VariableGradientComponent

Creates a field consisting of one component of the gradient of a coupled variable.

The result of this operation is stored in an auxiliary variable: variable. The analysis of gradients is useful to examine a solution or the adequacy of a mesh discretization.

note

AuxVariables currently do not contain the Automatic Differentiation information about the derivatives. Using this object in the solve, to compute a material property for example, will lead to an imperfect Jacobian which can impact convergence.

note

VariableGradientComponent may only be applied to elemental variables, and only considers the gradient within an element. For example, the reported gradient of a CONSTANT MONOMIAL is identically zero.

Example Input File Syntax

In this example, u is the (linear) solution of a 2D diffusion equation with no source term. We compute the two gradient components using the AuxKernels below, which each store a gradient component in a separate auxiliary variable. We can then examine the gradient of u, for example to decide to use a finer mesh in a given direction if the corresponding gradient is not well resolved.

[AuxKernels]
  [./grad_u_x_aux]
    type = VariableGradientComponent
    variable = grad_u_x
    component = x
    gradient_variable = u
  [../]
  [./grad_u_y_aux]
    type = VariableGradientComponent
    variable = grad_u_y
    component = y
    gradient_variable = u
  [../]
[]

Input Parameters

gradient_variableThe variable from which to compute the gradient component
C++ Type:std::vector<VariableName>
Options:
Description:The variable from which to compute the gradient component
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Options:
Description:The name of the variable that this object applies to

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector<SubdomainName>
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector<BoundaryName>
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Options:
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
componentThe gradient component to compute
C++ Type:MooseEnum
Options:x, y, z
Description:The gradient component to compute
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
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

Input Files

(test/tests/auxkernels/grad_component/grad_component_monomial.i)
(test/tests/auxkernels/grad_component/grad_component.i)
(modules/navier_stokes/test/tests/ins/mms/supg/supg_pspg_adv_dominated_mms.i)
(modules/navier_stokes/test/tests/ins/mms/pspg/pspg_mms_test.i)
(modules/navier_stokes/test/tests/ins/mms/supg/supg_mms_test.i)
(modules/navier_stokes/test/tests/ins/mms/supg/supg_adv_dominated_mms.i)
(modules/navier_stokes/test/tests/scalar_adr/supg/2d_advection_error_testing.i)
(modules/navier_stokes/test/tests/scalar_adr/supg/advection_error_testing.i)

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

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

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./grad_u_x]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./grad_u_y]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

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

[AuxKernels]
  [./grad_u_x_aux]
    type = VariableGradientComponent
    variable = grad_u_x
    component = x
    gradient_variable = u
  [../]
  [./grad_u_y_aux]
    type = VariableGradientComponent
    variable = grad_u_y
    component = y
    gradient_variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(test/tests/auxkernels/grad_component/grad_component_monomial.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 2
  nx = 20
  ny = 10
[]

[Variables]
  [./not_u]
  [../]
[]

[AuxVariables]
  [./u]
    family = MONOMIAL
    order = FIRST
  [../]
  [./grad_u_x]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./u]
    type = FunctionIC
    variable = u
    function = 'if(x>0.5,if(x<1.5,2*x,3),0)'
  [../]
[]

[AuxKernels]
  [./grad_u_x_aux]
    type = VariableGradientComponent
    variable = grad_u_x
    component = x
    gradient_variable = u
    execute_on = initial
  [../]
[]

[Problem]
  type = FEProblem
  solve = false
  kernel_coverage_check = false
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

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

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

[Variables]
  [./u]
  [../]
[]

[AuxVariables]
  [./grad_u_x]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./grad_u_y]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

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

[AuxKernels]
  [./grad_u_x_aux]
    type = VariableGradientComponent
    variable = grad_u_x
    component = x
    gradient_variable = u
  [../]
  [./grad_u_y_aux]
    type = VariableGradientComponent
    variable = grad_u_y
    component = y
    gradient_variable = u
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./right]
    type = DirichletBC
    variable = u
    boundary = right
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/ins/mms/supg/supg_pspg_adv_dominated_mms.i)

mu=1.5e-4
rho=2.5

[GlobalParams]
  gravity = '0 0 0'
  supg = true
  pspg = true
  convective_term = true
  integrate_p_by_parts = false
  transient_term = true
  laplace = true
  u = vel_x
  v = vel_y
  p = p
  alpha = 1e0
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    elem_type = QUAD9
    nx = 4
    ny = 4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
    order = FIRST
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
    x_vel_forcing_func = vel_x_source_func
    y_vel_forcing_func = vel_y_source_func
  [../]

