Function Path Gaussian Heat Source

This class creates a Gaussian heat source (Yushu et al., 2022) (see ADGaussianHeatSourceBase for more information) whose center follows user specified path along three directions. The spatial location of the heat source center $var element = document.getElementById("moose-equation-590d5a8c-b6e0-42b5-b31f-99653891b6dd");katex.render("\\boldsymbol{p}(\\boldsymbol{x},t)", element, {displayMode:false,throwOnError:false});$ is decomposed along three directions, i.e., $var element = document.getElementById("moose-equation-e2b80237-47a9-4947-b3e9-a46ff1d94a88");katex.render(" \\boldsymbol{p}(\\boldsymbol{x}, t) = [ p_x(t), p_y(t), p_y(t)],", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-a18f182f-98e4-4cf7-ae52-d99831e02d2d");katex.render("p_x(t), p_y(t), p_y(t)", element, {displayMode:false,throwOnError:false});$ are user defined time-varying spatial locations along three directions.

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [volumetric_heat]
    type = ADFunctionPathGaussianHeatSource<<<{"description": "Gaussian heat source whose center moves along a specified function path.", "href": "ADFunctionPathGaussianHeatSource.html"}>>>
    r<<<{"description": "effective radii (mm) along three directions. If only one parameter is provided, then we assume the effective radius to be equal along three directions."}>>> = 0.2
    power<<<{"description": "laser power (1e-3 W)"}>>> = 0.3
    efficiency<<<{"description": "process efficiency"}>>> = 0.3
    factor<<<{"description": "scaling factor that is multiplied to the heat source to adjust the intensity"}>>> = 2
    function_x<<<{"description": "The x component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms]."}>>> = heat_source_x
    function_y<<<{"description": "The y component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms]."}>>> = heat_source_y
    function_z<<<{"description": "The z component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms]."}>>> = heat_source_z
    heat_source_type<<<{"description": "Type of the heat source"}>>> = 'mixed'
    threshold_length<<<{"description": "Threshold size (mm) when we change the way of computing heat source"}>>> = 0.1
  []
[]

Input Parameters

powerlaser power (1e-3 W)
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:laser power (1e-3 W)

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.
efficiency1process efficiency
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:process efficiency
factor1scaling factor that is multiplied to the heat source to adjust the intensity
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:Yes
Description:scaling factor that is multiplied to the heat source to adjust the intensity
feed_rate0powder material feed rate (g/ms). This value is used only when use_input_r = false.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:powder material feed rate (g/ms). This value is used only when use_input_r = false.
function_x0The x component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms].
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The x component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms].
function_y0The y component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms].
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The y component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms].
function_z0The z component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms].
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The z component of the center of the heating spot as a function of time, length unit is [mm], time unit is [ms].
heat_source_typepointType of the heat source
Default:point
C++ Type:MooseEnum
Options:point, line, mixed
Controllable:No
Description:Type of the heat source
number_time_integration10Number of points to do time integration for averaged heat source calculation
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Number of points to do time integration for averaged heat source calculation
reffective radii (mm) along three directions. If only one parameter is provided, then we assume the effective radius to be equal along three directions.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:Yes
Description:effective radii (mm) along three directions. If only one parameter is provided, then we assume the effective radius to be equal along three directions.
std_factor1factor to the std to sample r
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:factor to the std to sample r
threshold_length1Threshold size (mm) when we change the way of computing heat source
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Threshold size (mm) when we change the way of computing heat source
use_input_rTrueoption to use user input effective radii or from experimentally fitted formulations. Default is to use user input data.
Default:True
C++ Type:bool
Controllable:No
Description:option to use user input effective radii or from experimentally fitted formulations. Default is to use user input data.

