Melt pool INS residual material

Computes extra residuals from melt pool for the INS equations.

Description

The momentum conservation equations(Wen and Shin, 2010) are described by

$var element = document.getElementById("moose-equation-54dd317f-f127-4123-980d-9a9d3afa3dcf");katex.render("\\rho\\left(\\frac{\\partial{\\overrightarrow {u}}}{\\partial t}+ \\overrightarrow{u}\\cdot{\\nabla\\overrightarrow {u}}\\right)- \\nabla\\left [ -p\\mathbf{I}+\\mu\\left(\\nabla\\overrightarrow {u} + \\nabla \\overrightarrow u ^T\\right) \\right ] = -\\frac{\\mu_m}{K}\\overrightarrow{u} + \\gamma\\overrightarrow {n} \\kappa \\delta(\\phi)-\\nabla_s\\gamma\\delta(\\phi)-0.55P_{sat}\\delta(\\phi).", element, {displayMode:true,throwOnError:false});$

The first term on the right is a Darcy term, representing the damping force when fluid passes through mushy zone. $var element = document.getElementById("moose-equation-4e1f0d8a-0c25-4f19-af20-c92ef2428bfb");katex.render("K", element, {displayMode:false,throwOnError:false});$ is the isotropic permeability given by $var element = document.getElementById("moose-equation-d66b6921-a226-42a5-a88f-73652db3b9eb");katex.render("K^{-1}=K_0^{-1}\\frac{(1-f_l)^2}{f_l^3+\\tau},", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-e2d23991-5fb0-4f35-bff0-888eeb06ecd7");katex.render("K_0", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-cac710bf-6d83-42c5-a768-7acb5def3874");katex.render("\\tau", element, {displayMode:false,throwOnError:false});$ are constants and $var element = document.getElementById("moose-equation-6f588185-b2bc-4363-a86e-96ad9edc2d11");katex.render("f_l", element, {displayMode:false,throwOnError:false});$ is fluid mass fraction.

The second and third terms represent surface tension and Marangoni forces at the free surfaces. The surface tension acts in the normal direction while Marangoni force acts in the tangential direction of the free surface. The surface gradient is expressed as $var element = document.getElementById("moose-equation-f316213c-d036-451c-bd10-fd05cf158c61");katex.render("\\nabla_s\\gamma = \\gamma_T\\nabla_sT = \\gamma_T (\\mathbf{I}-\\overrightarrow n \\otimes \\overrightarrow n)\\nabla T.", element, {displayMode:true,throwOnError:false});$

The fourth term is the recoil pressure at the keyhole(Tan et al., 2013).

The mass conservation equation(Wen and Shin, 2010; Esmaeeli and Tryggvason, 2004) is modified to account for the phase change from liquid to vapor: $var element = document.getElementById("moose-equation-eb16f246-ca43-4a3a-b9af-154960991186");katex.render("\\nabla\\cdot \\overrightarrow {u} = \\dot{m}\\delta(\\phi)\\left(\\frac{1}{\\rho_g}-\\frac{1}{\\rho_l}\\right),", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-24e5b861-527e-4687-bf89-5955d6a7c02a");katex.render("\\dot{m}", element, {displayMode:false,throwOnError:false});$ is mass transfer rate (INSMeltPoolMassTransferMaterial) and $var element = document.getElementById("moose-equation-2456e24c-6e49-4dd5-bc05-496517fe50a8");katex.render("\\rho_g", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-16542505-e121-46a1-ad87-699d9f902951");katex.render("\\rho_l", element, {displayMode:false,throwOnError:false});$ are gas density and liquid density, respectively.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [ins_melt_pool_mat]
    type = INSMeltPoolMaterial<<<{"description": "Computes extra residuals from melt pool for the INS equations.", "href": "INSMeltPoolMaterial.html"}>>>
    level_set_gradient<<<{"description": "Regularized gradient of Level set variable"}>>> = grad_ls
    velocity<<<{"description": "The velocity"}>>> = velocity
    pressure<<<{"description": "The pressure"}>>> = p
    alpha<<<{"description": "Multiplicative factor on the stabilization parameter tau."}>>> = .1
    temperature<<<{"description": "The temperature"}>>> = temp
    curvature<<<{"description": "Regularized curvature variable"}>>> = curvature
    surface_tension<<<{"description": "Surface tension coefficient."}>>> = 1.169
    thermal_capillary<<<{"description": "Thermalcapillary coefficient."}>>> = -4.3e-4
    rho_l<<<{"description": "Liquid density."}>>> = 8000
    rho_g<<<{"description": "Gas density."}>>> = 1.184
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
    output_properties<<<{"description": "List of material properties, from this material, to output (outputs must also be defined to an output type)"}>>> = melt_pool_mass_rate
    cp_name<<<{"description": "The name of the specific heat capacity"}>>> = specific_heat
    k_name<<<{"description": "the name of the thermal conductivity material property"}>>> = thermal_conductivity
  []
[]

