VectorDirichletBC

Imposes the essential boundary condition $var element = document.getElementById("moose-equation-f6c006c8-b471-4cb0-afb4-2f662d94901d");katex.render("\\vec{u}=\\vec{g}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , where $var element = document.getElementById("moose-equation-425bbfb4-85da-4234-95e9-c1f4bccabfcb");katex.render("\\vec{g}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are constant, controllable values.

Description

VectorDirichletBC is the extension of DirichletBC to Lagrange vector variables and is used for imposing so-called "essential" boundary conditions on systems of partial differential equations (PDEs). Such boundary conditions force a particular set of degrees of freedom (DOFs) defined by the boundary parameter to take on controllable values. This class is appropriate to use for PDEs of the form $var element = document.getElementById("moose-equation-777ff7d0-68df-4953-9c8a-018eb78de7d1");katex.render("\\begin{aligned} -\\nabla^2 \\vec{u} &= \\vec{f} && \\quad \\in \\Omega \\\\ \\vec{u} &= \\vec{g} && \\quad \\in \\partial \\Omega_D \\\\ \\frac{\\partial \\vec{u}}{\\partial n} &= \\vec{h} && \\quad \\in \\partial \\Omega_N \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-1cb16a30-4cd4-497f-a783-c9d6b6a1c18b");katex.render("\\Omega \\subset \\mathbb{R}^n", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the domain, and $var element = document.getElementById("moose-equation-da43cf54-8ad8-4acd-b081-df7333429d03");katex.render("\\partial \\Omega = \\partial \\Omega_D \\cup \\partial \\Omega_N", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is its boundary. In this case, a VectorDirichletBC object is used to impose the condition (2) on the subset of the boundary denoted by $var element = document.getElementById("moose-equation-bc95db5c-a651-4f89-81e8-371b712dd4d8");katex.render("\\partial \\Omega_D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . In this case, the values correspond to the constant components of $var element = document.getElementById("moose-equation-b6a71599-6a1b-4173-941d-516dde7e00dd");katex.render("\\vec{g}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and the user must define one or more sidesets corresponding to the boundary subset $var element = document.getElementById("moose-equation-cedc2d12-36b5-4299-ad72-93ec098c5eab");katex.render("\\partial \\Omega_D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

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
valuesThe values the components must take on the boundary
C++ Type:libMesh::VectorValue<double>
Controllable:Yes
Description:The values the components must take on the boundary
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
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>
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>
Controllable:No
Description:The displacements
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>
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
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

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

Input Files

(test/tests/preconditioners/fsp/vector-test.i)
(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_square_constant_names.i)
(test/tests/kernels/vector_fe/coupled_vector_gradient.i)
(test/tests/interfacekernels/ad_coupled_vector_value/coupled.i)
(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_square.i)
(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_stabilized.i)
(test/tests/dirackernels/constant_point_source/vector_2d_point_source.i)
(test/tests/auxkernels/vector_variable_nodal/vector_variable_nodal.i)
(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/benchmark/benchmark.i)
(test/tests/kernels/coupled_time_derivative/vector_coupled_time_derivative_test.i)
(test/tests/dirackernels/constant_point_source/vector_3d_point_source.i)

(test/tests/preconditioners/fsp/vector-test.i)

[Mesh]
  type = GeneratedMesh
  nx = 5
  ny = 5
  dim = 2
[]

[Variables]
  [u]
    family = LAGRANGE_VEC
  []
  [v]
    family = LAGRANGE_VEC
  []
[]

[Kernels]
  [time_u]
    type = VectorTimeDerivative
    variable = u
  []
  [fn_u]
    type = VectorBodyForce
    variable = u
    function_x = 1
    function_y = 1
  []
  [time_v]
    type = VectorCoupledTimeDerivative
    variable = v
    v = u
  []
  [diff_v]
    type = VectorDiffusion
    variable = v
  []
[]

[BCs]
  [left]
    type = VectorDirichletBC
    variable = v
    boundary = 'left'
    values = '0 0 0'
  []
  [right]
    type = VectorDirichletBC
    variable = v
    boundary = 'right'
    values = '1 1 0'
  []
[]

[Preconditioning]
  [FSP]
    type = FSP
    topsplit = 'uv'
    [uv]
      splitting = 'u v'
      # Generally speaking, there are four types of splitting we could choose
      # <additive,multiplicative,symmetric_multiplicative,schur>
      splitting_type  = symmetric_multiplicative
    []
    [u]
      vars = 'u'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre preonly'
    []
    [v]
      vars = 'v'
      petsc_options_iname = '-pc_type -ksp_type'
      petsc_options_value = '     hypre  preonly'
    []
  []
[]