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/directed_energy_deposition/hollow_cylinder/sub_app_thermal.i)
(test/tests/gaussian_heat_source/gaussian_heat_source_experiment_r.i)
(examples/directed_energy_deposition/cylinder/sub_app_thermal.i)
(test/tests/gaussian_heat_source/gaussian_heat_source.i)
(test/tests/gaussian_heat_source/gaussian_heat_source_vary_r.i)
(test/tests/function_path_gaussian_heat_source/func_path_gaussian_heat_source.i)

References

Dewen Yushu, Michael D. McMurtrey, Wen Jiang, and Fande Kong. Directed energy deposition process modeling: a geometry-free thermo-mechanical model with adaptive subdomain construction. The International Journal of Advanced Manufacturing Technhology, 122(2):849–868, 2022. URL: https://link.springer.com/article/10.1007/s00170-022-09887-6, doi:10.1007/s00170-022-09887-6.

@article{yushu2022directed,
    author = "Yushu, Dewen and McMurtrey, Michael D. and Jiang, Wen and Kong, Fande",
    title = "Directed energy deposition process modeling: A geometry-free thermo-mechanical model with adaptive subdomain construction",
    journal = "The International Journal of Advanced Manufacturing Technhology",
    volume = "122",
    number = "2",
    pages = "849-868",
    year = "2022",
    issn = "2352-7110",
    publisher = "Springer",
    doi = "10.1007/s00170-022-09887-6",
    url = "https://link.springer.com/article/10.1007/s00170-022-09887-6"
}

(test/tests/gaussian_heat_source/gaussian_heat_source.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 0.5
    zmin = 0
    zmax = 0.1
    nx = 10
    ny = 5
    nz = 1
  []
[]

[Variables]
  [temp]
  []
[]

[ICs]
  [temp_substrate]
    type = ConstantIC
    variable = temp
    value = 300
  []
[]

[Kernels]
  [time]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat_conduct]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = thermal_conductivity
  []
  [heatsource]
    type = ADMatHeatSource
    material_property = volumetric_heat
    variable = temp
    scalar = 1
  []
[]

[Functions]
  [heat_source_x]
    type = ParsedFunction
    expression = '0.05*t'
  []
  [heat_source_y]
    type = ParsedFunction
    expression = 0.25
  []
  [heat_source_z]
    type = ParsedFunction
    expression = 0.1
  []
[]

[BCs]
  [temp_bottom_fix]
    type = ADDirichletBC
    variable = temp
    boundary = back
    value = 300
  []
[]

[Materials]
  [volumetric_heat]
    type = ADFunctionPathGaussianHeatSource
    r = 0.2
    power = 0.3
    efficiency = 0.3
    factor = 2
    function_x = heat_source_x
    function_y = heat_source_y
    function_z = heat_source_z
    heat_source_type = 'mixed'
    threshold_length = 0.1
  []
  [density]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 7609e-9
  []
  [heat]
    type = ADHeatConductionMaterial
    specific_heat_temperature_function = 500
    thermal_conductivity_temperature_function = 25e-6
    temp = temp
  []
[]

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

[Executioner]
  type = Transient

  automatic_scaling = true

  solve_type = 'PJFNK'

  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 10
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8

  start_time = 0.0
  end_time = 20
  dt = 1
  dtmin = 1e-4
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [avg_temp]
    type = ElementAverageValue
    variable = temp
  []
  [max_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
  []
  [min_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = min
  []
[]

(examples/directed_energy_deposition/hollow_cylinder/sub_app_thermal.i)

# The material properties used in this example are based on typical values for stainless steel.
# For detailed reference, please consult the following paper:
# https://www.sciencedirect.com/science/article/pii/S2214860418301246

T_room = 300
T_ambient = 300
T_melt = 1700

power = 0.3 # 300W = kg*m^2/s^3 = 300e-3 kg*mm^2/ms^3
r = 0.3 # 300 um = 300e-3 mm
dt = 20

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -4.5
    xmax = 4.5
    ymin = -4.5
    ymax = 4.5
    zmin = 0
    zmax = 3.3
    nx = 30
    ny = 30
    nz = 11
  []
  [add_set1]
    type = SubdomainBoundingBoxGenerator
    input = mesh
    block_id = 3
    bottom_left = '-50 -50 0'
    top_right = '50 50 0.9'
  []
  [add_set2]
    type = SubdomainBoundingBoxGenerator
    input = add_set1
    block_id = 1
    bottom_left = '-50 -50 0.9'
    top_right = '50 50 3.3'
  []