Input Parameters

curvatureRegularized curvature variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Regularized curvature variable
level_set_gradientRegularized gradient of Level set variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Regularized gradient of Level set variable
pressureThe pressure
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The pressure
rho_gGas density.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Gas density.
rho_lLiquid density.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Liquid density.
surface_tensionSurface tension coefficient.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Surface tension coefficient.
temperatureThe temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The temperature
thermal_capillaryThermalcapillary coefficient.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thermalcapillary coefficient.
velocityThe velocity
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The velocity

Required Parameters

alpha1Multiplicative factor on the stabilization parameter tau.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Multiplicative factor on the stabilization parameter tau.
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
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
cp_namecpThe name of the specific heat capacity
Default:cp
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The name of the specific heat capacity
declare_suffixAn optional suffix parameter that can be appended to any declared 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 declared properties. The suffix will be prepended with a '_' character.
grad_k_namegrad_kthe name of the gradient of the thermal conductivity material property
Default:grad_k
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:the name of the gradient of the thermal conductivity material property
k_namekthe name of the thermal conductivity material property
Default:k
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:the name of the thermal conductivity material property
mu_namemuThe name of the dynamic viscosity
Default:mu
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The name of the dynamic viscosity
rho_namerhoThe name of the density
Default:rho
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The name of the density

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: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

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs 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/melt_pool_fluid/fluid.i)
(examples/melt_pool_2d/melt_pool.i)
(test/tests/melt_pool_level_set/level_set.i)
(examples/melt_pool_3d/melt_pool.i)

References

Asghar Esmaeeli and Grétar Tryggvason. Computations of film boiling. part i: numerical method. International Journal of Heat and Mass Transfer, 47(25):5451 – 5461, 2004. URL: http://www.sciencedirect.com/science/article/pii/S0017931004002947, doi:https://doi.org/10.1016/j.ijheatmasstransfer.2004.07.027.

@article{ESMAEELI2004,
    author = "Esmaeeli, Asghar and Tryggvason, Grétar",
    title = "Computations of film boiling. Part I: numerical method",
    journal = "International Journal of Heat and Mass Transfer",
    volume = "47",
    number = "25",
    pages = "5451 - 5461",
    year = "2004",
    issn = "0017-9310",
    doi = "https://doi.org/10.1016/j.ijheatmasstransfer.2004.07.027",
    url = "http://www.sciencedirect.com/science/article/pii/S0017931004002947"
}

Wenda Tan, Neil S Bailey, and Yung C Shin. Investigation of keyhole plume and molten pool based on a three-dimensional dynamic model with sharp interface formulation. Journal of Physics D: Applied Physics, 46(5):055501, 2013.

@article{Tan2013,
    author = "Tan, Wenda and Bailey, Neil S and Shin, Yung C",
    year = "2013",
    publisher = "IOP Publishing",
    volume = "46",
    number = "5",
    pages = "055501",
    title = "Investigation of keyhole plume and molten pool based on a three-dimensional dynamic model with sharp interface formulation",
    journal = "Journal of Physics D: Applied Physics"
}

Shaoyi Wen and Yung C. Shin. Modeling of transport phenomena during the coaxial laser direct deposition process. Journal of Applied Physics, 108(4):044908, 2010. doi:10.1063/1.3474655.

@article{ShaoyiWen2010,
    author = "Wen, Shaoyi and Shin, Yung C.",
    title = "Modeling of transport phenomena during the coaxial laser direct deposition process",
    journal = "Journal of Applied Physics",
    volume = "108",
    number = "4",
    pages = "044908",
    year = "2010",
    doi = "10.1063/1.3474655"
}

(test/tests/melt_pool_fluid/fluid.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.01
    ymin = 0
    ymax = 0.01
    nx = 50
    ny = 50
    elem_type = QUAD4
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    coord = '0.0 0.01'
    input = gen
  []
[]

[ICs]
  [ls_ic]
    type = FunctionIC
    function = ls_exact
    variable = ls
  []
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Variables]
  [temp]
    initial_condition = 300
  []
  [grad_ls]
    family = LAGRANGE_VEC
  []
  [velocity]
    family = LAGRANGE_VEC
  []
  [p]
  []
  [curvature]
  []
[]