[Executioner]
  type = Transient
  num_steps = 1
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_square_constant_names.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = .05
    ymax = .05
    nx = 20
    ny = 20
    elem_type = QUAD9
  []
  [bottom_left]
    type = ExtraNodesetGenerator
    new_boundary = corner
    coord = '0 0'
    input = gen
  []
[]


[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
    order = SECOND
  []
  [p][]
  [temp]
    order = SECOND
    initial_condition = 340
    scaling = 1e-4
  []
[]


[BCs]
  [velocity_dirichlet]
    type = VectorDirichletBC
    boundary = 'left right bottom top'
    variable = velocity
    # The third entry is to satisfy RealVectorValue
    values = '0 0 0'
  []
  # Even though we are integrating by parts, because there are no integrated
  # boundary conditions on the velocity p doesn't appear in the system of
  # equations. Thus we must pin the pressure somewhere in order to ensure a
  # unique solution
  [p_zero]
    type = DirichletBC
    boundary = corner
    variable = p
    value = 0
  []
  [cold]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  []
  [hot]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 400
  []
[]


[Kernels]
  [mass]
    type = INSADMass
    variable = p
  []
  [momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  []
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []
  [temp_advection]
    type = INSADEnergyAdvection
    variable = temp
  []
  [temp_conduction]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = 'k'
  []
  [buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    temperature = temp
    gravity = '0 -9.81 0'
    ref_temp = 900
    alpha_name = 2.9e-3
  []
  [gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -9.81 0'
  []
[]

[Materials]
  [ad_const]
    type = ADGenericConstantMaterial
    prop_names =  'mu        rho    k        cp'
    prop_values = '30.74e-6  .5757  46.38e-3 1054'
  []
  [ins_mat]
    type = INSAD3Eqn
    velocity = velocity
    pressure = p
    temperature = temp
  []
[]

(test/tests/kernels/vector_fe/coupled_vector_gradient.i)

# This example demonstrates ability to set Dirichlet boundary conditions for LAGRANGE_VEC variables

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    family = LAGRANGE_VEC
    order = FIRST
  [../]
  [./v]
    family = LAGRANGE_VEC
    order = FIRST
  [../]
  [./w]
    family = LAGRANGE_VEC
    order = FIRST
  [../]
  [./s]
    family = LAGRANGE_VEC
    order = FIRST
  [../]
  [./q]
  [../]
[]

[Kernels]
  [./u_diff]
    type = VectorDiffusion
    variable = u
  [../]
  [./v_diff]
    type = VectorDiffusion
    variable = v
  [../]
  [./w_diff]
    type = VectorDiffusion
    variable = w
  [../]
  [./s_diff]
    type = VectorDiffusion
    variable = s
  [../]
  [./v_coupled_diff]
    type = CoupledVectorDiffusion
    variable = v
    v = u
  [../]
  [./w_coupled_diff]
    type = CoupledVectorDiffusion
    variable = w
    v = u
    state = old
  [../]
  [./s_coupled_diff]
    type = CoupledVectorDiffusion
    variable = s
    v = u
    state = older
  [../]
  [./q_diff]
    type = Diffusion
    variable = q
  [../]
[]

[BCs]
  [./left_u]
    type = VectorDirichletBC
    variable = u
    values = '0 0 0'
    boundary = 'left'
  [../]
  [./left_v]
    type = VectorDirichletBC
    variable = v
    values = '0 0 0'
    boundary = 'left'
  [../]
  [./left_w]
    type = VectorDirichletBC
    variable = w
    values = '0 0 0'
    boundary = 'left'
  [../]
  [./left_s]
    type = VectorDirichletBC
    variable = s
    values = '0 0 0'
    boundary = 'left'
  [../]
  [./right_u]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'right'
    function_x = 'x_exact'
    function_y = 'y_exact'
  [../]
  [./right_v]
    type = VectorFunctionDirichletBC
    variable = v
    boundary = 'right'
    function_x = 'x_exact'
    function_y = 'y_exact'
  [../]
  [./right_w]
    type = VectorFunctionDirichletBC
    variable = w
    boundary = 'right'
    function_x = 'x_exact_old'
    function_y = 'y_exact_old'
  [../]
  [./right_s]
    type = VectorFunctionDirichletBC
    variable = s
    boundary = 'right'
    function_x = 'x_exact_older'
    function_y = 'y_exact_older'
  [../]
  [./left_q]
    type = DirichletBC
    variable = q
    boundary = 'left'
    value = 1
  [../]
  [./right_q]
    type = NeumannBC
    variable = q
    boundary = 'right'
    value = 1
  [../]
[]

