Mass transfer rate due to liquid-vapor phase change

Computes extra residuals from mass transfer for the INS equations.

Description

The mass transfer rate $var element = document.getElementById("moose-equation-e2587a59-0a8b-41e8-a117-8862888841a7");katex.render("\\dot{m}", element, {displayMode:false,throwOnError:false});$ (Courtois et al., 2014) is described by $var element = document.getElementById("moose-equation-4b1ffbe0-c0e1-495c-8bd7-614cc91e9a01");katex.render("\\dot{m}=\\sqrt{\\frac{m}{2\\pi k_b}}\\frac{p_{sat}(T)}{\\sqrt{T}}(1-\\beta_r),", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-588e8b1d-01b7-4a25-9305-d6c1f33a3a0c");katex.render("m", element, {displayMode:false,throwOnError:false});$ is the atomic weight, $var element = document.getElementById("moose-equation-6fe39fcc-0ea3-44f6-aa66-0d304e80d874");katex.render("k_b", element, {displayMode:false,throwOnError:false});$ is the Boltzmann constant, $var element = document.getElementById("moose-equation-ebaeab0b-0b86-450d-9dd5-3f36dc6ed708");katex.render("\\beta_r", element, {displayMode:false,throwOnError:false});$ the retrodiffusion coefficient and $var element = document.getElementById("moose-equation-5c65dbd5-58fa-404c-baaa-847668fe4f07");katex.render("p_{sat}(T)", element, {displayMode:false,throwOnError:false});$ is the saturated vapor pressure given by $var element = document.getElementById("moose-equation-e8789a12-4e81-45a5-8fee-d746f34ff801");katex.render("p_{sat}(T)=p_0\\exp\\left[\\frac{mL_v}{k_b T_{vap}}\\left(1-\\frac{T_{vap}}{T} \\right) \\right],", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-640b4837-a656-46ae-b2c8-36e648439459");katex.render("p_o", element, {displayMode:false,throwOnError:false});$ is reference temperature, $var element = document.getElementById("moose-equation-d6ccfbec-1e96-4acd-8cdb-ef689abce54f");katex.render("L_v", element, {displayMode:false,throwOnError:false});$ is the latent heat of vaporization and $var element = document.getElementById("moose-equation-3c3f5a63-c995-47d2-92a4-2ad5294532e7");katex.render("T_{vap}", element, {displayMode:false,throwOnError:false});$ is the vaporization temperature.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [mass_transfer]
    type = INSMeltPoolMassTransferMaterial<<<{"description": "Computes extra residuals from mass transfer for the INS equations.", "href": "INSMeltPoolMassTransferMaterial.html"}>>>
    temperature<<<{"description": "Temperature variable"}>>> = temp
    Boltzmann_constant<<<{"description": "Stefan Boltzmann constant."}>>> = 1.38064852e-23
    vaporization_latent_heat<<<{"description": "Latent heat of vaporization."}>>> = 6.1e6
    atomic_weight<<<{"description": "Atomic weight of metal."}>>> = 97.43e-27
    vaporization_temperature<<<{"description": "Vaporization temperature."}>>> = 3134
    reference_pressure<<<{"description": "Reference pressure for vaporization."}>>> = 1.01e5
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

Input Parameters

Boltzmann_constantStefan Boltzmann constant.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Stefan Boltzmann constant.
atomic_weightAtomic weight of metal.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Atomic weight of metal.
reference_pressureReference pressure for vaporization.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Reference pressure for vaporization.
temperatureTemperature variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Temperature variable
vaporization_latent_heatLatent heat of vaporization.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Latent heat of vaporization.
vaporization_temperatureVaporization temperature.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Vaporization temperature.

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
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
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.
retrodiffusion_coefficient0Retrodiffusion coefficient.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Retrodiffusion coefficient.

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

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

(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_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
[]

(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_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
[]

Description
Example Input Syntax
Input Parameters
Input Files
References