Melt pool heat source

Computes the laser heat source and heat loss in the melt pool heat equation

Description

The energy conservation equation(Wen and Shin, 2010; Courtois et al., 2014) is described by

$var element = document.getElementById("moose-equation-f35d3002-20c2-46db-b3fe-08a38f1b9ee9");katex.render("\\rho\\frac{\\partial h}{\\partial t}+ \\rho\\nabla \\cdot (\\overrightarrow{u}h) = \\nabla\\cdot(k\\nabla T) + Q,", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-c5a0f48b-2676-4035-8c7c-596dea42356f");katex.render("Q", element, {displayMode:false,throwOnError:false});$ is the source term, consisting of laser heat source and heat loss flux at the interface $var element = document.getElementById("moose-equation-7834aa07-9c31-4a8c-874a-5e5dcdd016ca");katex.render("Q = \\frac{2P\\alpha}{\\pi R_b^2}\\exp\\left(\\frac{-2r^2}{R_b^2}\\right)\\delta(\\phi) -A_h(T-T_0)\\delta(\\phi) -\\sigma\\epsilon(T^4-T_0^4)|\\nabla\\phi|-L_v\\dot{m}\\delta(\\phi),", element, {displayMode:true,throwOnError:false});$ where the three terms on the right represent heat flux from the laser, heat losses through convection and radiation, and energy loss by evaporation, respectively. Mass transfer rate $var element = document.getElementById("moose-equation-5aea72b5-6934-4e7f-97a3-ddf12e85a65f");katex.render("\\dot{m}", element, {displayMode:false,throwOnError:false});$ is computed by INSMeltPoolMassTransferMaterial.

Example Input Syntax

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [heat_source]
    type = MeltPoolHeatSource<<<{"description": "Computes the laser heat source and heat loss in the melt pool heat equation", "href": "MeltPoolHeatSource.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temp
    laser_power<<<{"description": "Laser power."}>>> = 100
    effective_beam_radius<<<{"description": "Effective beam radius."}>>> = 0.2
    absorption_coefficient<<<{"description": "Absorption coefficient."}>>> = 0.27
    heat_transfer_coefficient<<<{"description": "Heat transfer coefficient."}>>> = 100
    StefanBoltzmann_constant<<<{"description": "Stefan Boltzmann constant."}>>> = 5.67e-8
    material_emissivity<<<{"description": "Material emissivity."}>>> = 0.59
    ambient_temperature<<<{"description": "Ambient temperature."}>>> = 300
    laser_location_x<<<{"description": "The laser center function of x coordinate."}>>> = '0.5 + t'
    laser_location_y<<<{"description": "The laser center function of y coordinate."}>>> = '0.5'
    rho_l<<<{"description": "Liquid density."}>>> = 8000
    rho_g<<<{"description": "Gas density."}>>> = 1.184
    vaporization_latent_heat<<<{"description": "Latent heat of vaporization."}>>> = 6.1e6
  []
[]

Input Parameters

StefanBoltzmann_constantStefan Boltzmann constant.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Stefan Boltzmann constant.
absorption_coefficientAbsorption coefficient.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Absorption coefficient.
ambient_temperatureAmbient temperature.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Ambient temperature.
effective_beam_radiusEffective beam radius.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Effective beam radius.
heat_transfer_coefficientHeat transfer coefficient.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Heat transfer coefficient.
laser_powerLaser power.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Laser power.
material_emissivityMaterial emissivity.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Material emissivity.
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.
vaporization_latent_heatLatent heat of vaporization.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Latent heat of vaporization.
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

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
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
laser_location_x0The laser center function of x coordinate.
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The laser center function of x coordinate.
laser_location_y0The laser center function of y coordinate.
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The laser center function of y coordinate.
laser_location_z0The laser center function of z coordinate.
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The laser center function of z coordinate.
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
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<TagName>
Controllable:No
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
Controllable:No
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
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data 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.
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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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
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
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<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
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
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

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_heat/thermal_material.i)
(examples/melt_pool_3d/melt_pool.i)
(test/tests/melt_pool_fluid/fluid.i)
(examples/melt_pool_2d/melt_pool.i)
(test/tests/melt_pool_level_set/level_set.i)
(test/tests/melt_pool_heat/heat.i)

References

Mickael Courtois, Muriel Carin, Philippe Le Masson, Sadok Gaied, and Mikhaël Balabane. A complete model of keyhole and melt pool dynamics to analyze instabilities and collapse during laser welding. Journal of Laser Applications, 26(4):042001, 2014. doi:10.2351/1.4886835.

