SinDirichletBC

Imposes a time-varying essential boundary condition $var element = document.getElementById("moose-equation-069809df-8029-469e-ba1e-83c4cf6b6052");katex.render("u=g(t)", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-e7d2483f-059a-4e66-a9da-4a3bba6bb13c");katex.render("g(t)", element, {displayMode:false,throwOnError:false});$ varies from an given initial value at time $var element = document.getElementById("moose-equation-293a3834-5f76-40b4-a703-9f44aae626d7");katex.render("t=0", element, {displayMode:false,throwOnError:false});$ to a given final value over a specified duration.

Description

SinDirichletBC is a NodalBC which imposes a time-varying boundary value of the form

$var element = document.getElementById("moose-equation-4e67debe-0f67-4605-84c2-4c4d9c6f6b1a");katex.render(" g(t) = \\left\\{ \\begin{array}{ll} g_0 + (g_T - g_0) \\sin \\left( \\frac{\\pi t}{2T} \\right), & 0 < t \\leq T \\\\ g_T, & t \\geq T \\end{array} \\right.", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-93a4b45b-e1a7-424d-91b9-3cd877f4df78");katex.render("g_0", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-90b788d1-17ce-4e13-a8b5-7c27cec5163c");katex.render("g_T", element, {displayMode:false,throwOnError:false});$ are the initial and final values of $var element = document.getElementById("moose-equation-4c4e1a7d-d7cf-458c-be1f-e46744f80284");katex.render("g", element, {displayMode:false,throwOnError:false});$ , respectively, and $var element = document.getElementById("moose-equation-78855b95-7506-47cb-80ee-d2e3b0fdc87c");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the final time. These values are controlled by the initial, final, and duration parameters, respectively. The value is applied on one or more sidesets specified by the boundary parameter and does not vary in space. This type of boundary condition is applicable to time-varying PDEs, for example:

$var element = document.getElementById("moose-equation-a5c811aa-5c22-45b5-989b-a38cea197fbe");katex.render("\\begin{aligned} \\frac{\\partial u}{\\partial t} -\\nabla^2 u &= f && \\quad \\in \\Omega \\\\ u &= g(t) && \\quad \\in \\partial \\Omega \\end{aligned}", element, {displayMode:true,throwOnError:false});$

and is frequently used to "ramp" a difficult boundary condition to its final value over a short time interval, rather than imposing it instantaneously at time $var element = document.getElementById("moose-equation-42af22a3-ae33-4ac4-a50c-f0e79dc4999d");katex.render("t=0", element, {displayMode:false,throwOnError:false});$ . This approach can make nonlinear solvers more robust by improving the initial guess used by the Newton iterations, as well as preventing the solver from converging to non-physical solutions in nonlinear PDEs.

Example Input Syntax

[BCs]
  active = 'left right'

  [./left]
    type = SinDirichletBC
    variable = u
    boundary = 3
    initial = 0.0
    final = 1.0
    duration = 10.0
  [../]

  [./right]
    type = SinDirichletBC
    variable = u
    boundary = 1
    initial = 1.0
    final = 0.0
    duration = 10.0
  [../]
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
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

diag_save_inThe name of auxiliary variables to save this BC'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 BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
duration0
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
final0
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
initial0
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
save_inThe name of auxiliary variables to save this BC'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 BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

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_tagsresidualThe tag for the vectors this Kernel should fill
Default:residual
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:nontime, time, residual
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

(moose/test/tests/bcs/sin_bc/sin_dirichlet_test.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  nz = 0
  zmin = 0
  zmax = 0
  elem_type = QUAD4
[]

[Functions]
  [./initial_value]
    type = ParsedFunction
    expression = 'x'
  [../]
[]

[Variables]
  active = 'u'

  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = FunctionIC
      function = initial_value
    [../]
  [../]
[]

[Kernels]
  active = 'diff ie'

  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./ie]
    type = TimeDerivative
    variable = u
  [../]
[]

[BCs]
  active = 'left right'

  [./left]
    type = SinDirichletBC
    variable = u
    boundary = 3
    initial = 0.0
    final = 1.0
    duration = 10.0
  [../]

  [./right]
    type = SinDirichletBC
    variable = u
    boundary = 1
    initial = 1.0
    final = 0.0
    duration = 10.0
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  num_steps = 10
  dt = 1.0
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters