LevelSetCFLCondition

Computes the minimum timestep based on the Courant-Friedrichs-Lewy (CFL) condition. The CFL condition, is defined as

$var element = document.getElementById("moose-equation-4da89aec-39bd-41fd-828b-f7ba23ee0ae3");katex.render("C = \\Delta t \\sum_{i=1}^{n}\\frac{u_{x_i}}{\\Delta x_i} \\leq C_{max},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-a094ceea-ef1c-4b9b-b5e1-7220f50a73f4");katex.render("C", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the Courant number, $var element = document.getElementById("moose-equation-b05eda22-646e-4578-bd04-9509e7994e96");katex.render("C_{max}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the maximum allowed Courant number, $var element = document.getElementById("moose-equation-d186996e-c92c-4a04-a515-f9e16c5f77f2");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the magnitude of the velocity, $var element = document.getElementById("moose-equation-065b3bad-df61-4801-bad5-33c36b27efec");katex.render("\\Delta t", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the time step, and $var element = document.getElementById("moose-equation-f9e69b58-476f-4318-84cb-6aaed71462dc");katex.render("\\Delta x", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the interval distance, and $var element = document.getElementById("moose-equation-3314011b-d984-4fe0-b779-108ef0fd9277");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , in three dimensions, represents the index for the $var element = document.getElementById("moose-equation-18666124-b922-4038-a1de-a0d1f2ff91fe");katex.render("x", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , $var element = document.getElementById("moose-equation-499d8951-5d4e-41d2-bf62-8e05e7b9e17e");katex.render("y", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , and $var element = document.getElementById("moose-equation-329d54ab-8d90-4f22-aad1-752b30f1e0f2");katex.render("z", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ components.

The LevelSetCFLCondition postprocessor estimates $var element = document.getElementById("moose-equation-7f567cc3-0ee8-4c8c-af00-4a0a44880d72");katex.render("C", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ by using the the magnitude of the maximum velocity across quadrature points of an element ( $var element = document.getElementById("moose-equation-389ab871-9f2c-464f-8a78-ff9234a7b0cf");katex.render("u_{max}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ ) and computing the minimum element length for all elements in the finite element mesh ( $var element = document.getElementById("moose-equation-185147aa-494e-4d37-9b35-f9ecc438111b");katex.render("h_min", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ ):

$var element = document.getElementById("moose-equation-599a911c-c416-4b8f-a70c-1cfd13492ab2");katex.render("C = \\frac{u_{max}\\Delta t}{h_{min}} \\leq C_{max}.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

Finally, assuming that $var element = document.getElementById("moose-equation-0b34a580-6d66-4f8a-8b22-6c17d2faab84");katex.render("C_{max} = 1", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the maximum allowable Courant number, the maximum allowable timestep is computed as:

$var element = document.getElementById("moose-equation-7f7555ef-917d-49e0-b6f5-6aff0c8afa2d");katex.render("\\Delta t \\leq \\frac{h_{min}}{u_{max}}.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

Example Syntax

The LevelSetCFLCondition is added to the input file in the Postprocessors block as follows.

[Postprocessors]

  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]

[]

and it is designed to work to set the timestep within the TimeStepper block. Also, notice that at this point is possible to apply a "scaling" factor to the computed timestep to allow the simulation to operate at some level below the timestep limitation.

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1
  nl_rel_tol = 1e-12
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 1
  [../]

[]

Input Parameters

velocityVelocity vector variable.
C++ Type:std::vector<VariableName>
Options:
Description:Velocity vector variable.