  [add_set3]
    type = GeneratedMeshGenerator
    dim = 3
    xmax = 0.001
    ymax = 0.001
    zmin = -0.001
    subdomain_ids = 2
  []
  [moving_boundary]
    type = SideSetsAroundSubdomainGenerator
    input = add_set3
    block = 2
    new_boundary = 'moving_boundary'
  []
  # [middle]
  #   type = SideSetsAroundSubdomainGenerator
  #   input = moving_boundary
  #   block = 3
  #   new_boundary = 'middle'
  #   normal = '0 0 1'
  # []

  [cmbn]
    type = CombinerGenerator
    inputs = 'add_set2 moving_boundary'
  []

  skip_partitioning = true
[]

[Problem]
  material_coverage_check = false
[]

[Variables]
  [temp]
    block = '1 2 3'
  []
[]

[ICs]
  [temp_substrate]
    type = ConstantIC
    variable = temp
    value = ${T_room}
    block = '1 3'
  []
  [temp_product]
    type = FunctionIC
    variable = temp
    function = temp_ic
    block = '2'
  []
[]

[AuxVariables]
  [processor_id]
    order = CONSTANT
    family = MONOMIAL
  []
  [x_coord]
    order = FIRST
    family = LAGRANGE
  []
  [y_coord]
    order = FIRST
    family = LAGRANGE
  []
  [z_coord]
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [time]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat_conduc]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = thermal_conductivity
  []
  [heatsource]
    type = ADMatHeatSource
    material_property = volumetric_heat
    variable = temp
    scalar = 1
  []
[]

[AuxKernels]
  [processor_id_aux]
    type = ProcessorIDAux
    variable = processor_id
    execute_on = timestep_begin
  []
  [x_coord]
    type = FunctionAux
    function = x_coord
    variable = x_coord
  []
  [y_coord]
    type = FunctionAux
    function = y_coord
    variable = y_coord
  []
  [z_coord]
    type = FunctionAux
    function = z_coord
    variable = z_coord
  []
[]

[BCs]
  [bottom_temp]
    type = ADDirichletBC
    variable = temp
    boundary = 'back'
    value = ${T_room}
  []
  [convective]
    type = ADConvectiveHeatFluxBC
    variable = temp
    boundary = 'bottom front left right top'
    heat_transfer_coefficient = 2e-5
    T_infinity = ${T_ambient}
  []
[]

[Functions]
  [heat_source_x]
    type = ParsedFunction
    expression = 2.0*cos(2.0*pi/c*t)
    symbol_names = 'c'
    symbol_values = '1257'
  []
  [heat_source_y]
    type = ParsedFunction
    expression = 2.0*sin(2.0*pi/c*t)
    symbol_names = 'c'
    symbol_values = '1257'
  []
  [heat_source_z]
    type = PiecewiseConstant
    xy_data = '0 0.9
               1257 1.35
               2514 1.8
               3771 2.25'
  []
  [specific_heat_metal]
    type = PiecewiseLinear
    x = '-1e7 197.79  298.46  600.31 1401.01 1552.59 1701.44 1e7'
    y = '426.69 426.69 479.77 549.54 676.94  695.14 726.99 726.99'
    scale_factor = 1.0
  []
  # the properties are scaled to the right value and unit (see D. Yushu et al., 2022)
  [thermal_conductivity_metal]
    type = PiecewiseLinear
    x = '-1e7 198.84  298.10  398.75 500.76 601.40 700.64 801.27 901.89 1001.12 1098.98 1200.96 1301.56 1400.78 1501.37 1601.96 1e7'
    y = '247.72 247.72 285.64 323.55 358.44 390.29 417.59 446.41 469.16 491.91 510.11 528.31 540.44 554.09 561.67 569.26 569.26'
    scale_factor = 0.05e-6
  []
  # for monitoring the deposited material geometry
  [x_coord]
    type = ParsedFunction
    expression = 'x'
  []
  [y_coord]
    type = ParsedFunction
    expression = 'y'
  []
  [z_coord]
    type = ParsedFunction
    expression = 'z'
  []
  [temp_ic]
    type = ParsedFunction
    expression = 'if(t<=0, temp_room, temp_melt)'
    symbol_names = 'temp_room temp_melt'
    symbol_values = '${T_room} ${T_melt}'
  []
[]