  [./x_time]
    type = INSMomentumTimeDerivative
    variable = vel_x
  [../]
  [./y_time]
    type = INSMomentumTimeDerivative
    variable = vel_y
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
    forcing_func = vel_x_source_func
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
    forcing_func = vel_y_source_func
  [../]

  [./p_source]
    type = BodyForce
    function = p_source_func
    variable = p
  [../]
[]

[BCs]
  [./vel_x]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_x_func
    variable = vel_x
  [../]
  [./vel_y]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_y_func
    variable = vel_y
  [../]
  [./p]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = p_func
    variable = p
  [../]
[]

[Functions]
  [./vel_x_source_func]
    type = ParsedFunction
    value = '-${mu}*(-0.028*pi^2*x^2*sin(0.2*pi*x*y) - 0.028*pi^2*y^2*sin(0.2*pi*x*y) - 0.1*pi^2*sin(0.5*pi*x) - 0.4*pi^2*sin(pi*y)) + ${rho}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
  [./vel_y_source_func]
    type = ParsedFunction
    value = '-${mu}*(-0.018*pi^2*x^2*sin(0.3*pi*x*y) - 0.018*pi^2*y^2*sin(0.3*pi*x*y) - 0.384*pi^2*sin(0.8*pi*x) - 0.027*pi^2*sin(0.3*pi*y)) + ${rho}*(0.06*pi*x*cos(0.3*pi*x*y) + 0.09*pi*cos(0.3*pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.06*pi*y*cos(0.3*pi*x*y) + 0.48*pi*cos(0.8*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*x*cos(0.2*pi*x*y) + 0.3*pi*cos(0.3*pi*y)'
  [../]
  [./p_source_func]
    type = ParsedFunction
    value = '-0.06*pi*x*cos(0.3*pi*x*y) - 0.14*pi*y*cos(0.2*pi*x*y) - 0.2*pi*cos(0.5*pi*x) - 0.09*pi*cos(0.3*pi*y)'
  [../]
  [./vel_x_func]
    type = ParsedFunction
    value = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vel_y_func]
    type = ParsedFunction
    value = '0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3'
  [../]
  [./p_func]
    type = ParsedFunction
    value = '0.5*sin(0.5*pi*x) + 1.0*sin(0.3*pi*y) + 0.5*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vxx_func]
    type = ParsedFunction
    value = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  [../]
[]

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

[Executioner]
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_view'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu NONZERO superlu_dist'
  line_search = 'none'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-12
  nl_max_its = 10
  l_tol = 1e-6
  l_max_its = 10
  # To run to steady-state, set num-steps to some large number (1000000 for example)
  type = Transient
  num_steps = 10
  steady_state_detection = true
  steady_state_tolerance = 1e-10
  [./TimeStepper]
    dt = .1
    type = IterationAdaptiveDT
    cutback_factor = 0.4
    growth_factor = 1.2
    optimal_iterations = 20
  [../]
[]

[Outputs]
  execute_on = 'final'
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2vel_x]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_func
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2vel_y]
    variable = vel_y
    function = vel_y_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = p
    function = p_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2vxx]
    variable = vxx
    function = vxx_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./vxx]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./vxx]
    type = VariableGradientComponent
    component = x
    variable = vxx
    gradient_variable = vel_x
  [../]
[]

(modules/navier_stokes/test/tests/ins/mms/pspg/pspg_mms_test.i)

mu=1.5
rho=2.5

[GlobalParams]
  gravity = '0 0 0'
  pspg = true
  convective_term = true
  integrate_p_by_parts = true
  laplace = true
  u = vel_x
  v = vel_y
  p = p
  alpha = 1e-6
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    elem_type = QUAD9
    nx = 4
    ny = 4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
    x_vel_forcing_func = vel_x_source_func
    y_vel_forcing_func = vel_y_source_func
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
    forcing_func = vel_x_source_func
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
    forcing_func = vel_y_source_func
  [../]

