FluctuationsIC

construction:Undocumented Class

The FluctuationsIC has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.

Overview

Useful ICs function for benchmarking purposes. Typically in numerical simulations, the randomness of a function is prescribed by a random number generator which can depend on the processors. This IC allows for a pseudo-random function which will be the same on any machine.

$var element = document.getElementById("moose-equation-1e43456a-c03f-4840-8eff-aa57716731b6");katex.render(" \\begin{aligned} \\delta_\\eta = \\cos{q_1 x - 4}\\sin{q_1 y} + \\cos{q_2 x} \\cos{q_2 y} + ... \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$

Example Input File Syntax

Input Parameters

epsilonepsilon value for psudorandom function
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:epsilon value for psudorandom function
hh factor on cos^2 term
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:h factor on cos^2 term
q1first q-vector for pseudorandom function
C++ Type:libMesh::Point
Controllable:No
Description:first q-vector for pseudorandom function
q2second q-vector for pseudorandom function
C++ Type:libMesh::Point
Controllable:No
Description:second q-vector for pseudorandom function
q3third q-vector for pseudorandom function
C++ Type:libMesh::Point
Controllable:No
Description:third q-vector for pseudorandom function
q4fourth q-vector for pseudorandom function
C++ Type:libMesh::Point
Controllable:No
Description:fourth q-vector for pseudorandom function
variableThe variable this initial condition is supposed to provide values for.
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:The variable this initial condition is supposed to provide values for.

Required Parameters

base_value0Value that is fluctuated about
Default:0
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:Value that is fluctuated about
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
stateCURRENTThis parameter is used to set old state solutions at the start of simulation. If specifying multiple states at the start of simulation, use one IC object for each state being specified. The states are CURRENT=0 OLD=1 OLDER=2. States older than 2 are not currently supported. When the user only specifies current state, the solution is copied to the old and older states, as expected. This functionality is mainly used for dynamic simulations with explicit time integration schemes, where old solution states are used in the velocity and acceleration approximations.
Default:CURRENT
C++ Type:MooseEnum
Options:CURRENT, OLD, OLDER
Controllable:No
Description:This parameter is used to set old state solutions at the start of simulation. If specifying multiple states at the start of simulation, use one IC object for each state being specified. The states are CURRENT=0 OLD=1 OLDER=2. States older than 2 are not currently supported. When the user only specifies current state, the solution is copied to the old and older states, as expected. This functionality is mainly used for dynamic simulations with explicit time integration schemes, where old solution states are used in the velocity and acceleration approximations.

Optional 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:No
Description:Set the enabled status of the MooseObject.
ignore_uo_dependencyFalseWhen set to true, a UserObject retrieved by this IC will not be executed before the this IC
Default:False
C++ Type:bool
Controllable:No
Description:When set to true, a UserObject retrieved by this IC will not be executed before the this IC

Advanced Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/ics/PTO_3D_fluct.i)

(test/tests/ics/PTO_3D_fluct.i)

TC   = 25.0
um   = -0.01
l0   = 1.0
L    = 4.0
nx   = 4

alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110   = ${fparse l0*l0*abs(alpha1)}

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = ${nx}
    ny = ${nx}
    nz = ${nx}
    xmin = 0.0
    xmax = ${L}
    ymin = 0.0
    ymax = ${L}
    zmin = 0.0
    zmax = ${L}
    elem_type = HEX8
  []
  [pin]
    type = ExtraNodesetGenerator
    input = gen
    new_boundary = 'pin_node'
    coord = '2.0 2.0 2.0'
    use_closest_node = true
  []
[]

[GlobalParams]
  polar_x = polar_x
  polar_y = polar_y
  polar_z = polar_z
[]

[Variables]
  [polar_x]
    order = FIRST
    family = LAGRANGE
    [InitialCondition]
      type = FluctuationsIC
      epsilon = 1.0e-5
      q1 = '354 1005 645'
      q2 = '715 1065 1132'
      q3 = '391 305 1106'
      q4 = '1053 1116 627'
      h = 0.22
    []
  []
  [polar_y]
    order = FIRST
    family = LAGRANGE
    [InitialCondition]
      type = FluctuationsIC
      epsilon = 1.0e-5
      q1 = '354 850 10'
      q2 = '715 28 5'
      q3 = '391 305 1106'
      q4 = '653 1116 627'
      h = 0.15
    []
  []
  [polar_z]
    order = FIRST
    family = LAGRANGE
    [InitialCondition]
      type = FluctuationsIC
      epsilon = 1.0e-5
      q1 = '860 165 645'
      q2 = '715 665 1332'
      q3 = '361 15 706'
      q4 = '253 1116 627'
      h = 0.05
    []
  []
  [u_x]
    order = FIRST
    family = LAGRANGE
  []
  [u_y]
    order = FIRST
    family = LAGRANGE
  []
  [u_z]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [Pmag]
    order = FIRST
    family = LAGRANGE
  []
  [wE]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [Pmag]
    type = ParsedAux
    variable = Pmag
    coupled_variables = 'polar_x polar_y polar_z'
    expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
    execute_on = 'initial timestep_end'
  []
  [wE]
    type = WallEnergyDensity
    variable = wE
    execute_on = 'initial timestep_end'
  []
  [strain_xx]
    type = RankTwoAux
    variable = strain_xx
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
    execute_on = 'initial timestep_end'
  []
  [strain_zz]
    type = RankTwoAux
    variable = strain_zz
    rank_two_tensor = total_strain
    index_i = 2
    index_j = 2
    execute_on = 'initial timestep_end'
  []
[]

