AdvectionBC

Boundary conditions for outflow/outflow of advected quantities: phi * velocity * normal, where phi is the advected quantitiy

This boundary condition accounts for advection of a scalar quantity $var element = document.getElementById("moose-equation-f93ea938-571b-4c54-b6bf-7891d7c46a1b");katex.render("\\phi", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ by velocity $var element = document.getElementById("moose-equation-805f6380-478e-4d2d-b458-248909cf14ec");katex.render("\\vec{v}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ .

It is usually applied on outflow boundary conditions and originates from integration by parts of $var element = document.getElementById("moose-equation-d64009fc-56ef-463b-ba3c-13ec3a0893b4");katex.render("\\nabla \\cdot (\\vec{v} \\phi)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . Multiplying by test function $var element = document.getElementById("moose-equation-fbf94fed-aee3-4dfa-9006-46389380370e");katex.render("\\psi", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and using Green's identity gives: $var element = document.getElementById("moose-equation-dfc924e6-a4da-45d1-a74d-68de88263344");katex.render(" \\int_{\\Omega} \\psi \\nabla \\cdot (\\vec{v} \\phi) d \\Omega = - \\int_{\\Omega} \\nabla \\psi \\cdot (\\vec{v} \\phi) d \\Omega + \\int_{\\partial \\Omega} \\psi \\phi \\vec{n} \\cdot \\vec{v} d S.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ The boundary $var element = document.getElementById("moose-equation-93221b10-0b34-4751-9ebc-7f47b9f89920");katex.render("\\partial \\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ can be divided into two parts, inflow and outflow satsifying: $var element = document.getElementById("moose-equation-ce7a8614-7ff1-4cec-b2bb-63e5b4edefcd");katex.render("\\begin{aligned} \\partial \\Omega^-:&\\vec{n} \\cdot \\vec{v} < 0 \\\\ \\partial \\Omega^+:&\\vec{n} \\cdot \\vec{v} > 0 \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ Boundary conditions are applied on the inflow boundaries, e.g. the value of $var element = document.getElementById("moose-equation-1d224b85-41fd-4211-ab50-ed58b43ecdaf");katex.render("\\phi", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ may be known and is set by a Dirichlet boundary conditions. However, term: $var element = document.getElementById("moose-equation-8f06ec0f-5c12-4a64-9616-ff70b6a498b7");katex.render(" \\int_{\\partial \\Omega^+} \\psi \\phi \\vec{n} \\cdot \\vec{v} d S.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ still needs to be applied in the PDE. This is covered by AdvectionBC.

Input Parameters

boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this boundary condition applies to
velocity_vectorThe components of the velocity vector up to problem dimension
C++ Type:std::vector
Options:
Description:The components of the velocity vector up to problem dimension

Required Parameters

displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements

Optional Parameters

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

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
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
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime system
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

modules/navier_stokes/test/tests/bcs/advection_bc/advection_bc.i
modules/navier_stokes/test/tests/bcs/advection_bc/2d_advection_bc.i

modules/navier_stokes/test/tests/bcs/advection_bc/advection_bc.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 10.0
  nx = 100
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./vx]
  [../]

  [./force]
  [../]
[]

[ICs]
  [./vx]
    type = FunctionIC
    variable = vx
    function = vx_function
  [../]

  [./force]
    type = FunctionIC
    variable = force
    function = forcing
  [../]
[]

[Kernels]
  [./advection]
    type = MassConvectiveFlux
    variable = phi
    vel_x = vx
  [../]

  [./rhs]
    type = CoupledForce
    variable = phi
    v = force
  [../]
[]

[BCs]
  [./inflow_enthalpy]
    type = DirichletBC
    variable = phi
    boundary = 'left'
    value = 1
  [../]

  [./outflow_term]
    type = AdvectionBC
    variable = phi
    velocity_vector = 'vx'
    boundary = 'right'
  [../]
[]

[Functions]
  [./vx_function]
    type = ParsedFunction
    value = '1 + x * x'
  [../]

  [./forcing]
    type = ParsedFunction
    value = 'x'
  [../]

  [./analytical]
    type = ParsedFunction
    value = '(1 + 0.5 * x * x) / (1 + x * x)'
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = phi
    function = analytical
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

modules/navier_stokes/test/tests/bcs/advection_bc/2d_advection_bc.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10.0
  ymax = 10
  nx = 10
  ny = 10
[]

[Variables]
  [./phi]
  [../]
[]

[AuxVariables]
  [./vx]
  [../]

  [./force]
  [../]
[]

[ICs]
  [./vx]
    type = FunctionIC
    variable = vx
    function = vx_function
  [../]

  [./force]
    type = FunctionIC
    variable = force
    function = forcing
  [../]
[]

[Kernels]
  [./advection]
    type = MassConvectiveFlux
    variable = phi
    vel_x = vx
  [../]

  [./rhs]
    type = CoupledForce
    variable = phi
    v = force
  [../]
[]

[BCs]
  [./inflow_enthalpy]
    type = DirichletBC
    variable = phi
    boundary = 'left'
    value = 1
  [../]

  [./outflow_term]
    type = AdvectionBC
    variable = phi
    velocity_vector = 'vx'
    boundary = 'right'
  [../]
[]

[Functions]
  [./vx_function]
    type = ParsedFunction
    value = '1 + x * x'
  [../]

  [./forcing]
    type = ParsedFunction
    value = 'x'
  [../]

  [./analytical]
    type = ParsedFunction
    value = '(1 + 0.5 * x * x) / (1 + x * x)'
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = phi
    function = analytical
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

Input Parameters
Input Files

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