  [./p_source]
    type = BodyForce
    function = p_source_func
    variable = p
  [../]
[]

[BCs]
  [./vel_x]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_x_func
    variable = vel_x
  [../]
  [./vel_y]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_y_func
    variable = vel_y
  [../]
  [./p]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = p_func
    variable = p
  [../]
[]

[Functions]
  [./vel_x_source_func]
    type = ParsedFunction
    value = '-${mu}*(-0.028*pi^2*x^2*sin(0.2*pi*x*y) - 0.028*pi^2*y^2*sin(0.2*pi*x*y) - 0.1*pi^2*sin(0.5*pi*x) - 0.4*pi^2*sin(pi*y)) + ${rho}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
  [./vel_y_source_func]
    type = ParsedFunction
    value = '-${mu}*(-0.018*pi^2*x^2*sin(0.3*pi*x*y) - 0.018*pi^2*y^2*sin(0.3*pi*x*y) - 0.384*pi^2*sin(0.8*pi*x) - 0.027*pi^2*sin(0.3*pi*y)) + ${rho}*(0.06*pi*x*cos(0.3*pi*x*y) + 0.09*pi*cos(0.3*pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.06*pi*y*cos(0.3*pi*x*y) + 0.48*pi*cos(0.8*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*x*cos(0.2*pi*x*y) + 0.3*pi*cos(0.3*pi*y)'
  [../]
  [./p_source_func]
    type = ParsedFunction
    value = '-0.06*pi*x*cos(0.3*pi*x*y) - 0.14*pi*y*cos(0.2*pi*x*y) - 0.2*pi*cos(0.5*pi*x) - 0.09*pi*cos(0.3*pi*y)'
  [../]
  [./vel_x_func]
    type = ParsedFunction
    value = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vel_y_func]
    type = ParsedFunction
    value = '0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3'
  [../]
  [./p_func]
    type = ParsedFunction
    value = '0.5*sin(0.5*pi*x) + 1.0*sin(0.3*pi*y) + 0.5*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vxx_func]
    type = ParsedFunction
    value = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
  [./px_func]
    type = ParsedFunction
    value = '0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  [../]
[]

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

[Executioner]
  type = Steady
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2vel_x]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_func
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2vel_y]
    variable = vel_y
    function = vel_y_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = p
    function = p_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2vxx]
    variable = vxx
    function = vxx_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2px]
    variable = px
    function = px_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./vxx]
    family = MONOMIAL
    order = FIRST
  [../]
  [./px]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./vxx]
    type = VariableGradientComponent
    component = x
    variable = vxx
    gradient_variable = vel_x
  [../]
  [./px]
    type = VariableGradientComponent
    component = x
    variable = px
    gradient_variable = p
  [../]
[]

(modules/navier_stokes/test/tests/ins/mms/supg/supg_mms_test.i)

mu=1.5
rho=2.5

[GlobalParams]
  gravity = '0 0 0'
  supg = true
  convective_term = true
  integrate_p_by_parts = false
  laplace = true
  u = vel_x
  v = vel_y
  p = p
  alpha = 1
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    elem_type = QUAD9
    nx = 4
    ny = 4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
    order = FIRST
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
    forcing_func = vel_x_source_func
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
    forcing_func = vel_y_source_func
  [../]

  [./p_source]
    type = BodyForce
    function = p_source_func
    variable = p
  [../]
[]

[BCs]
  [./vel_x]
    type = FunctionDirichletBC
    preset = false
    boundary = 'left right top bottom'
    function = vel_x_func
    variable = vel_x
  [../]
  [./vel_y]
    type = FunctionDirichletBC
    preset = false
    boundary = 'left right top bottom'
    function = vel_y_func
    variable = vel_y
  [../]
  [./p]
    type = FunctionDirichletBC
    preset = false
    boundary = 'left right top bottom'
    function = p_func
    variable = p
  [../]
[]