@article{Courtois2014,
    author = "Courtois, Mickael and Carin, Muriel and Le Masson, Philippe and Gaied, Sadok and Balabane, Mikhaël",
    title = "A complete model of keyhole and melt pool dynamics to analyze instabilities and collapse during laser welding",
    journal = "Journal of Laser Applications",
    volume = "26",
    number = "4",
    pages = "042001",
    year = "2014",
    doi = "10.2351/1.4886835"
}

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_heat/heat.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 40
    ny = 40
    elem_type = QUAD4
  []
[]

[ICs]
  [ls_ic]
    type = FunctionIC
    function = ls_exact
    variable = ls
  []
[]

[Variables]
  [temp]
    initial_condition = 300
  []
  [grad_ls]
    family = LAGRANGE_VEC
  []
[]

[AuxVariables]
  [ls]
  []
[]

[Functions]
  [ls_exact]
    type = LevelSetOlssonPlane
    epsilon = 0.04
    point = '0.5 0.5 0'
    normal = '0 1 0'
  []
[]

[Kernels]
  [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_source]
    type = MeltPoolHeatSource
    variable = temp
    laser_power = 100
    effective_beam_radius = 0.2
    absorption_coefficient = 0.27
    heat_transfer_coefficient = 100
    StefanBoltzmann_constant = 5.67e-8
    material_emissivity = 0.59
    ambient_temperature = 300
    laser_location_x = '0.5 + t'
    laser_location_y = '0.5'
    rho_l = 8000
    rho_g = 1.184
    vaporization_latent_heat = 6.1e6
  []
[]

[Materials]
  [thermal]
    type = ADGenericConstantMaterial
    prop_names = 'rho thermal_conductivity specific_heat melt_pool_mass_rate'
    prop_values = '8000 50 500 0'
  []
  [delta]
    type = LevelSetDeltaFunction
    level_set_gradient = grad_ls
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1e-2
  nl_abs_tol = 1e-7
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(test/tests/melt_pool_heat/thermal_material.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 40
    ny = 40
    elem_type = QUAD4
  []
[]

[ICs]
  [ls_ic]
    type = FunctionIC
    function = ls_exact
    variable = ls
  []
[]

[Variables]
  [temp]
    initial_condition = 300
  []
  [grad_ls]
    family = LAGRANGE_VEC
  []
[]

[AuxVariables]
  [ls]
  []
[]

[Functions]
  [ls_exact]
    type = LevelSetOlssonPlane
    epsilon = 0.04
    point = '0.5 0.5 0'
    normal = '0 1 0'
  []
[]

[Kernels]
  [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_source]
    type = MeltPoolHeatSource
    variable = temp
    laser_power = 250
    effective_beam_radius = 0.1
    absorption_coefficient = 0.27
    heat_transfer_coefficient = 100
    StefanBoltzmann_constant = 5.67e-8
    material_emissivity = 0.59
    ambient_temperature = 300
    laser_location_x = '0.5'
    laser_location_y = '0.5'
    rho_l = 8000
    rho_g = 1.184
    vaporization_latent_heat = 6.1e6
  []
[]

[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
  []
  [mushy]
    type = MushyZoneMaterial
    temperature = temp
    liquidus_temperature = 1673
    solidus_temperature = 1648
    rho_s = 8000
    rho_l = 8000
  []
  [rho]
    type = ADGenericConstantMaterial
    prop_names = 'rho melt_pool_mass_rate'
    prop_values = '8000 0'
  []
  [heaviside]
    type = LevelSetHeavisideFunction
    level_set = ls
  []
  [delta]
    type = LevelSetDeltaFunction
    level_set_gradient = grad_ls
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1
  nl_abs_tol = 1e-7
  num_steps = 2
[]

[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
[]

(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
[]

(test/tests/melt_pool_heat/heat.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 40
    ny = 40
    elem_type = QUAD4
  []
[]

[ICs]
  [ls_ic]
    type = FunctionIC
    function = ls_exact
    variable = ls
  []
[]

[Variables]
  [temp]
    initial_condition = 300
  []
  [grad_ls]
    family = LAGRANGE_VEC
  []
[]

[AuxVariables]
  [ls]
  []
[]

[Functions]
  [ls_exact]
    type = LevelSetOlssonPlane
    epsilon = 0.04
    point = '0.5 0.5 0'
    normal = '0 1 0'
  []
[]

[Kernels]
  [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_source]
    type = MeltPoolHeatSource
    variable = temp
    laser_power = 100
    effective_beam_radius = 0.2
    absorption_coefficient = 0.27
    heat_transfer_coefficient = 100
    StefanBoltzmann_constant = 5.67e-8
    material_emissivity = 0.59
    ambient_temperature = 300
    laser_location_x = '0.5 + t'
    laser_location_y = '0.5'
    rho_l = 8000
    rho_g = 1.184
    vaporization_latent_heat = 6.1e6
  []
[]

[Materials]
  [thermal]
    type = ADGenericConstantMaterial
    prop_names = 'rho thermal_conductivity specific_heat melt_pool_mass_rate'
    prop_values = '8000 50 500 0'
  []
  [delta]
    type = LevelSetDeltaFunction
    level_set_gradient = grad_ls
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 1e-2
  nl_abs_tol = 1e-7
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References