TimeDerivative

Description

The TimeDerivative kernel implements a simple time derivative for the domain $var element = document.getElementById("moose-equation-aa139d10-f114-4fc8-bb3f-8cfdc7e75b42");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ given by

$var element = document.getElementById("moose-equation-3b8b4e7c-5fee-42ec-aa3c-8184934bbb51");katex.render("\\underbrace{\\frac{\\partial u}{\\partial t}}_{\\textrm{TimeDerivative}} + \\sum_{i=1}^n \\beta_i = 0 \\in \\Omega.", element, {displayMode:true,throwOnError:false});$ where the second term on the left hand side corresponds to the strong forms of other kernels. The corresponding TimeDerivative weak form using inner-product notation is

$var element = document.getElementById("moose-equation-81c8197a-4de6-43eb-9204-252227d6862a");katex.render("R_i(u_h) = (\\psi_i, \\frac{\\partial u_h}{\\partial t}) \\quad \\forall \\psi_i,", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-5461bcb6-c37f-4628-a35b-b88efcb14145");katex.render("u_h", element, {displayMode:false,throwOnError:false});$ is the approximate solution and $var element = document.getElementById("moose-equation-5b682572-3043-40a5-8652-84b803b4997a");katex.render("\\psi_i", element, {displayMode:false,throwOnError:false});$ is a finite element test function.

The Jacobian is given by

$var element = document.getElementById("moose-equation-ba6bf767-4b84-40b4-b270-e0ee4cc79ba7");katex.render("\\frac{\\partial R_i(u_h)}{\\partial u_j} = (\\psi_i, a\\phi_j).", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-669db0b1-39d7-4b4f-adf0-18d4c519e11f");katex.render("a", element, {displayMode:false,throwOnError:false});$ is referred to as du_dot_du in MOOSE syntax. More information about time kernels can be found on the Kernels description page.

Example Syntax

Time derivative terms are ubiquitous in any transient simulation. The kernel block for a transient advection-diffusion-reaction problem that demonstrates the TimeDerivative syntax is shown below:

[Kernels]

  active = 'trans advection diffusion source'

  [./trans]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = Advection0
    variable = phi
    Au = 10.
    Bu = -6.
    Cu = 5.
    Av = 10.
    Bv = 8.
    Cv = -1.
  [../]

  [./diffusion]
    type = Diffusion0
    variable = phi
    Ak = 10.
    Bk = 0.1
    Ck = 0.1
  [../]

  [./source]
    type = ForcingFunctionXYZ0
    variable = phi
    omega0 = 2.
    A0 = 1.
    B0 = 1.2
    C0 = 0.8
    Au = 10.
    Bu = -6.
    Cu = 5.
    Av = 10.
    Bv = 8.
    Cv = -1.
    Ak = 10.
    Bk = 0.1
    Ck = 0.1
  [../]
[]

Input Parameters

variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

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
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
lumpingFalseTrue for mass matrix lumping, false otherwise
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:True for mass matrix lumping, false otherwise
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

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_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, system, time
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, 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.
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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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
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
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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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
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/kernels/adv_diff_reaction/adv_diff_reaction_transient_test.i)

[Mesh]
  dim              = 2
  file             = Mesh12.e
[]

[Variables]
  active = 'phi'

  [./phi]
    order  = SECOND
    family = LAGRANGE
  [../]

[]

[Kernels]

  active = 'trans advection diffusion source'

  [./trans]
    type     = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type     = Advection0
    variable = phi
    Au       = 10.
    Bu       = -6.
    Cu       =  5.
    Av       = 10.
    Bv       =  8.
    Cv       = -1.
  [../]

  [./diffusion]
    type     = Diffusion0
    variable = phi
    Ak       = 10.
    Bk       = 0.1
    Ck       = 0.1
  [../]

  [./source]
    type     = ForcingFunctionXYZ0
    variable = phi
    omega0   = 2.
    A0       = 1.
    B0       = 1.2
    C0       = 0.8
    Au       = 10.
    Bu       = -6.
    Cu       =  5.
    Av       = 10.
    Bv       =  8.
    Cv       = -1.
    Ak       = 10.
    Bk       = 0.1
    Ck       = 0.1
  [../]

[]

[BCs]

  active = 'btm_sca rgt_sca top_sca lft_sca'

  [./btm_sca]
    type     = DirichletBCfuncXYZ0
    variable = phi
    boundary = 1
    omega0   = 2.
    A0       = 1.
    B0       = 1.2
    C0       = 0.8
  [../]

  [./rgt_sca]
    type     = DirichletBCfuncXYZ0
    variable = phi
    boundary = 2
    omega0   = 2.
    A0       = 1.
    B0       = 1.2
    C0       = 0.8
  [../]

  [./top_sca]
    type     = DirichletBCfuncXYZ0
    variable = phi
    boundary = 3
    omega0   = 2.
    A0       = 1.
    B0       = 1.2
    C0       = 0.8
  [../]

  [./lft_sca]
    type     = DirichletBCfuncXYZ0
    variable = phi
    boundary = 4
    omega0   = 2.
    A0       = 1.
    B0       = 1.2
    C0       = 0.8
  [../]

[]

[Executioner]
  type                 = Transient #Steady
  scheme               = bdf2
  nl_rel_tol           = 1e-10

  solve_type = 'PJFNK'

  petsc_options_iname  = '-pc_factor_levels -pc_factor_mat_ordering_type'
  petsc_options_value  = '20 rcm'

  start_time      = 0.0
  end_time        = 1.
  num_steps       = 60000
  dt              = .2
  n_startup_steps = 0
[]

[Outputs]
  exodus = true
[]

Description
Example Syntax
Input Parameters