SinDirichletBC

Imposes a time-varying essential boundary condition $var element = document.getElementById("moose-equation-1a287787-6d1a-4657-8467-69e6b0fa54fd");katex.render("u=g(t)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , where $var element = document.getElementById("moose-equation-25d39b09-25fd-4ea1-94de-9c8a5dd60c16");katex.render("g(t)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ varies from an given initial value at time $var element = document.getElementById("moose-equation-3eba7e95-ef20-4ea8-87aa-1bf93fbb33c0");katex.render("t=0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ to a given final value over a specified duration.

Description

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

$var element = document.getElementById("moose-equation-eee88ebc-ec0a-4106-9993-87e816220982");katex.render(" g(t) = \\left\\{ \\begin{array}{ll} g_0 + (g_T - g_0) \\sin \\left( \\frac{\\pi t}{2T} \\right), & 0 < t \\leq T \\\\ g_T, & t \\geq T \\end{array} \\right.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-ba9404bc-a6d1-471e-9b68-d940d68f3401");katex.render("g_0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-c497f2a7-6db7-4bed-b1a7-3bdd34a1c6c9");katex.render("g_T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are the initial and final values of $var element = document.getElementById("moose-equation-d63e4f7a-709b-403e-b811-95692cfff26d");katex.render("g", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , respectively, and $var element = document.getElementById("moose-equation-78e57f99-7432-454a-8261-f9c50255161a");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 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:

$var element = document.getElementById("moose-equation-227f8abf-93e4-4ca5-8ec3-306961b09cf1");katex.render("\\begin{aligned} \\frac{\\partial u}{\\partial t} -\\nabla^2 u &= f && \\quad \\in \\Omega \\\\ u &= g(t) && \\quad \\in \\partial \\Omega \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

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 $var element = document.getElementById("moose-equation-bfac832c-4183-4b8b-9acb-33b75250b2cc");katex.render("t=0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . 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<<<{"href": "../../syntax/BCs/index.html"}>>>]
  active<<<{"description": "If specified only the blocks named will be visited and made active"}>>> = 'left right'

  [./left]
    type = SinDirichletBC<<<{"description": "Imposes a time-varying essential boundary condition $u=g(t)$, where $g(t)$ varies from an given initial value at time $t=0$ to a given final value over a specified duration.", "href": "SinDirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 3
    initial = 0.0
    final = 1.0
    duration = 10.0
  [../]

  [./right]
    type = SinDirichletBC<<<{"description": "Imposes a time-varying essential boundary condition $u=g(t)$, where $g(t)$ varies from an given initial value at time $t=0$ to a given final value over a specified duration.", "href": "SinDirichletBC.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = u
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 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>
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
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
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>
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>
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>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill

Contribution To Tagged Field Data Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
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
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
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
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
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

matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
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
Options:nontime, time, residual
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

(test/tests/bcs/misc_bcs/weak_gradient_bc_test.i)
(test/tests/bcs/sin_bc/sin_dirichlet_test.i)
(modules/chemical_reactions/examples/calcium_bicarbonate/calcium_bicarbonate.i)

(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
[]

(test/tests/bcs/misc_bcs/weak_gradient_bc_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 top bottom'

  [./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
  [../]

  # Explicit Natural Boundary Conditions
  [./top]
    type = WeakGradientBC
    variable = u
    boundary = 2
  [../]

  [./bottom]
    type = WeakGradientBC
    variable = u
    boundary = 0
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  num_steps = 10
  dt = 1.0
[]

[Outputs]
  exodus = true
[]

(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
[]

(modules/chemical_reactions/examples/calcium_bicarbonate/calcium_bicarbonate.i)

# Example of reactive transport model with precipitation and dissolution.
# Calcium (ca2) and bicarbonate (hco3) reaction to form calcite (CaCO3).
# Models bicarbonate injection following calcium injection, so that a
# moving reaction front forms a calcite precipitation zone. As the front moves,
# the upstream side of the front continues to form calcite via precipitation,
# while at the downstream side, dissolution of the solid calcite occurs.
#
# The reaction network considered is as follows:
# Aqueous equilibrium reactions:
# a)  h+ + hco3- = CO2(aq),             Keq = 10^(6.341)
# b)  hco3- = h+ + CO23-,               Keq = 10^(-10.325)
# c)  ca2+ + hco3- = h+ + CaCO3(aq),    Keq = 10^(-7.009)
# d)  ca2+ + hco3- = cahco3+,           Keq = 10^(-0.653)
# e)  ca2+ = h+ + CaOh+,                Keq = 10^(-12.85)
# f)  - h+ = oh-,                       Keq = 10^(-13.991)
#
# Kinetic reactions
# g)  ca2+ + hco3- = h+ + CaCO3(s),     A = 0.461 m^2/L, k = 6.456542e-2 mol/m^2 s,
#                                       Keq = 10^(1.8487)
#
# The primary chemical species are h+, hco3- and ca2+. The pressure gradient is fixed,
# and a conservative tracer is also included.
#
# This example is taken from:
# Guo et al, A parallel, fully coupled, fully implicit solution to reactive
# transport in porous media using the preconditioned Jacobian-Free Newton-Krylov
# Method, Advances in Water Resources, 53, 101-108 (2013).