[Functions]
  [./x_exact]
    type = ParsedFunction
    expression = 't'
  [../]
  [./y_exact]
    type = ParsedFunction
    expression = 't'
  [../]
  [./x_exact_old]
    type = ParsedFunction
    expression = 'if(t < 1, 0, t - 1)'
  [../]
  [./y_exact_old]
    type = ParsedFunction
    expression = 'if(t < 1, 0, t - 1)'
  [../]
  [./x_exact_older]
    type = ParsedFunction
    expression = 'if(t < 2, 0, t - 2)'
  [../]
  [./y_exact_older]
    type = ParsedFunction
    expression = 'if(t < 2, 0, t - 2)'
  [../]
[]

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

[Executioner]
  type = Transient
  dt = 1
  num_steps = 3
  solve_type = 'NEWTON'
  petsc_options = '-ksp_converged_reason -snes_converged_reason'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '100'
  nl_max_its = 3
  l_max_its = 100
  dtmin = 1
[]

[Outputs]
  exodus = true
[]

(test/tests/interfacekernels/ad_coupled_vector_value/coupled.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 20
    xmax = 2
  []
  [./subdomain1]
    input = gen
    type = SubdomainBoundingBoxGenerator
    bottom_left = '1.0 0 0'
    block_id = 1
    top_right = '2.0 1.0 0'
  [../]
  [./interface]
    input = subdomain1
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'primary0_interface'
  [../]
[]

[Variables]
  [./u]
    block = '0'
    family = LAGRANGE_VEC
  [../]
  [./v]
    block = '1'
    family = LAGRANGE_VEC
  [../]
  [w]
    family = LAGRANGE_VEC
  []
[]

[Kernels]
  [./diff_u]
    type = VectorDiffusion
    variable = u
    block = 0
  [../]
  [./diff_v]
    type = VectorDiffusion
    variable = v
    block = 1
  [../]
  [diff_w]
    type = VectorDiffusion
    variable = w
  []
[]

[InterfaceKernels]
  [./interface]
    type = ADVectorCoupledInterfacialSource
    variable = u
    neighbor_var = v
    var_source = w
    boundary = primary0_interface
    D = 1
    D_neighbor = 1
  [../]
[]

[BCs]
  [./left]
    type = VectorDirichletBC
    variable = u
    boundary = 'left'
    values = '0 0 0'
  [../]
  [./right]
    type = VectorDirichletBC
    variable = v
    boundary = 'right'
    values = '10 0 0'
  [../]
  [./middle]
    type = ADVectorMatchedValueBC
    variable = v
    boundary = 'primary0_interface'
    v = u
  [../]
  [w_left]
    type = VectorDirichletBC
    variable = w
    boundary = 'left'
    values = '0 0 0'
  []
  [w_right]
    type = VectorDirichletBC
    variable = w
    boundary = 'right'
    values = '4 0 0'
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_square.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = .05
    ymax = .05
    nx = 20
    ny = 20
    elem_type = QUAD9
  []
  [./bottom_left]
    type = ExtraNodesetGenerator
    new_boundary = corner
    coord = '0 0'
    input = gen
  [../]
[]


[Preconditioning]
  [./Newton_SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady

  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'bjacobi  lu           NONZERO                   200'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
    order = SECOND
  []
  [p][]
  [./temp]
    order = SECOND
    initial_condition = 340
    scaling = 1e-4
  [../]
[]


[BCs]
  [./velocity_dirichlet]
    type = VectorDirichletBC
    boundary = 'left right bottom top'
    variable = velocity
    # The third entry is to satisfy RealVectorValue
    values = '0 0 0'
  [../]
  # Even though we are integrating by parts, because there are no integrated
  # boundary conditions on the velocity p doesn't appear in the system of
  # equations. Thus we must pin the pressure somewhere in order to ensure a
  # unique solution
  [./p_zero]
    type = DirichletBC
    boundary = corner
    variable = p
    value = 0
  [../]
  [./cold]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  [../]
  [./hot]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 400
  [../]
[]