[Functions]
  [./vel_x_source_func]
    type = ParsedFunction
    value = '-${mu}*(-0.028*pi^2*x^2*sin(0.2*pi*x*y) - 0.028*pi^2*y^2*sin(0.2*pi*x*y) - 0.1*pi^2*sin(0.5*pi*x) - 0.4*pi^2*sin(pi*y)) + ${rho}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
  [./vel_y_source_func]
    type = ParsedFunction
    value = '-${mu}*(-0.018*pi^2*x^2*sin(0.3*pi*x*y) - 0.018*pi^2*y^2*sin(0.3*pi*x*y) - 0.384*pi^2*sin(0.8*pi*x) - 0.027*pi^2*sin(0.3*pi*y)) + ${rho}*(0.06*pi*x*cos(0.3*pi*x*y) + 0.09*pi*cos(0.3*pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.06*pi*y*cos(0.3*pi*x*y) + 0.48*pi*cos(0.8*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*x*cos(0.2*pi*x*y) + 0.3*pi*cos(0.3*pi*y)'
  [../]
  [./p_source_func]
    type = ParsedFunction
    value = '-0.06*pi*x*cos(0.3*pi*x*y) - 0.14*pi*y*cos(0.2*pi*x*y) - 0.2*pi*cos(0.5*pi*x) - 0.09*pi*cos(0.3*pi*y)'
  [../]
  [./vel_x_func]
    type = ParsedFunction
    value = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vel_y_func]
    type = ParsedFunction
    value = '0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3'
  [../]
  [./p_func]
    type = ParsedFunction
    value = '0.5*sin(0.5*pi*x) + 1.0*sin(0.3*pi*y) + 0.5*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vxx_func]
    type = ParsedFunction
    value = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  [../]
[]

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

[Executioner]
  type = Steady
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2vel_x]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_func
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2vel_y]
    variable = vel_y
    function = vel_y_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = p
    function = p_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2vxx]
    variable = vxx
    function = vxx_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./vxx]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./vxx]
    type = VariableGradientComponent
    component = x
    variable = vxx
    gradient_variable = vel_x
  [../]
[]

(modules/navier_stokes/test/tests/ins/mms/supg/supg_adv_dominated_mms.i)

mu=1.5e-2
rho=2.5

[GlobalParams]
  gravity = '0 0 0'
  supg = true
  convective_term = true
  integrate_p_by_parts = false
  transient_term = true
  laplace = true
  u = vel_x
  v = vel_y
  p = p
  alpha = 1e0
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    elem_type = QUAD9
    nx = 4
    ny = 4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
    order = FIRST
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
  [../]

  [./x_time]
    type = INSMomentumTimeDerivative
    variable = vel_x
  [../]
  [./y_time]
    type = INSMomentumTimeDerivative
    variable = vel_y
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
    forcing_func = vel_x_source_func
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
    forcing_func = vel_y_source_func
  [../]

  [./p_source]
    type = BodyForce
    function = p_source_func
    variable = p
  [../]
[]

[BCs]
  [./vel_x]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_x_func
    variable = vel_x
  [../]
  [./vel_y]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_y_func
    variable = vel_y
  [../]
  [./p]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = p_func
    variable = p
  [../]
[]

[Functions]
  [./vel_x_source_func]
    type = ParsedFunction
    value = '-${mu}*(-0.028*pi^2*x^2*sin(0.2*pi*x*y) - 0.028*pi^2*y^2*sin(0.2*pi*x*y) - 0.1*pi^2*sin(0.5*pi*x) - 0.4*pi^2*sin(pi*y)) + ${rho}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
  [./vel_y_source_func]
    type = ParsedFunction
    value = '-${mu}*(-0.018*pi^2*x^2*sin(0.3*pi*x*y) - 0.018*pi^2*y^2*sin(0.3*pi*x*y) - 0.384*pi^2*sin(0.8*pi*x) - 0.027*pi^2*sin(0.3*pi*y)) + ${rho}*(0.06*pi*x*cos(0.3*pi*x*y) + 0.09*pi*cos(0.3*pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.06*pi*y*cos(0.3*pi*x*y) + 0.48*pi*cos(0.8*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*x*cos(0.2*pi*x*y) + 0.3*pi*cos(0.3*pi*y)'
  [../]
  [./p_source_func]
    type = ParsedFunction
    value = '-0.06*pi*x*cos(0.3*pi*x*y) - 0.14*pi*y*cos(0.2*pi*x*y) - 0.2*pi*cos(0.5*pi*x) - 0.09*pi*cos(0.3*pi*y)'
  [../]
  [./vel_x_func]
    type = ParsedFunction
    value = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vel_y_func]
    type = ParsedFunction
    value = '0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3'
  [../]
  [./p_func]
    type = ParsedFunction
    value = '0.5*sin(0.5*pi*x) + 1.0*sin(0.3*pi*y) + 0.5*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vxx_func]
    type = ParsedFunction
    value = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  [../]
[]