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
execute_onTIMESTEP_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.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, TRANSFER
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.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
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.
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
outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
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

(modules/level_set/examples/vortex/vortex_supg.i)
(modules/level_set/examples/circle/circle_16.i)
(modules/level_set/examples/rotating_circle/circle_rotate_master.i)
(modules/level_set/test/tests/reinitialization/master.i)
(modules/level_set/examples/rotating_circle/circle_rotate.i)
(modules/level_set/examples/vortex/vortex.i)
(modules/level_set/examples/rotating_circle/circle_rotate_supg.i)
(modules/level_set/examples/vortex/vortex_reinit.i)

(modules/level_set/test/tests/reinitialization/master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 8
  ny = 8
  uniform_refine = 3 #1/64
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

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

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.05
    center = '0.5 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '1'
    value_y = '1'
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = phi
      auto_direction = 'x y'
    [../]
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]

  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]

  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1
  nl_rel_tol = 1e-12
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 1
  [../]

[]

[MultiApps]
  [./reinit]
    type = LevelSetReinitializationMultiApp
    input_files = 'reinit.i'
    execute_on = 'timestep_end'
  [../]
[]

[Transfers]
  [./to_sub]
    type = MultiAppCopyTransfer
    variable = phi
    source_variable = phi
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]

  [./to_sub_init]
    type = MultiAppCopyTransfer
    variable = phi_0
    source_variable = phi
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]

  [./from_sub]
    type = MultiAppCopyTransfer
    variable = phi
    source_variable = phi
    direction = from_multiapp
    multi_app = reinit
    execute_on = timestep_end
  [../]
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/level_set/test/tests/reinitialization/master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 8
  ny = 8
  uniform_refine = 3 #1/64
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

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

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.05
    center = '0.5 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '1'
    value_y = '1'
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = phi
      auto_direction = 'x y'
    [../]
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]

  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]

  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1
  nl_rel_tol = 1e-12
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 1
  [../]

[]

[MultiApps]
  [./reinit]
    type = LevelSetReinitializationMultiApp
    input_files = 'reinit.i'
    execute_on = 'timestep_end'
  [../]
[]

[Transfers]
  [./to_sub]
    type = MultiAppCopyTransfer
    variable = phi
    source_variable = phi
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]

  [./to_sub_init]
    type = MultiAppCopyTransfer
    variable = phi_0
    source_variable = phi
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]

  [./from_sub]
    type = MultiAppCopyTransfer
    variable = phi
    source_variable = phi
    direction = from_multiapp
    multi_app = reinit
    execute_on = timestep_end
  [../]
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/level_set/examples/vortex/vortex_supg.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 1
  ymax = 1
  nx = 16
  ny = 16
  uniform_refine = 2
  elem_type = QUAD9
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[AuxKernels]
  [./vec]
    type = VectorFunctionAux
    variable = velocity
    function = velocity_func
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

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

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.01184
    center = '0.5 0.75 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = LevelSetOlssonVortex
    reverse_time = 2
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]
  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
  [./advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = phi
  [../]
  [./time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 2
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/level_set/examples/circle/circle_16.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 16
  ny = 16
[]

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

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.05
    center = '0.5 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '3'
    value_y = '3'
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = phi
      auto_direction = 'x y'
    [../]
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/level_set/examples/rotating_circle/circle_rotate_master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 32
  ny = 32
  uniform_refine = 2
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

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

[BCs]
  [./all]
    type = DirichletBC
    variable = phi
    boundary = 'top bottom left right'
    value = 0
  [../]
[]

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.03
    center = '0 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '4*y'
    value_y = '-4*x'
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1.570796
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[MultiApps]
  [./reinit]
    type = LevelSetReinitializationMultiApp
    input_files = 'circle_rotate_sub.i'
    execute_on = 'timestep_end'
  [../]
[]

[Transfers]
  [./to_sub]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]
  [./to_sub_init]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi_0
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]
  [./from_sub]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi
    direction = from_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/level_set/test/tests/reinitialization/master.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 8
  ny = 8
  uniform_refine = 3 #1/64
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

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

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.05
    center = '0.5 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '1'
    value_y = '1'
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      variable = phi
      auto_direction = 'x y'
    [../]
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]

  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]

  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]

[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1
  nl_rel_tol = 1e-12
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 1
  [../]

[]

[MultiApps]
  [./reinit]
    type = LevelSetReinitializationMultiApp
    input_files = 'reinit.i'
    execute_on = 'timestep_end'
  [../]
[]

[Transfers]
  [./to_sub]
    type = MultiAppCopyTransfer
    variable = phi
    source_variable = phi
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]