[Materials]
  [heat_metal]
    type = ADHeatConductionMaterial
    specific_heat_temperature_function = specific_heat_metal
    thermal_conductivity_temperature_function = thermal_conductivity_metal
    temp = temp
    block = '1 2 3'
  []
  [volumetric_heat_metal]
    type = ADFunctionPathGaussianHeatSource
    r = ${r}
    power = ${power}
    efficiency = 0.36
    factor = 1.6
    function_x = heat_source_x
    function_y = heat_source_y
    function_z = heat_source_z
    heat_source_type = 'line'
    threshold_length = 0.1 #mm
    number_time_integration = 10
    block = '1 2 3'
  []
  [density_metal]
    type = ADDensity
    density = 7609e-9 # kg/m^3 -> 1e-9 kg/mm^3
    block = '1 2 3'
  []
[]

[MeshModifiers]
  [activated_elem_uo_beam]
    type = CoupledVarThresholdElementSubdomainModifier
    execute_on = 'TIMESTEP_BEGIN'
    coupled_var = temp
    block = 1
    subdomain_id = 2
    criterion_type = ABOVE
    threshold = ${T_melt}
    moving_boundaries = 'moving_boundary'
    moving_boundary_subdomain_pairs = '2 1'
  []
[]

[Adaptivity]
  marker = marker
  initial_marker = marker
  max_h_level = 2
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = temp
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      coarsen = 0 # coarsening is pending MOOSE PR #23078 being merged
      refine = 0.5
    []
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'preonly lu       superlu_dist NONZERO 1e-10'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10

  start_time = 0.0
  end_time = 3771
  dt = ${dt} # ms
  dtmin = 1e-6

  auto_advance = true # cut time-step when subapp fails

  error_on_dtmin = false
[]

[Outputs]
  file_base = 'output/Thermal'
  csv = true
  [exodus]
    type = Exodus
    file_base = 'output/Exodus/Thermal'
    time_step_interval = 1
  []
[]

[Postprocessors]
  [bead_max_temperature]
    type = ElementExtremeValue
    variable = temp
    value_type = max
    block = '2'
    outputs = 'csv'
  []
  [bead_min_temperature]
    type = ElementExtremeValue
    variable = temp
    value_type = min
    block = '2'
    outputs = 'csv'
  []
  [bead_volume]
    type = VolumePostprocessor
    block = '2'
    outputs = 'csv console'
  []
  [bead_x_coord_max]
    type = ElementExtremeValue
    variable = x_coord
    value_type = max
    block = '2'
    outputs = 'csv console'
  []
  [bead_x_coord_min]
    type = ElementExtremeValue
    variable = x_coord
    value_type = min
    block = '2'
    outputs = 'csv'
  []
  [bead_y_coord_max]
    type = ElementExtremeValue
    variable = y_coord
    value_type = max
    block = '2'
    outputs = 'csv console'
  []
  [bead_y_coord_min]
    type = ElementExtremeValue
    variable = y_coord
    value_type = min
    block = '2'
    outputs = 'csv console'
  []
  [bead_z_coord_max]
    type = ElementExtremeValue
    variable = z_coord
    value_type = max
    block = '2'
    outputs = 'csv console'
  []
[]

(test/tests/gaussian_heat_source/gaussian_heat_source_experiment_r.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 0.5
    zmin = 0
    zmax = 0.1
    nx = 10
    ny = 5
    nz = 1
  []
[]

[Variables]
  [temp]
  []
[]

[ICs]
  [temp_substrate]
    type = ConstantIC
    variable = temp
    value = 300
  []
[]

[Kernels]
  [time]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat_conduct]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = thermal_conductivity
  []
  [heatsource]
    type = ADMatHeatSource
    material_property = volumetric_heat
    variable = temp
    scalar = 1
  []
[]

[Functions]
  [heat_source_x]
    type = ParsedFunction
    expression = '6.773e-3*t' # 16 ipm
  []
  [heat_source_y]
    type = ParsedFunction
    expression = 0.25
  []
  [heat_source_z]
    type = ParsedFunction
    expression = 0.1
  []
[]