[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []
  [temp_advection]
    type = INSADEnergyAdvection
    variable = temp
  []
  [temp_conduction]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = 'k'
  [../]
  [./buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    temperature = temp
    gravity = '0 -9.81 0'
  [../]
  [./gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -9.81 0'
  [../]
[]

[Materials]
  [./ad_const]
    type = ADGenericConstantMaterial
    # alpha = coefficient of thermal expansion where rho  = rho0 -alpha * rho0 * delta T
    prop_names =  'mu        rho   alpha   k        cp'
    prop_values = '30.74e-6  .5757 2.9e-3  46.38e-3 1054'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'temp_ref'
    prop_values = '900'
  [../]
  [ins_mat]
    type = INSAD3Eqn
    velocity = velocity
    pressure = p
    temperature = temp
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_stabilized.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = .05
    ymax = .05
    nx = 20
    ny = 20
    elem_type = QUAD9
  []
  [./bottom_left]
    type = ExtraNodesetGenerator
    new_boundary = corner
    coord = '0 0'
    input = gen
  [../]
[]


[Preconditioning]
  [./Newton_SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady

  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'bjacobi  lu           NONZERO                   200'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
  []
  [p][]
  [temp]
    initial_condition = 340
    scaling = 1e-4
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[BCs]
  [./velocity_dirichlet]
    type = VectorDirichletBC
    boundary = 'left right bottom top'
    variable = velocity
    # The third entry is to satisfy RealVectorValue
    values = '0 0 0'
  [../]
  # Even though we are integrating by parts, because there are no integrated
  # boundary conditions on the velocity p doesn't appear in the system of
  # equations. Thus we must pin the pressure somewhere in order to ensure a
  # unique solution
  [./p_zero]
    type = DirichletBC
    boundary = corner
    variable = p
    value = 0
  [../]
  [./cold]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  [../]
  [./hot]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 400
  [../]
[]


[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []
  [./buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    temperature = temp
    gravity = '0 -9.81 0'
  [../]
  [./gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -9.81 0'
  [../]
  [supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [temp_advection]
    type = INSADEnergyAdvection
    variable = temp
  []
  [temp_conduction]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = 'k'
  [../]
  [temp_supg]
    type = INSADEnergySUPG
    variable = temp
    velocity = velocity
  []
[]

[Materials]
  [./ad_const]
    type = ADGenericConstantMaterial
    # alpha = coefficient of thermal expansion where rho  = rho0 -alpha * rho0 * delta T
    prop_names =  'mu        rho   alpha   k        cp'
    prop_values = '30.74e-6  .5757 2.9e-3  46.38e-3 1054'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'temp_ref'
    prop_values = '900'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temp
  []
[]

(test/tests/dirackernels/constant_point_source/vector_2d_point_source.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  []
  uniform_refine = 4
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE_VEC
  []
[]

[Kernels]
  [diff]
    type = VectorDiffusion
    variable = u
  []
[]

[DiracKernels]
  [point_source1]
    type = VectorConstantPointSource
    variable = u
    values = '1.0 1.0 1.0'
    point = '0.2 0.3'
  []
  [point_source2]
    type = VectorConstantPointSource
    variable = u
    values = '-0.5 -0.5 -0.5'
    point = '0.2 0.8'
  []
[]

[BCs]
  [left]
    type = VectorDirichletBC
    variable = u
    boundary = 3
    values = '0 0 0'
  []
  [right]
    type = VectorDirichletBC
    variable = u
    boundary = 1
    values = '1 1 1'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
[]

[Outputs]
  file_base = vector_2d_out
  exodus = true
[]

(test/tests/auxkernels/vector_variable_nodal/vector_variable_nodal.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = -1
  xmax =  1
  ymin = -1
  ymax =  1
  zmin = -1
  zmax =  1
  nx = 2
  ny = 2
  nz = 2
[../]

[Variables]
  [./u]
    family = LAGRANGE_VEC
    order = first
  [../]
[]

[Kernels]
  [./none]
    type = VectorDiffusion
    variable = u
  [../]
[]

[BCs]
  [./left]
    type = VectorDirichletBC
    variable = u
    boundary = left
    values = '0 0 0'
  [../]
  [./right]
    type = VectorDirichletBC
    variable = u
    boundary = right
    values = '1 2 3'
  [../]
[]

[AuxVariables]
  [./u_mag]
  [../]
[]