  [./to_sub_init]
    type = MultiAppCopyTransfer
    variable = phi_0
    source_variable = phi
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  [../]

  [./from_sub]
    type = MultiAppCopyTransfer
    variable = phi
    source_variable = phi
    direction = from_multiapp
    multi_app = reinit
    execute_on = timestep_end
  [../]
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/level_set/examples/rotating_circle/circle_rotate.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 32
  ny = 32
  uniform_refine = 2
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

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

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.03
    center = '0 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '4*y'
    value_y = '-4*x'
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]

  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial' #timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1.570796
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/level_set/examples/vortex/vortex.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 1
  ymax = 1
  nx = 16
  ny = 16
  uniform_refine = 2
  elem_type = QUAD9
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[AuxKernels]
  [./vec]
    type = VectorFunctionAux
    variable = velocity
    function = velocity_func
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

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

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.01184
    center = '0.5 0.75 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = LevelSetOlssonVortex
    reverse_time = 2
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]
  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 2
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/level_set/examples/rotating_circle/circle_rotate_supg.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = -1
  xmax = 1
  ymin = -1
  ymax = 1
  nx = 32
  ny = 32
  uniform_refine = 2
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

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

[Functions]
  [./phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.03
    center = '0 0.5 0'
    radius = 0.15
  [../]
  [./velocity_func]
    type = ParsedVectorFunction
    value_x = '4*y'
    value_y = '-4*x'
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  [../]
  [./vel_ic]
    type = VectorFunctionIC
    variable = velocity
    function = velocity_func
  []
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]
  [./advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  [../]
  [./advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = phi
  [../]
  [./time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = phi
  [../]
[]

[Postprocessors]
  [./area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  [../]
  [./cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  end_time = 1.570796
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  [./TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  [../]
[]

[Outputs]
  csv = true
  exodus = true
[]

(modules/level_set/examples/vortex/vortex_reinit.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmax = 1
  ymax = 1
  nx = 16
  ny = 16
  uniform_refine = 2
  elem_type = QUAD9
  second_order = true
[]

[AuxVariables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
[]

[AuxKernels]
  [./vec]
    type = VectorFunctionAux
    variable = velocity
    function = velocity_func
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Variables]
  [phi]
    family = LAGRANGE
  []
[]

[Functions]
  [phi_exact]
    type = LevelSetOlssonBubble
    epsilon = 0.03
    center = '0.5 0.75 0'
    radius = 0.15
  []
  [./velocity_func]
    type = LevelSetOlssonVortex
    reverse_time = 2
  [../]
[]

[ICs]
  [phi_ic]
    type = FunctionIC
    function = phi_exact
    variable = phi
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = phi
  []
  [advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = phi
  []
  [advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = phi
  []
  [time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = phi
  []
[]

[Postprocessors]
  [area]
    type = LevelSetVolume
    threshold = 0.5
    variable = phi
    location = outside
    execute_on = 'initial timestep_end'
  []
  [cfl]
    type = LevelSetCFLCondition
    velocity = velocity
    execute_on = 'initial timestep_end'
  []
[]

[Problem]
  type = LevelSetProblem
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  start_time = 0
  end_time = 2
  scheme = crank-nicolson
  [TimeStepper]
    type = PostprocessorDT
    postprocessor = cfl
    scale = 0.8
  []
[]

[MultiApps]
  [reinit]
    type = LevelSetReinitializationMultiApp
    input_files = 'vortex_reinit_sub.i'
    execute_on = TIMESTEP_END
  []
[]

[Transfers]
  [to_sub]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  []

  [to_sub_init]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi_0
    direction = to_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  []

  [from_sub]
    type = MultiAppCopyTransfer
    source_variable = phi
    variable = phi
    direction = from_multiapp
    multi_app = reinit
    execute_on = 'timestep_end'
  []
[]

[Outputs]
  csv = true
  exodus = true
[]

Example Syntax
Input Parameters
Input Files

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LevelSetCFLCondition

Example Syntax

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Input Files