TimeDerivative

Description

The TimeDerivative kernel implements a simple time derivative for the domain $var element = document.getElementById("moose-equation-60deca0d-9540-4a00-b008-3414ff291bc0");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ given by

$(1)var element = document.getElementById("moose-equation-c4e192eb-73ad-4ae0-8d87-76fbc2ef68f2");katex.render("\\underbrace{\\frac{\\partial u}{\\partial t}}_{\\textrm{TimeDerivative}} + \\sum_{i=1}^n \\beta_i = 0 \\in \\Omega.", element, {displayMode:true,throwOnError:false});$ 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

$(2)var element = document.getElementById("moose-equation-b5b31060-e0fb-4718-bd42-6c02d3129527");katex.render("R_i(u_h) = (\\psi_i, \\frac{\\partial u_h}{\\partial t}) \\quad \\forall \\psi_i,", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-186152d6-7285-4d78-ba54-fa7de192a3c3");katex.render("u_h", element, {displayMode:false,throwOnError:false});$ is the approximate solution and $var element = document.getElementById("moose-equation-98410f67-03f0-454c-acc8-db9d4eac1932");katex.render("\\psi_i", element, {displayMode:false,throwOnError:false});$ is a finite element test function.

The Jacobian is given by

$(3)var element = document.getElementById("moose-equation-06947aa3-9377-4f67-9ee1-e6edf84e4e35");katex.render("\\frac{\\partial R_i(u_h)}{\\partial u_j} = (\\psi_i, a\\phi_j).", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-95d119f1-790a-4436-ac94-97535c71f4c2");katex.render("a", element, {displayMode:false,throwOnError:false});$ 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 Kernel operates on
C++ Type:NonlinearVariableName
Description:The name of the variable that this Kernel operates on

Required Parameters

lumpingFalseTrue for mass matrix lumping, false otherwise
Default:False
C++ Type:bool
Description:True for mass matrix lumping, false otherwise
blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Description:The list of block ids (SubdomainID) that this object will be applied

Optional Parameters

enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
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
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.)
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
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.
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Description:Adds user-defined labels for accessing object parameters via control logic.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Description:The seed for the master random number generator
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
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.)
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Description:Determines whether this object is calculated using an implicit or explicit form

Advanced Parameters

vector_tagstimeThe tag for the vectors this Kernel should fill
Default:time
C++ Type:MultiMooseEnum
Description:The tag for the vectors this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
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
Description:The tag for the matrices this Kernel should fill
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Description:The extra tags for the matrices this Kernel should fill

Tagging Parameters

Description
Example Syntax
Input Parameters