[Materials]
  [Landau_P]
    type = GenericConstantMaterial
    prop_names  = 'alpha1     alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
    prop_values = '${alpha1}  -0.073  0.75    0.26     0.61     -3.7     0.0       0.0       0.0       0.0'
  []
  [Landau_G]
    type = GenericConstantMaterial
    prop_names  = 'G110     G11_G110 G12_G110 G44_G110 G44P_G110'
    prop_values = '${G110}  0.6      0.0      0.3      0.3'
  []
  [mat_C]
    type = GenericConstantMaterial
    prop_names  = 'C11     C12    C44'
    prop_values = '174.269 79.029 47.62'
  []
  [mat_Q]
    type = GenericConstantMaterial
    prop_names  = 'Q11   Q12    Q44'
    prop_values = '0.089 -0.026 0.03375'
  []
  [elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
  []
  [misfit]
    type = GenericConstantRankTwoTensor
    tensor_name = global_strain
    tensor_values = '${um} 0 0   0 ${um} 0   0 0 0'
  []
  [strain]
    type = ComputeSmallStrain
    displacements = 'u_x u_y u_z'
    eigenstrain_names = 'ferro'
    global_strain = global_strain
  []
  [ferro]
    type = ComputeCubicParentElectrostrictiveStrain
    eigenstrain_name = ferro
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Kernels]
  [time_x]
    type = TimeDerivative
    variable = polar_x
  []
  [time_y]
    type = TimeDerivative
    variable = polar_y
  []
  [time_z]
    type = TimeDerivative
    variable = polar_z
  []

  [div_x]
    type = StressDivergenceTensors
    variable = u_x
    displacements = 'u_x u_y u_z'
    component = 0
  []
  [div_y]
    type = StressDivergenceTensors
    variable = u_y
    displacements = 'u_x u_y u_z'
    component = 1
  []
  [div_z]
    type = StressDivergenceTensors
    variable = u_z
    displacements = 'u_x u_y u_z'
    component = 2
  []

  [bed_x]
    type = BulkEnergyDerivativeEighth
    variable = polar_x
    component = 0
  []
  [bed_y]
    type = BulkEnergyDerivativeEighth
    variable = polar_y
    component = 1
  []
  [bed_z]
    type = BulkEnergyDerivativeEighth
    variable = polar_z
    component = 2
  []

  [walled_x]
    type = WallEnergyDerivative
    variable = polar_x
    component = 0
  []
  [walled_y]
    type = WallEnergyDerivative
    variable = polar_y
    component = 1
  []
  [walled_z]
    type = WallEnergyDerivative
    variable = polar_z
    component = 2
  []

  [electrostr_x]
    type = CubicParentElasticPDerivative
    variable = polar_x
    component = 0
    displacements = 'u_x u_y u_z'
  []
  [electrostr_y]
    type = CubicParentElasticPDerivative
    variable = polar_y
    component = 1
    displacements = 'u_x u_y u_z'
  []
  [electrostr_z]
    type = CubicParentElasticPDerivative
    variable = polar_z
    component = 2
    displacements = 'u_x u_y u_z'
  []
[]

[BCs]
  [Periodic]
    [xyz]
      auto_direction = 'x y z'
      variable = 'polar_x polar_y polar_z u_x u_y u_z'
    []
  []
  [pin_ux]
    type = DirichletBC
    variable = u_x
    boundary = 'pin_node'
    value = 0
  []
  [pin_uy]
    type = DirichletBC
    variable = u_y
    boundary = 'pin_node'
    value = 0
  []
  [pin_uz]
    type = DirichletBC
    variable = u_z
    boundary = 'pin_node'
    value = 0
  []
[]

[Postprocessors]
  [Fbulk]
    type = BulkEnergyEighth
    execute_on = 'initial timestep_end'
  []
  [Fwall]
    type = WallEnergy
    execute_on = 'initial timestep_end'
  []
  [Felastic]
    type = CubicParentElasticEnergy
    execute_on = 'initial timestep_end'
  []
  [Ftotal]
    type = LinearCombinationPostprocessor
    pp_names = 'Fbulk Fwall Felastic'
    pp_coefs = '1 1 1'
    execute_on = 'timestep_end'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
    petsc_options_value = 'bjacobi  ilu          gmres     1e-6      100'
  []
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = PJFNK

  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10

  l_max_its = 200
  end_time = 5.0
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.5
    growth_factor = 1.3
    cutback_factor = 0.8
    optimal_iterations = 8
    linear_iteration_ratio = 1000
  []
  dtmax = 5.0

  num_steps = 3
[]

[Outputs]
  print_linear_residuals = false
  [exo]
    type = Exodus
  []
[]