[AuxVariables]
  [ls]
  []
[]

[Functions]
  [ls_exact]
    type = LevelSetOlssonPlane
    epsilon = 0.0002
    point = '0.005 0.005 0'
    normal = '0 1 0'
  []
[]

[BCs]
  [no_slip]
    type = ADVectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom left right'
  []
  [no_bc]
    type = INSADMomentumNoBCBC
    variable = velocity
    viscous_form = 'traction'
    boundary = 'top'
    pressure = p
  []
  [pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  []
[]

[Kernels]
  [curvature]
    type = LevelSetCurvatureRegularization
    level_set_regularized_gradient = grad_ls
    variable = curvature
    varepsilon = 2e-3
  []

  [grad_ls]
    type = VariableGradientRegularization
    regularized_var = ls
    variable = grad_ls
  []

  [heat_time]
    type = ADHeatConductionTimeDerivative
    specific_heat = specific_heat
    density_name = rho
    variable = temp
  []

  [heat_cond]
    type = ADHeatConduction
    thermal_conductivity = thermal_conductivity
    variable = temp
  []

  [heat_conv]
    type = INSADEnergyAdvection
    variable = temp
  []

  [heat_source]
    type = MeltPoolHeatSource
    variable = temp
    laser_power = 100
    effective_beam_radius = 0.25e-3
    absorption_coefficient = 0.27
    heat_transfer_coefficient = 100
    StefanBoltzmann_constant = 5.67e-8
    material_emissivity = 0.59
    ambient_temperature = 300
    laser_location_x = '0.005 + 6e-3*t'
    laser_location_y = '0.005'
    rho_l = 8000
    rho_g = 1.184
    vaporization_latent_heat = 6.1e6
  []

  [mass]
    type = INSADMass
    variable = p
  []

  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  []

  [momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  []

  [momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
    viscous_form = 'traction'
  []

  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []

  [momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [melt_pool_momentum_source]
    type = INSMeltPoolMomentumSource
    variable = velocity
  []
[]

[Materials]
  [thermal]
    type = LevelSetThermalMaterial
    temperature = temp
    c_g = 300
    c_s = 500
    c_l = 500
    k_g = 0.017
    k_s = 31.8724
    k_l = 209.3
    solidus_temperature = 1648
    latent_heat = 2.5e5
    outputs = all
  []
  [mushy]
    type = MushyZoneMaterial
    temperature = temp
    liquidus_temperature = 1673
    solidus_temperature = 1648
    rho_s = 8000
    rho_l = 8000
    outputs = all
  []
  [delta]
    type = LevelSetDeltaFunction
    level_set_gradient = grad_ls
    outputs = all
  []
  [heaviside]
    type = LevelSetHeavisideFunction
    level_set = ls
    outputs = all
  []
  [ins_melt_pool_mat]
    type = INSMeltPoolMaterial
    level_set_gradient = grad_ls
    velocity = velocity
    pressure = p
    alpha = .1
    temperature = temp
    curvature = curvature
    surface_tension = 1.169
    thermal_capillary = -4.3e-4
    rho_l = 8000
    rho_g = 1.184
    outputs = all
    output_properties = melt_pool_mass_rate
    cp_name = specific_heat
    k_name = thermal_conductivity
  []
  [mass_transfer]
    type = INSMeltPoolMassTransferMaterial
    temperature = temp
    Boltzmann_constant = 1.38064852e-23
    vaporization_latent_heat = 6.1e6
    atomic_weight = 97.43e-27
    vaporization_temperature = 3134
    reference_pressure = 1.01e5
    outputs = all
  []
  [fluid]
    type = LevelSetFluidMaterial
    rho_g = 1.184
    rho_s = 8000
    rho_l = 8000
    mu_g = 1.81e-5
    mu_l = 0.1
    permeability_constant = 1e-8
    outputs = all
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12
  num_steps = 2
  line_search = 'none'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  nl_div_tol = 1e20
  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
[]

[Outputs]
  exodus = true
[]

(test/tests/melt_pool_fluid/fluid.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.01
    ymin = 0
    ymax = 0.01
    nx = 50
    ny = 50
    elem_type = QUAD4
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    coord = '0.0 0.01'
    input = gen
  []
[]