[BCs]
  [temp_bottom_fix]
    type = ADDirichletBC
    variable = temp
    boundary = back
    value = 300
  []
[]

[Materials]
  [volumetric_heat]
    type = ADFunctionPathGaussianHeatSource
    use_input_r = false
    feed_rate = 0.000124 # 4 rpm
    power = 0.3
    efficiency = 0.3
    factor = 2
    function_x = heat_source_x
    function_y = heat_source_y
    function_z = heat_source_z
    heat_source_type = 'point'
    # we turn off the std to be able to test
    std_factor = 0.0
    threshold_length = 0.1
  []
  [density]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 7609e-9
  []
  [heat]
    type = ADHeatConductionMaterial
    specific_heat_temperature_function = 500
    thermal_conductivity_temperature_function = 25e-6
    temp = temp
  []
[]

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

[Executioner]
  type = Transient

  automatic_scaling = true

  solve_type = 'PJFNK'

  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 10
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8

  start_time = 0.0
  end_time = 20
  dt = 1
  dtmin = 1e-4
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [avg_temp]
    type = ElementAverageValue
    variable = temp
  []
  [max_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
  []
  [min_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = min
  []
[]

(examples/directed_energy_deposition/cylinder/sub_app_thermal.i)

# The material properties used in this example are based on typical values for stainless steel.
# For detailed reference, please consult the following paper:
# https://www.sciencedirect.com/science/article/pii/S2214860418301246

# unit of length (mm), time (ms)

T_room = 300
T_ambient = 300
T_melt = 1700

power = 0.3 # 300W = kg*m^2/s^3 = 300e-3 kg*mm^2/ms^3
r = 0.3 # 300 um = 300e-3 mm
dt = 200

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -4.5
    xmax = 4.5
    ymin = -4.5
    ymax = 4.5
    zmin = 0
    zmax = 3.3
    nx = 30
    ny = 30
    nz = 11
  []
  [add_set1]
    type = SubdomainBoundingBoxGenerator
    input = mesh
    block_id = 3
    bottom_left = '-50 -50 0'
    top_right = '50 50 0.9'
  []
  [add_set2]
    type = SubdomainBoundingBoxGenerator
    input = add_set1
    block_id = 1
    bottom_left = '-50 -50 0.9'
    top_right = '50 50 3.3'
  []

  [add_set3]
    type = GeneratedMeshGenerator
    dim = 3
    xmax = 0.001
    ymax = 0.001
    zmin = -0.001
    subdomain_ids = 2
  []
  [moving_boundary]
    type = SideSetsAroundSubdomainGenerator
    input = add_set3
    block = 2
    new_boundary = 'moving_boundary'
  []

  [cmbn]
    type = CombinerGenerator
    inputs = 'add_set2 moving_boundary'
  []

  skip_partitioning = true
[]

[Problem]
  material_coverage_check = false
[]

[Variables]
  [temp]
    block = '1 2 3'
  []
[]

[ICs]
  [temp_substrate]
    type = ConstantIC
    variable = temp
    value = ${T_room}
    block = '1 3'
  []
  [temp_product]
    type = FunctionIC
    variable = temp
    function = temp_ic
    block = '2'
  []
[]

[AuxVariables]
  [processor_id]
    order = CONSTANT
    family = MONOMIAL
  []
  [x_coord]
    order = FIRST
    family = LAGRANGE
  []
  [y_coord]
    order = FIRST
    family = LAGRANGE
  []
  [z_coord]
    order = FIRST
    family = LAGRANGE
  []
[]

[Kernels]
  [time]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat_conduc]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = thermal_conductivity
  []
  [heatsource]
    type = ADMatHeatSource
    material_property = volumetric_heat
    variable = temp
    scalar = 1
  []
[]

[AuxKernels]
  [processor_id_aux]
    type = ProcessorIDAux
    variable = processor_id
    execute_on = timestep_begin
  []
  [x_coord]
    type = FunctionAux
    function = x_coord
    variable = x_coord
  []
  [y_coord]
    type = FunctionAux
    function = y_coord
    variable = y_coord
  []
  [z_coord]
    type = FunctionAux
    function = z_coord
    variable = z_coord
  []
[]

