LevelSetOlssonReinitialization

This kernel implements the non-time portion of the conservative "re-initialization" algorithm of Olsson et al. (2007) that transforms $var element = document.getElementById("moose-equation-8894b932-34c5-46f6-a9c6-a27f347a5e42");katex.render("u_h", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ into a smooth function in the range $var element = document.getElementById("moose-equation-41b31e51-9215-4331-aa39-7eae322febd0");katex.render("[0, 1]", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ rather than a signed distance, which is useful for certain types of problems such as phase identification. The weak form of the re-initialization equation is: find $var element = document.getElementById("moose-equation-9999e6fb-fb37-4969-a9a2-68aacbb900fc");katex.render("U_h", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ such that

$var element = document.getElementById("moose-equation-739383ff-9be4-4b64-b23a-047c113c4b1b");katex.render(" \\left(\\frac{\\partial U_h}{\\partial \\tau}, \\psi_i\\right) + \\underbrace{\\left(\\nabla\\psi_i, (-f + \\epsilon\\nabla U_h\\cdot\\hat{n}_{\\ast})\\hat{n}_{\\ast}\\right)}_{\\textrm{LevelSetOlssonReinitialization}} = 0,", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-655b18e2-1f9b-4316-a556-29bbefeedbab");katex.render("\\tau", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the pseudo time during the re-initialization, $var element = document.getElementById("moose-equation-4fe9bd08-56b0-4191-b839-d31939c56e00");katex.render("\\hat{n}_{\\ast}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the normal vector computed from the level set variable $var element = document.getElementById("moose-equation-fdfc3c19-e3f5-40ca-9e59-a914ca73a755");katex.render("u_h", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ at pseudo time $var element = document.getElementById("moose-equation-2782069d-1498-48c0-b947-311da6389bc1");katex.render("\\tau=0", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , $var element = document.getElementById("moose-equation-7b94d794-3367-4e49-82b2-a4eb47fffd0d");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the interface thickness, $var element = document.getElementById("moose-equation-03191590-c5e3-4bc5-8bbe-b6bb938ccb6e");katex.render("f\\equiv U_h(1-U_h)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , and $var element = document.getElementById("moose-equation-1c2b33f9-cb3c-4f46-999d-bf8c32ab1ae7");katex.render("U_h(\\tau=0) = u_h", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ .

When steady-state for $var element = document.getElementById("moose-equation-cb274b08-93f4-4655-b31e-d7a2c068e7e8");katex.render("U_h", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is detected when (see LevelSetOlssonTerminator the entire process is repeated at time $var element = document.getElementById("moose-equation-df570033-d570-48c9-a455-fa27e5a358c2");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ .

Example Syntax

The LevelSetOlssonReinitialization kernel is typically employed in a reinitialization sub-app (see the MOOSE MultiApp system), within this context this Kernel is invoked with the [Kernels] as follows.

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

  [./reinit]
    type = LevelSetOlssonReinitialization
    variable = phi
    phi_0 = phi_0
    epsilon = 0.05
  [../]
[]

/opt/civet/build_0/moose/modules/level_set/test/tests/reinitialization/reinit.i

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

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

[AuxVariables]
  [./phi_0]
  [../]
[]

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

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

  [./reinit]
    type = LevelSetOlssonReinitialization
    variable = phi
    phi_0 = phi_0
    epsilon = 0.05
  [../]
[]

[Problem]
  type = LevelSetReinitializationProblem
[]

[UserObjects]
  [./arnold]
    type = LevelSetOlssonTerminator
    tol = 1
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  num_steps = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type -ksp_gmres_restart'
  petsc_options_value = 'hypre    boomeramg    300'
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.001
    optimal_iterations = 5
    growth_factor = 5
  [../]
[]

[Outputs]
[]

Input Parameters

epsilonThe epsilon coefficient to be used in the reinitialization calculation.
C++ Type:PostprocessorName
Options:
Description:The epsilon coefficient to be used in the reinitialization calculation.
phi_0The level set variable to be reinitialized as signed distance function.
C++ Type:std::vector
Options:
Description:The level set variable to be reinitialized as signed distance function.
variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this Kernel operates on

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Options:
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

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

Tagging Parameters

Input Files

modules/level_set/examples/vortex/vortex_reinit_sub.i
modules/level_set/test/tests/kernels/olsson_reinitialization/olsson_1d.i
modules/level_set/examples/rotating_circle/circle_rotate_sub.i
modules/level_set/test/tests/reinitialization/reinit.i

modules/level_set/examples/vortex/vortex_reinit_sub.i

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

[Variables/phi]
    family = LAGRANGE
[]

[AuxVariables]
  [phi_0]
    family = LAGRANGE
  []
  [marker]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[Kernels]
  [time]
    type = TimeDerivative
    variable = phi
  []
  [reinit]
    type = LevelSetOlssonReinitialization
    variable = phi
    phi_0 = phi_0
    epsilon = 0.03
  []
[]