[ICs]
  [ls_ic]
    type = FunctionIC
    function = ls_exact
    variable = ls
  []
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Variables]
  [temp]
    initial_condition = 300
  []
  [grad_ls]
    family = LAGRANGE_VEC
  []
  [velocity]
    family = LAGRANGE_VEC
  []
  [p]
  []
  [curvature]
  []
[]

[AuxVariables]
  [ls]
  []
[]

[Functions]
  [ls_exact]
    type = LevelSetOlssonPlane
    epsilon = 0.0002
    point = '0.005 0.005 0'
    normal = '0 1 0'
  []
[]

[BCs]
  [no_slip]
    type = ADVectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom left right'
  []
  [no_bc]
    type = INSADMomentumNoBCBC
    variable = velocity
    viscous_form = 'traction'
    boundary = 'top'
    pressure = p
  []
  [pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  []
[]

[Kernels]
  [curvature]
    type = LevelSetCurvatureRegularization
    level_set_regularized_gradient = grad_ls
    variable = curvature
    varepsilon = 2e-3
  []

  [grad_ls]
    type = VariableGradientRegularization
    regularized_var = ls
    variable = grad_ls
  []

  [heat_time]
    type = ADHeatConductionTimeDerivative
    specific_heat = specific_heat
    density_name = rho
    variable = temp
  []

  [heat_cond]
    type = ADHeatConduction
    thermal_conductivity = thermal_conductivity
    variable = temp
  []

  [heat_conv]
    type = INSADEnergyAdvection
    variable = temp
  []

  [heat_source]
    type = MeltPoolHeatSource
    variable = temp
    laser_power = 100
    effective_beam_radius = 0.25e-3
    absorption_coefficient = 0.27
    heat_transfer_coefficient = 100
    StefanBoltzmann_constant = 5.67e-8
    material_emissivity = 0.59
    ambient_temperature = 300
    laser_location_x = '0.005 + 6e-3*t'
    laser_location_y = '0.005'
    rho_l = 8000
    rho_g = 1.184
    vaporization_latent_heat = 6.1e6
  []

  [mass]
    type = INSADMass
    variable = p
  []

  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  []

  [momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  []

  [momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
    viscous_form = 'traction'
  []

  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []

  [momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [melt_pool_momentum_source]
    type = INSMeltPoolMomentumSource
    variable = velocity
  []
[]

[Materials]
  [thermal]
    type = LevelSetThermalMaterial
    temperature = temp
    c_g = 300
    c_s = 500
    c_l = 500
    k_g = 0.017
    k_s = 31.8724
    k_l = 209.3
    solidus_temperature = 1648
    latent_heat = 2.5e5
    outputs = all
  []
  [mushy]
    type = MushyZoneMaterial
    temperature = temp
    liquidus_temperature = 1673
    solidus_temperature = 1648
    rho_s = 8000
    rho_l = 8000
    outputs = all
  []
  [delta]
    type = LevelSetDeltaFunction
    level_set_gradient = grad_ls
    outputs = all
  []
  [heaviside]
    type = LevelSetHeavisideFunction
    level_set = ls
    outputs = all
  []
  [ins_melt_pool_mat]
    type = INSMeltPoolMaterial
    level_set_gradient = grad_ls
    velocity = velocity
    pressure = p
    alpha = .1
    temperature = temp
    curvature = curvature
    surface_tension = 1.169
    thermal_capillary = -4.3e-4
    rho_l = 8000
    rho_g = 1.184
    outputs = all
    output_properties = melt_pool_mass_rate
    cp_name = specific_heat
    k_name = thermal_conductivity
  []
  [mass_transfer]
    type = INSMeltPoolMassTransferMaterial
    temperature = temp
    Boltzmann_constant = 1.38064852e-23
    vaporization_latent_heat = 6.1e6
    atomic_weight = 97.43e-27
    vaporization_temperature = 3134
    reference_pressure = 1.01e5
    outputs = all
  []
  [fluid]
    type = LevelSetFluidMaterial
    rho_g = 1.184
    rho_s = 8000
    rho_l = 8000
    mu_g = 1.81e-5
    mu_l = 0.1
    permeability_constant = 1e-8
    outputs = all
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12
  num_steps = 2
  line_search = 'none'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  nl_div_tol = 1e20
  automatic_scaling = true
  off_diagonals_in_auto_scaling = true
[]

[Outputs]
  exodus = true
[]

(examples/melt_pool_2d/melt_pool.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.01
    ymin = 0
    ymax = 0.01
    nx = 50
    ny = 50
    elem_type = QUAD4
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    coord = '0.0 0.01'
    input = gen
  []
[]