[AuxKernels]
  [./calc_u_mag]
    type = VectorVariableMagnitudeAux
    variable = u_mag # the auxvariable to compute
    vector_variable = u # vector variable to compute from
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/benchmark/benchmark.i)

rayleigh=1e3
hot_temp=${rayleigh}
temp_ref=${fparse hot_temp / 2.}

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 100
    ny = 100
  []
  [./bottom_left]
    type = ExtraNodesetGenerator
    new_boundary = corner
    coord = '0 0'
    input = gen
  [../]
[]


[Preconditioning]
  [./Newton_SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady

  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'bjacobi  lu           NONZERO                   200'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [out]
    type = Exodus
  []
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
  []
  [p][]
  [temp]
    initial_condition = 340
    scaling = 1e-4
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[BCs]
  [./velocity_dirichlet]
    type = VectorDirichletBC
    boundary = 'left right bottom top'
    variable = velocity
    # The third entry is to satisfy RealVectorValue
    values = '0 0 0'
  [../]
  # Even though we are integrating by parts, because there are no integrated
  # boundary conditions on the velocity p doesn't appear in the system of
  # equations. Thus we must pin the pressure somewhere in order to ensure a
  # unique solution
  [./p_zero]
    type = DirichletBC
    boundary = corner
    variable = p
    value = 0
  [../]
  [./hot]
    type = DirichletBC
    variable = temp
    boundary = left
    value = ${hot_temp}
  [../]
  [./cold]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 0
  [../]
[]


[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []
  [./buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    temperature = temp
    gravity = '0 -1 0'
  [../]
  [./gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -1 0'
  [../]
  [supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [temp_advection]
    type = INSADEnergyAdvection
    variable = temp
  []
  [temp_conduction]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = 'k'
  [../]
  [temp_supg]
    type = INSADEnergySUPG
    variable = temp
    velocity = velocity
  []
[]

[Materials]
  [./ad_const]
    type = ADGenericConstantMaterial
    # alpha = coefficient of thermal expansion where rho  = rho0 -alpha * rho0 * delta T
    prop_names =  'mu        rho   alpha   k        cp'
    prop_values = '1         1     1       1        1'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'temp_ref'
    prop_values = '${temp_ref}'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temp
  []
[]

(test/tests/kernels/coupled_time_derivative/vector_coupled_time_derivative_test.i)

###########################################################
# This is a simple test of the VectorCoupledTimeDerivative kernel.
# The expected solution for the vector variable v is
# v_x(x) = 1/2 * (x^2 + x)
# v_y(x) = 1/2 * (x^2 + x)
###########################################################

[Mesh]
  type = GeneratedMesh
  nx = 5
  ny = 5
  dim = 2
[]

[Variables]
  [./u]
    family = LAGRANGE_VEC
  [../]
  [./v]
    family = LAGRANGE_VEC
  [../]
[]

[Kernels]
  [./time_u]
    type = VectorTimeDerivative
    variable = u
  [../]
  [./fn_u]
    type = VectorBodyForce
    variable = u
    function_x = 1
    function_y = 1
  [../]
  [./time_v]
    type = VectorCoupledTimeDerivative
    variable = v
    v = u
  [../]
  [./diff_v]
    type = VectorDiffusion
    variable = v
  [../]
[]

[BCs]
  [./left]
    type = VectorDirichletBC
    variable = v
    boundary = 'left'
    values = '0 0 0'
  [../]
  [./right]
    type = VectorDirichletBC
    variable = v
    boundary = 'right'
    values = '1 1 0'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
[]

(test/tests/dirackernels/constant_point_source/vector_3d_point_source.i)

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 10
  ny = 10
  nz = 10
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE_VEC
  []
[]

[Kernels]
  [diff]
    type = VectorDiffusion
    variable = u
  []
[]

[DiracKernels]
  [point_source1]
    type = VectorConstantPointSource
    variable = u
    values = '0.1 0.1 0.1'
    point = '0.2 0.3 0.0'
  []
  [point_source2]
    type = VectorConstantPointSource
    variable = u
    values = '-0.1 -0.1 -0.1'
    point = '0.2 0.8 0.0'
  []
  [point_source3]
    type = VectorConstantPointSource
    variable = u
    values = '-1.0 -1.0 -1.0'
    point = '0.8 0.5 0.8'
  []
[]

[BCs]
  [left]
    type = VectorDirichletBC
    variable = u
    boundary = left
    values = '0 0 0'
  []
  [right]
    type = VectorDirichletBC
    variable = u
    boundary = right
    values = '1 1 1'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'

[]

[Outputs]
  file_base = vector_3d_out
  exodus = true
[]

Description
Input Parameters
Input Files