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 100
  xmax = 1
  ymax = 0.25
[]

[Variables]
  [./tracer]
  [../]
  [./ca2+]
  [../]
  [./h+]
    initial_condition = 1.0e-7
    scaling = 1e6
  [../]
  [./hco3-]
  [../]
[]

[AuxVariables]
  [./pressure]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[ICs]
  [./pressure_ic]
    type = FunctionIC
    variable = pressure
    function = pic
  [../]
  [./hco3_ic]
    type = BoundingBoxIC
    variable = hco3-
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 5.0e-2
    outside = 1.0e-6
  [../]
  [./ca2_ic]
    type = BoundingBoxIC
    variable = ca2+
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 1.0e-6
    outside = 5.0e-2
  [../]
  [./tracer_ic]
    type = BoundingBoxIC
    variable = tracer
    x1 = 0.0
    y1 = 0.0
    x2 = 1.0e-10
    y2 = 0.25
    inside = 1.0
    outside = 0.0
  [../]
[]

[Functions]
  [./pic]
    type = ParsedFunction
    expression = 60-50*x
  [../]
[]

[ReactionNetwork]
  [./AqueousEquilibriumReactions]
    primary_species = 'ca2+ hco3- h+'
    secondary_species = 'co2_aq co32- caco3_aq cahco3+ caoh+ oh-'
    pressure = pressure
    reactions = 'h+ + hco3- = co2_aq 6.341,
                 hco3- - h+ = co32- -10.325,
                 ca2+ + hco3- - h+ = caco3_aq -7.009,
                 ca2+ + hco3- = cahco3+ -0.653,
                 ca2+ - h+ = caoh+ -12.85,
                 - h+ = oh- -13.991'
  [../]
  [./SolidKineticReactions]
    primary_species = 'ca2+ hco3- h+'
    kin_reactions = 'ca2+ + hco3- - h+ = caco3_s'
    secondary_species = caco3_s
    log10_keq = 1.8487
    reference_temperature = 298.15
    system_temperature = 298.15
    gas_constant = 8.314
    specific_reactive_surface_area = 4.61e-4
    kinetic_rate_constant = 6.456542e-7
    activation_energy = 1.5e4
  [../]
[]

[Kernels]
  [./tracer_ie]
    type = PrimaryTimeDerivative
    variable = tracer
  [../]
  [./tracer_pd]
    type = PrimaryDiffusion
    variable = tracer
  [../]
  [./tracer_conv]
    type = PrimaryConvection
    variable = tracer
    p = pressure
  [../]
  [./ca2+_ie]
    type = PrimaryTimeDerivative
    variable = ca2+
  [../]
  [./ca2+_pd]
    type = PrimaryDiffusion
    variable = ca2+
  [../]
  [./ca2+_conv]
    type = PrimaryConvection
    variable = ca2+
    p = pressure
  [../]
  [./h+_ie]
    type = PrimaryTimeDerivative
    variable = h+
  [../]
  [./h+_pd]
    type = PrimaryDiffusion
    variable = h+
  [../]
  [./h+_conv]
    type = PrimaryConvection
    variable = h+
    p = pressure
  [../]
  [./hco3-_ie]
    type = PrimaryTimeDerivative
    variable = hco3-
  [../]
  [./hco3-_pd]
    type = PrimaryDiffusion
    variable = hco3-
  [../]
  [./hco3-_conv]
    type = PrimaryConvection
    variable = hco3-
    p = pressure
  [../]
[]

[BCs]
  [./tracer_left]
    type = DirichletBC
    variable = tracer
    boundary = left
    value = 1.0
  [../]
  [./tracer_right]
    type = ChemicalOutFlowBC
    variable = tracer
    boundary = right
  [../]
  [./ca2+_left]
    type = SinDirichletBC
    variable = ca2+
    boundary = left
    initial = 5.0e-2
    final = 1.0e-6
    duration = 1
  [../]
  [./ca2+_right]
    type = ChemicalOutFlowBC
    variable = ca2+
    boundary = right
  [../]
  [./hco3-_left]
    type = SinDirichletBC
    variable = hco3-
    boundary = left
    initial = 1.0e-6
    final = 5.0e-2
    duration = 1
  [../]
  [./hco3-_right]
    type = ChemicalOutFlowBC
    variable = hco3-
    boundary = right
  [../]
  [./h+_left]
    type = DirichletBC
    variable = h+
    boundary = left
    value = 1.0e-7
  [../]
  [./h+_right]
    type = ChemicalOutFlowBC
    variable = h+
    boundary = right
  [../]
[]

[Materials]
  [./porous]
    type = GenericConstantMaterial
    prop_names = 'diffusivity conductivity porosity'
    prop_values = '1e-7 2e-4 0.2'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  l_max_its = 50
  l_tol = 1e-5
  nl_max_its = 10
  nl_rel_tol = 1e-5
  end_time = 10
  [./TimeStepper]
    type = ConstantDT
    dt = 0.1
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Outputs]
  perf_graph = true
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files