[Adaptivity]
  steps = 3
  marker = box
  max_h_level = 3
  initial_steps = 3
  stop_time = 1.0e-10
  [Markers]
    [box]
      bottom_left = '0.000 0.004 0'
      inside = refine
      top_right = '0.01 0.006 0'
      outside = do_nothing
      type = BoxMarker
    []
  []
[]

[ICs]
  [ls_ic]
    type = FunctionIC
    function = ls_exact
    variable = ls
  []
  [velocity]
    type = VectorConstantIC
    x_value = 1e-10
    y_value = 1e-10
    variable = velocity
  []
[]

[Variables]
  [ls]
  []
  [temp]
    initial_condition = 300
  []
  [grad_ls]
    family = LAGRANGE_VEC
  []
  [velocity]
    family = LAGRANGE_VEC
  []
  [p]
  []
  [curvature]
  []
[]

[Functions]
  [ls_exact]
    type = LevelSetOlssonPlane
    epsilon = 0.00004
    point = '0.005 0.005 0'
    normal = '0 1 0'
  []
[]

[BCs]
  [no_slip]
    type = ADVectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom left right'
  []
  [no_bc]
    type = INSADMomentumNoBCBC
    variable = velocity
    viscous_form = 'traction'
    boundary = 'top'
    pressure = p
  []
  [pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  []
[]

[Kernels]
  [curvature]
    type = LevelSetCurvatureRegularization
    level_set_regularized_gradient = grad_ls
    variable = curvature
    varepsilon = 2e-4
  []

  [grad_ls]
    type = VariableGradientRegularization
    regularized_var = ls
    variable = grad_ls
  []

  [level_set_time]
    type = ADTimeDerivative
    variable = ls
  []

  [level_set_advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = ls
  []

  [level_set_time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = ls
  []

  [level_set_advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = ls
  []

  [level_set_phase_change]
    type = LevelSetPhaseChange
    variable = ls
    rho_l = 8000
    rho_g = 1.184
  []

  [level_set_phase_change_supg]
    type = LevelSetPhaseChangeSUPG
    variable = ls
    velocity = velocity
    rho_l = 8000
    rho_g = 1.184
  []

  [heat_time]
    type = ADHeatConductionTimeDerivative
    specific_heat = specific_heat
    density_name = rho
    variable = temp
  []

  [heat_cond]
    type = ADHeatConduction
    thermal_conductivity = thermal_conductivity
    variable = temp
  []

  [heat_conv]
    type = INSADEnergyAdvection
    variable = temp
  []

  [heat_source]
    type = MeltPoolHeatSource
    variable = temp
    laser_power = 100
    effective_beam_radius = 0.25e-3
    absorption_coefficient = 0.27
    heat_transfer_coefficient = 100
    StefanBoltzmann_constant = 5.67e-8
    material_emissivity = 0.59
    ambient_temperature = 300
    laser_location_x = '0.005 + 6e-3*t'
    laser_location_y = '0.005'
    rho_l = 8000
    rho_g = 1.184
    vaporization_latent_heat = 6.1e6
  []

  [mass]
    type = INSADMass
    variable = p
  []

  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  []

  [momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  []

  [momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
    viscous_form = 'traction'
  []

  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []

  [momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [melt_pool_momentum_source]
    type = INSMeltPoolMomentumSource
    variable = velocity
  []
[]

[Materials]
  [thermal]
    type = LevelSetThermalMaterial
    temperature = temp
    c_g = 300
    c_s = 500
    c_l = 500
    k_g = 0.017
    k_s = 31.8724
    k_l = 209.3
    solidus_temperature = 1648
    latent_heat = 2.5e5
    outputs = all
  []
  [mushy]
    type = MushyZoneMaterial
    temperature = temp
    liquidus_temperature = 1673
    solidus_temperature = 1648
    rho_s = 8000
    rho_l = 8000
    outputs = all
  []
  [delta]
    type = LevelSetDeltaFunction
    level_set_gradient = grad_ls
    outputs = all
  []
  [heaviside]
    type = LevelSetHeavisideFunction
    level_set = ls
    outputs = all
  []
  [ins_melt_pool_mat]
    type = INSMeltPoolMaterial
    level_set_gradient = grad_ls
    velocity = velocity
    pressure = p
    alpha = .1
    temperature = temp
    curvature = curvature
    surface_tension = 1.169
    thermal_capillary = -4.3e-4
    rho_l = 8000
    rho_g = 1.184
    outputs = all
    output_properties = melt_pool_mass_rate
    cp_name = specific_heat
    k_name = thermal_conductivity
  []
  [mass_transfer]
    type = INSMeltPoolMassTransferMaterial
    temperature = temp
    Boltzmann_constant = 1.38064852e-23
    vaporization_latent_heat = 6.1e6
    atomic_weight = 97.43e-27
    vaporization_temperature = 3134
    reference_pressure = 1.01e5
    outputs = all
  []
  [fluid]
    type = LevelSetFluidMaterial
    rho_g = 1.184
    rho_s = 8000
    rho_l = 8000
    mu_g = 1.81e-5
    mu_l = 0.1
    permeability_constant = 1e-8
    outputs = all
  []
[]