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

[Executioner]
  type = Transient
  num_steps = 10
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-14
  nl_max_its = 10
  l_tol = 1e-6
  l_max_its = 10
  [./TimeStepper]
    dt = .05
    type = IterationAdaptiveDT
    cutback_factor = 0.4
    growth_factor = 1.2
    optimal_iterations = 20
  [../]
[]

[Outputs]
  execute_on = 'final'
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2vel_x]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_func
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2vel_y]
    variable = vel_y
    function = vel_y_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = p
    function = p_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2vxx]
    variable = vxx
    function = vxx_func
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./vxx]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./vxx]
    type = VariableGradientComponent
    component = x
    variable = vxx
    gradient_variable = vel_x
  [../]
[]

(modules/navier_stokes/test/tests/scalar_adr/supg/2d_advection_error_testing.i)

ax=1
ay=1

[GlobalParams]
  u = ${ax}
  v = ${ay}
  p = 0
  tau_type = mod
  transient_term = true
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  xmax = 1
  ymax = 1
  elem_type = QUAD9
[]

[Variables]
  [./c]
    family = LAGRANGE
    order = SECOND
  [../]
[]

[Kernels]
  [./adv]
    type = Advection
    variable = c
    forcing_func = 'ffn'
  [../]
[]

[BCs]
  [./all]
    type = FunctionDirichletBC
    variable = c
    boundary = 'left right top bottom'
    function = 'c_func'
  [../]
[]

[Materials]
  [./mat]
    type = GenericConstantMaterial
    prop_names = 'mu rho'
    prop_values = '0 1'
  [../]
[]

[Functions]
  [./ffn]
    type = ParsedFunction
    value = '${ax}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)) + ${ay}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))'
  [../]
  [./c_func]
    type = ParsedFunction
    value = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./cx_func]
    type = ParsedFunction
    value = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
[]

# [Executioner]
#   type = Steady
#   petsc_options_iname = '-pc_type -pc_factor_shift_type'
#   petsc_options_value = 'lu NONZERO'
# []

[Executioner]
  type = Transient
  num_steps = 10
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_view'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu NONZERO superlu_dist'
  line_search = 'none'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-12
  nl_max_its = 10
  l_tol = 1e-6
  l_max_its = 10
  [./TimeStepper]
    dt = .05
    type = IterationAdaptiveDT
    cutback_factor = 0.4
    growth_factor = 1.2
    optimal_iterations = 20
  [../]
[]

[Outputs]
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2c]
    type = ElementL2Error
    variable = c
    function = c_func
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2cx]
    type = ElementL2Error
    variable = cx
    function = cx_func
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./cx]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./cx_aux]
    type = VariableGradientComponent
    component = x
    variable = cx
    gradient_variable = c
  [../]
[]

(modules/navier_stokes/test/tests/scalar_adr/supg/advection_error_testing.i)

velocity=1

[GlobalParams]
  u = ${velocity}
  p = 0
  tau_type = mod
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 4
  xmax = 1
  elem_type = EDGE2
[]

[Variables]
  [./c]
    family = LAGRANGE
    order = FIRST
  [../]
[]

[Kernels]
  [./adv]
    type = Advection
    variable = c
    forcing_func = 'ffn'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = c
    boundary = left
    value = 0
  [../]
[]

[Materials]
  [./mat]
    type = GenericConstantMaterial
    prop_names = 'mu rho'
    prop_values = '0 1'
  [../]
[]

[Functions]
  [./ffn]
    type = ParsedFunction
    value = '1-x^2'
  [../]
  [./c_func]
    type = ParsedFunction
    value = 'x-x^3/3'
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
[]

[Outputs]
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2c]
    type = ElementL2Error
    variable = c
    function = c_func
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [./L2cx]
    type = ElementL2Error
    variable = cx
    function = ffn
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./cx]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./cx]
    type = VariableGradientComponent
    component = x
    variable = cx
    gradient_variable = c
  [../]
[]

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