[Problem]
  type = LevelSetReinitializationProblem
[]

[UserObjects]
  [arnold]
    type = LevelSetOlssonTerminator
    tol = 0.5
    min_steps = 3
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  start_time = 0
  num_steps = 100
  nl_abs_tol = 1e-14
  scheme = crank-nicolson
  line_search = none
  dt = 0.003
[]

[Outputs]
[]

modules/level_set/test/tests/kernels/olsson_reinitialization/olsson_1d.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 8
  ny = 8
  uniform_refine = 2
[]

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

[AuxVariables]
  [./phi_0]
    family = MONOMIAL
    order = FIRST
  [../]
  [./phi_exact]
  [../]
[]

[AuxKernels]
  [./phi_exact]
    type = FunctionAux
    function = phi_exact
    variable = phi_exact
  [../]
[]

[Functions]
  [./phi_initial]
    type = ParsedFunction
    value = '1-x'
  [../]
  [./phi_exact]
    type = ParsedFunction
    vars = epsilon
    vals = 0.05
    value = '1 / (1+exp((x-0.5)/epsilon))'
  [../]
[]

[ICs]
  [./phi_ic]
    type = FunctionIC
    function = phi_initial
    variable = phi
  [../]
  [./phi_0_ic]
    type = FunctionIC
    function = phi_initial
    variable = phi_0
  [../]
[]

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

  [./reinit]
    type = LevelSetOlssonReinitialization
    variable = phi
    phi_0 = phi_0
    epsilon = 0.05
  [../]
[]

[UserObjects]
  [./arnold]
    type = LevelSetOlssonTerminator
    tol = 0.1
  [../]
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = phi
    function = phi_exact
    execute_on = 'initial timestep_end'
  [../]
  [./ndofs]
    type = NumDOFs
  [../]
[]

[VectorPostprocessors]
  [./line]
    type = LineValueSampler
    start_point = '0 0.5 0'
    end_point =  '1 0.5 0'
    variable = phi
    num_points = 100
    sort_by = x
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  l_max_its = 100
  nl_max_its = 100
  solve_type = PJFNK
  num_steps = 10
  start_time = 0
  nl_abs_tol = 1e-13
  scheme = implicit-euler
  dt = 0.05
  petsc_options_iname = '-pc_type -pc_sub_type -ksp_gmres_restart'
  petsc_options_value = 'hypre    boomeramg    300'
[]

[Outputs]
  exodus = true
  [./out]
    type = CSV
    time_data = true
    file_base = output/olsson_1d_out
  [../]
[]

modules/level_set/examples/rotating_circle/circle_rotate_sub.i

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

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

[AuxVariables]
  [./phi_0]
  [../]
  [./marker]
  [../]
[]

[Kernels]
  [./time]
    type = TimeDerivative
    variable = phi
  [../]
  [./reinit]
    type = LevelSetOlssonReinitialization
    variable = phi
    phi_0 = phi_0
    epsilon = 0.03
  [../]
[]

[Problem]
  type = LevelSetReinitializationProblem
[]

[UserObjects]
  [./arnold]
    type = LevelSetOlssonTerminator
    tol = 1
    min_steps = 3
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  start_time = 0
  num_steps = 100
  nl_abs_tol = 1e-14
  scheme = crank-nicolson
  line_search = none
  petsc_options_iname = '-pc_type -pc_sub_type'
  petsc_options_value = 'asm      ilu'
  dt = 0.003
[]

[Outputs]
[]

modules/level_set/test/tests/reinitialization/reinit.i

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

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

[AuxVariables]
  [./phi_0]
  [../]
[]

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

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

  [./reinit]
    type = LevelSetOlssonReinitialization
    variable = phi
    phi_0 = phi_0
    epsilon = 0.05
  [../]
[]

[Problem]
  type = LevelSetReinitializationProblem
[]

[UserObjects]
  [./arnold]
    type = LevelSetOlssonTerminator
    tol = 1
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  start_time = 0
  num_steps = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  scheme = crank-nicolson
  petsc_options_iname = '-pc_type -pc_sub_type -ksp_gmres_restart'
  petsc_options_value = 'hypre    boomeramg    300'
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.001
    optimal_iterations = 5
    growth_factor = 5
  [../]
[]

[Outputs]
[]

References

Elin Olsson, Gunilla Kreiss, and Sara Zahedi. A conservative level set method for two phase flow ii. Journal of Computational Physics, 225(1):785–807, 2007. URL: http://dx.doi.org/10.1016/j.jcp.2006.12.027.

@article{olsson2007conservative,
    author = "Olsson, Elin and Kreiss, Gunilla and Zahedi, Sara",
    title = "A conservative level set method for two phase flow II",
    journal = "Journal of Computational Physics",
    volume = "225",
    number = "1",
    pages = "785--807",
    year = "2007",
    publisher = "Elsevier",
    url = "http://dx.doi.org/10.1016/j.jcp.2006.12.027"
}

Example Syntax
Input Parameters
Input Files
References

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