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

[Transfers]
  [to_sub]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls
    to_multi_app = reinit
    execute_on = 'timestep_end'
  []

  [to_sub_init]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls_0
    to_multi_app = reinit
    execute_on = 'timestep_end'
  []

  [from_sub]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls
    from_multi_app = reinit
    execute_on = 'timestep_end'
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1e-3
  nl_abs_tol = 1e-7
  num_steps = 1000
  line_search = 'none'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_package -ksp_type'
  petsc_options_value = 'lu NONZERO superlu_dist preonly'
  nl_div_tol = 1e20
  automatic_scaling = true
[]

[Outputs]
  exodus = true
[]

(test/tests/melt_pool_level_set/level_set.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.01
    ymin = 0
    ymax = 0.01
    nx = 50
    ny = 50
    elem_type = QUAD4
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    coord = '0.0 0.01'
    input = gen
  []
[]

[ICs]
  [ls_ic]
    type = FunctionIC
    function = ls_exact
    variable = ls
  []
  [velocity]
    type = VectorConstantIC
    x_value = 1e-10
    y_value = 1e-10
    variable = velocity
  []
[]

[Variables]
  [ls]
  []
  [temp]
    initial_condition = 300
  []
  [grad_ls]
    family = LAGRANGE_VEC
  []
  [velocity]
    family = LAGRANGE_VEC
  []
  [p]
  []
  [curvature]
  []
[]

[Functions]
  [ls_exact]
    type = LevelSetOlssonPlane
    epsilon = 0.0002
    point = '0.005 0.005 0'
    normal = '0 1 0'
  []
[]

[BCs]
  [no_slip]
    type = ADVectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom left right'
  []
  [no_bc]
    type = INSADMomentumNoBCBC
    variable = velocity
    viscous_form = 'traction'
    boundary = 'top'
    pressure = p
  []
  [pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  []
[]

[Kernels]
  [curvature]
    type = LevelSetCurvatureRegularization
    level_set_regularized_gradient = grad_ls
    variable = curvature
    varepsilon = 2e-3
  []

  [grad_ls]
    type = VariableGradientRegularization
    regularized_var = ls
    variable = grad_ls
  []

  [level_set_time]
    type = ADTimeDerivative
    variable = ls
  []

  [level_set_advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = ls
  []

  [level_set_time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = ls
  []

  [level_set_advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = ls
  []

  [level_set_phase_change]
    type = LevelSetPhaseChange
    variable = ls
    rho_l = 8000
    rho_g = 1.184
  []

  [level_set_phase_change_supg]
    type = LevelSetPhaseChangeSUPG
    variable = ls
    velocity = velocity
    rho_l = 8000
    rho_g = 1.184
  []

  [heat_time]
    type = ADHeatConductionTimeDerivative
    specific_heat = specific_heat
    density_name = rho
    variable = temp
  []

  [heat_cond]
    type = ADHeatConduction
    thermal_conductivity = thermal_conductivity
    variable = temp
  []

  [heat_conv]
    type = INSADEnergyAdvection
    variable = temp
  []

  [heat_source]
    type = MeltPoolHeatSource
    variable = temp
    laser_power = 100
    effective_beam_radius = 0.25e-3
    absorption_coefficient = 0.27
    heat_transfer_coefficient = 100
    StefanBoltzmann_constant = 5.67e-8
    material_emissivity = 0.59
    ambient_temperature = 300
    laser_location_x = '0.005 + 6e-3*t'
    laser_location_y = '0.005'
    rho_l = 8000
    rho_g = 1.184
    vaporization_latent_heat = 6.1e6
  []

  [mass]
    type = INSADMass
    variable = p
  []

  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  []

  [momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  []

  [momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
    viscous_form = 'traction'
  []

  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []

  [momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [melt_pool_momentum_source]
    type = INSMeltPoolMomentumSource
    variable = velocity
  []
[]

[Materials]
  [thermal]
    type = LevelSetThermalMaterial
    temperature = temp
    c_g = 300
    c_s = 500
    c_l = 500
    k_g = 0.017
    k_s = 31.8724
    k_l = 209.3
    solidus_temperature = 1648
    latent_heat = 2.5e5
    outputs = all
  []
  [mushy]
    type = MushyZoneMaterial
    temperature = temp
    liquidus_temperature = 1673
    solidus_temperature = 1648
    rho_s = 8000
    rho_l = 8000
    outputs = all
  []
  [delta]
    type = LevelSetDeltaFunction
    level_set_gradient = grad_ls
    outputs = all
  []
  [heaviside]
    type = LevelSetHeavisideFunction
    level_set = ls
    outputs = all
  []
  [ins_melt_pool_mat]
    type = INSMeltPoolMaterial
    level_set_gradient = grad_ls
    velocity = velocity
    pressure = p
    alpha = .1
    temperature = temp
    curvature = curvature
    surface_tension = 1.169
    thermal_capillary = -4.3e-4
    rho_l = 8000
    rho_g = 1.184
    outputs = all
    output_properties = melt_pool_mass_rate
    cp_name = specific_heat
    k_name = thermal_conductivity
  []
  [mass_transfer]
    type = INSMeltPoolMassTransferMaterial
    temperature = temp
    Boltzmann_constant = 1.38064852e-23
    vaporization_latent_heat = 6.1e6
    atomic_weight = 97.43e-27
    vaporization_temperature = 3134
    reference_pressure = 1.01e5
    outputs = all
  []
  [fluid]
    type = LevelSetFluidMaterial
    rho_g = 1.184
    rho_s = 8000
    rho_l = 8000
    mu_g = 1.81e-5
    mu_l = 0.1
    permeability_constant = 1e-8
    outputs = all
  []
[]

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

[Transfers]
  [to_sub]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls
    to_multi_app = reinit
    execute_on = 'timestep_end'
  []

  [to_sub_init]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls_0
    to_multi_app = reinit
    execute_on = 'timestep_end'
  []

  [from_sub]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls
    from_multi_app = reinit
    execute_on = 'timestep_end'
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1e-4
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-12
  num_steps = 2
  line_search = 'none'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_package -ksp_type'
  petsc_options_value = 'lu NONZERO superlu_dist preonly'
  nl_div_tol = 1e20
  automatic_scaling = true
[]

[Outputs]
  exodus = true
[]

(examples/melt_pool_3d/melt_pool.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 0.01
    ymin = 0
    ymax = 0.01
    zmin = 0
    zmax = 0.01
    nx = 50
    ny = 50
    nz = 50
    elem_type = HEX8
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    coord = '0.0 0 0.01'
    input = gen
  []
[]

[Adaptivity]
  steps = 2
  marker = box
  max_h_level = 2
  initial_steps = 2
  stop_time = 1.0e-10
  [Markers]
    [box]
      bottom_left = '0.000 0 0.004'
      inside = refine
      top_right = '0.01 0.01 0.006'
      outside = do_nothing
      type = BoxMarker
    []
  []
[]

[ICs]
  [ls_ic]
    type = FunctionIC
    function = ls_exact
    variable = ls
  []
  [velocity]
    type = VectorConstantIC
    x_value = 1e-10
    y_value = 1e-10
    variable = velocity
  []
[]

[Variables]
  [ls]
  []
  [temp]
    initial_condition = 300
  []
  [grad_ls]
    family = LAGRANGE_VEC
  []
  [velocity]
    family = LAGRANGE_VEC
  []
  [p]
  []
  [curvature]
  []
[]

[Functions]
  [ls_exact]
    type = LevelSetOlssonPlane
    epsilon = 0.00008
    point = '0.005 0.005 0.005'
    normal = '0 0 1'
  []
[]

[BCs]
  [no_slip]
    type = ADVectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom left right top back'
  []
  [no_bc]
    type = INSADMomentumNoBCBC
    variable = velocity
    viscous_form = 'traction'
    boundary = 'front'
    pressure = p
  []
  [pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  []
[]

[Kernels]
  [curvature]
    type = LevelSetCurvatureRegularization
    level_set_regularized_gradient = grad_ls
    variable = curvature
    varepsilon = 4e-4
  []

  [grad_ls]
    type = VariableGradientRegularization
    regularized_var = ls
    variable = grad_ls
  []

