThe variable to be integrated
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The variable to be integrated

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
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
coefficient1A simple coefficient multiplying the integral
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:A simple coefficient multiplying the integral
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
order2The order of global truncation error: midpoint=1, trapezoidal=2, Simpson=3
Default:2
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The order of global truncation error: midpoint=1, trapezoidal=2, Simpson=3
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional 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.
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

(moose/test/tests/auxkernels/time_integration/time_integration.i)

# This test covers the usage of the VariableTimeIntegrationAux
# kernel. Here we test three different schemes for integrating a field
# variable in time.  Midpoint, Trapezoidal, and Simpson's rule are
# used.  For this test, we use a manufactured solution and we compare
# the Trapezoidal and Simpson's rule, which must be exact for this
# exact solution, which is a linear function of time.
#
# The set up problem is
#
#  du/dt - Laplacian(u) = Q
#
# with exact solution: u = t*(x*x+y*y).
[Mesh]
  type = GeneratedMesh
  dim = 2
  elem_type = QUAD9
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
[]

[Functions]
  [./dts]
    type = PiecewiseLinear
    x = '0.01 0.1'
    y = '0.005 0.05'
  [../]
[]

[Variables]
  [./u]
    initial_condition = 0.0
    family = LAGRANGE
    order = SECOND
  [../]
[]

[Kernels]
  [./diff]
     type = Diffusion
     variable = u
  [../]
  [./timederivative]
     type = TimeDerivative
     variable = u
  [../]
  [./sourceterm]
     type = BodyForce
     variable = u
     function = Source
  [../]
[]

[AuxVariables]
  [./v_midpoint]
  [../]
  [./v_trapazoid]
  [../]
  [./v_simpson]
  [../]
[]

[AuxKernels]
  [./MidpointTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_midpoint
    order = 1
  [../]
  [./TrapazoidalTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_trapazoid
    order = 2
  [../]
  [./SimpsonsTimeIntegrator]
    type = VariableTimeIntegrationAux
    variable_to_integrate = u
    variable = v_simpson
    order = 3
  [../]
[]

[BCs]
 [./RightBC]
    type = FunctionDirichletBC
    variable = u
    function = RightBC
    boundary = 'right'
 [../]
 [./LeftBC]
    type = FunctionDirichletBC
    variable = u
    function = LeftBC
    boundary = 'left'
 [../]
 [./TopBC]
    type = FunctionDirichletBC
    variable = u
    function = TopBC
    boundary = 'top'
 [../]
 [./BottomBC]
    type = FunctionDirichletBC
    variable = u
    function = BottomBC
    boundary = 'bottom'
 [../]
[]

[Functions]
 [./Soln]
    type = ParsedFunction
    expression = 't*(x*x+y*y)'
 [../]
 [./Source]
    type = ParsedFunction
    expression = '(x*x + y*y) - 4*t'
 [../]
 [./TopBC]
    type = ParsedFunction
    expression = 't*(x*x+1)'
 [../]
 [./BottomBC]
    type = ParsedFunction
    expression = 't*x*x'
 [../]
 [./RightBC]
   type = ParsedFunction
   expression = 't*(y*y+1)'
 [../]
 [./LeftBC]
    type = ParsedFunction
    expression = 't*y*y'
  [../]
[]
[Postprocessors]
  [./l2_error]
    type = NodalL2Error
    variable = u
    function = Soln
  [../]
[]

[Executioner]
  type = Transient

  end_time = 0.1
#  dt = 0.1
#  num_steps = 10
  [./TimeStepper]
     type = FunctionDT
     function = dts
  [../]

  nl_abs_tol = 1.e-15
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
[]

Example syntax
Input Parameters