  [level_set_time]
    type = ADTimeDerivative
    variable = ls
  []

  [level_set_advection_supg]
    type = LevelSetAdvectionSUPG
    velocity = velocity
    variable = ls
  []

  [level_set_time_supg]
    type = LevelSetTimeDerivativeSUPG
    velocity = velocity
    variable = ls
  []

  [level_set_advection]
    type = LevelSetAdvection
    velocity = velocity
    variable = ls
  []

  [level_set_phase_change]
    type = LevelSetPhaseChange
    variable = ls
    rho_l = 8000
    rho_g = 1.184
  []

  [level_set_phase_change_supg]
    type = LevelSetPhaseChangeSUPG
    variable = ls
    velocity = velocity
    rho_l = 8000
    rho_g = 1.184
  []

  [heat_time]
    type = ADHeatConductionTimeDerivative
    specific_heat = specific_heat
    density_name = rho
    variable = temp
  []

  [heat_cond]
    type = ADHeatConduction
    thermal_conductivity = thermal_conductivity
    variable = temp
  []

  [heat_conv]
    type = INSADEnergyAdvection
    variable = temp
  []

  [heat_source]
    type = MeltPoolHeatSource
    variable = temp
    laser_power = 100
    effective_beam_radius = 0.25e-3
    absorption_coefficient = 0.27
    heat_transfer_coefficient = 100
    StefanBoltzmann_constant = 5.67e-8
    material_emissivity = 0.59
    ambient_temperature = 300
    laser_location_x = '0.005 + 6e-3*t'
    laser_location_y = '0.005'
    laser_location_z = '0.005'
    rho_l = 8000
    rho_g = 1.184
    vaporization_latent_heat = 6.1e6
  []

  [mass]
    type = INSADMass
    variable = p
  []

  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  []

  [momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  []

  [momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
    viscous_form = 'traction'
  []

  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []

  [momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [melt_pool_momentum_source]
    type = INSMeltPoolMomentumSource
    variable = velocity
  []
[]

[Materials]
  [thermal]
    type = LevelSetThermalMaterial
    temperature = temp
    c_g = 300
    c_s = 500
    c_l = 500
    k_g = 0.017
    k_s = 31.8724
    k_l = 209.3
    solidus_temperature = 1648
    latent_heat = 2.5e5
    outputs = all
  []
  [mushy]
    type = MushyZoneMaterial
    temperature = temp
    liquidus_temperature = 1673
    solidus_temperature = 1648
    rho_s = 8000
    rho_l = 8000
    outputs = all
  []
  [delta]
    type = LevelSetDeltaFunction
    level_set_gradient = grad_ls
    outputs = all
  []
  [heaviside]
    type = LevelSetHeavisideFunction
    level_set = ls
    outputs = all
  []
  [ins_melt_pool_mat]
    type = INSMeltPoolMaterial
    level_set_gradient = grad_ls
    velocity = velocity
    pressure = p
    alpha = .1
    temperature = temp
    curvature = curvature
    surface_tension = 1.169
    thermal_capillary = -4.3e-4
    rho_l = 8000
    rho_g = 1.184
    outputs = all
    output_properties = melt_pool_mass_rate
    cp_name = specific_heat
    k_name = thermal_conductivity
  []
  [mass_transfer]
    type = INSMeltPoolMassTransferMaterial
    temperature = temp
    Boltzmann_constant = 1.38064852e-23
    vaporization_latent_heat = 6.1e6
    atomic_weight = 97.43e-27
    vaporization_temperature = 3134
    reference_pressure = 1.01e5
    outputs = all
  []
  [fluid]
    type = LevelSetFluidMaterial
    rho_g = 1.184
    rho_s = 8000
    rho_l = 8000
    mu_g = 1.81e-5
    mu_l = 0.1
    permeability_constant = 1e-8
    outputs = all
  []
[]

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

[Transfers]
  [to_sub]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls
    to_multi_app = reinit
    execute_on = 'timestep_end'
  []

  [to_sub_init]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls_0
    to_multi_app = reinit
    execute_on = 'timestep_end'
  []

  [from_sub]
    type = MultiAppCopyTransfer
    source_variable = ls
    variable = ls
    from_multi_app = reinit
    execute_on = 'timestep_end'
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1e-4
  nl_abs_tol = 1e-7
  num_steps = 1000
  line_search = 'none'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_package -ksp_type'
  petsc_options_value = 'lu NONZERO superlu_dist preonly'
  nl_div_tol = 1e20
  automatic_scaling = true
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References