[BCs]
  [bottom_temp]
    type = ADDirichletBC
    variable = temp
    boundary = 'back'
    value = ${T_room}
  []
  [convective]
    type = ADConvectiveHeatFluxBC
    variable = temp
    boundary = 'bottom front left right top'
    heat_transfer_coefficient = 2e-5
    T_infinity = ${T_ambient}
  []
[]

[Functions]
  # the values are scaled to fit the size of the substrate
  [heat_source_x]
    type = PiecewiseLinear
    data_file = ./path_eq_t_x_coarse_ms.csv
    format = columns
    scale_factor = 0.12
  []
  [heat_source_y]
    type = PiecewiseLinear
    data_file = ./path_eq_t_y_coarse_ms.csv
    format = columns
    scale_factor = 0.12
  []
  [heat_source_z]
    type = PiecewiseLinear
    data_file = ./path_eq_t_z_coarse_ms.csv
    format = columns
    scale_factor = 0.15
  []
  # the properties are scaled to the right value and unit (see D. Yushu et al., 2022)
  [specific_heat_metal]
    type = PiecewiseLinear
    x = '-1e7 197.79  298.46  600.31 1401.01 1552.59 1701.44 1e7'
    y = '426.69 426.69 479.77 549.54 676.94  695.14 726.99 726.99'
    scale_factor = 1.0
  []
  [thermal_conductivity_metal]
    type = PiecewiseLinear
    x = '-1e7 198.84  298.10  398.75 500.76 601.40 700.64 801.27 901.89 1001.12 1098.98 1200.96 1301.56 1400.78 1501.37 1601.96 1e7'
    y = '247.72 247.72 285.64 323.55 358.44 390.29 417.59 446.41 469.16 491.91 510.11 528.31 540.44 554.09 561.67 569.26 569.26'
    scale_factor = 0.05e-6
  []
  # for monitoring the deposited material geometry
  [x_coord]
    type = ParsedFunction
    expression = 'x'
  []
  [y_coord]
    type = ParsedFunction
    expression = 'y'
  []
  [z_coord]
    type = ParsedFunction
    expression = 'z'
  []
  [temp_ic]
    type = ParsedFunction
    expression = 'if(t<=0, temp_room, temp_melt)'
    symbol_names = 'temp_room temp_melt'
    symbol_values = '${T_room} ${T_melt}'
  []
[]

[Materials]
  [heat_metal]
    type = ADHeatConductionMaterial
    specific_heat_temperature_function = specific_heat_metal
    thermal_conductivity_temperature_function = thermal_conductivity_metal
    temp = temp
    block = '1 2 3'
  []
  [volumetric_heat_metal]
    type = ADFunctionPathGaussianHeatSource
    r = ${r}
    power = ${power}
    efficiency = 0.36
    factor = 1.6
    function_x = heat_source_x
    function_y = heat_source_y
    function_z = heat_source_z
    heat_source_type = 'line'
    threshold_length = 0.1 #mm
    number_time_integration = 10
    block = '1 2 3'
  []
  [density_metal]
    type = ADDensity
    density = 7609e-9 # kg/m^3 -> 1e-9 kg/mm^3
    block = '1 2 3'
  []
[]

[MeshModifiers]
  [activated_elem_uo_beam]
    type = CoupledVarThresholdElementSubdomainModifier
    execute_on = 'TIMESTEP_BEGIN'
    coupled_var = temp
    block = 1
    subdomain_id = 2
    criterion_type = ABOVE
    threshold = ${T_melt}
    moving_boundaries = 'moving_boundary'
    moving_boundary_subdomain_pairs = '2 1'
  []
[]

[Adaptivity]
  marker = marker
  initial_marker = marker
  max_h_level = 2
  [Indicators]
    [indicator]
      type = GradientJumpIndicator
      variable = temp
    []
  []
  [Markers]
    [marker]
      type = ErrorFractionMarker
      indicator = indicator
      coarsen = 0 # coarsening is pending MOOSE PR #23078 being merged
      refine = 0.5
    []
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'preonly lu       superlu_dist NONZERO 1e-10'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10

  start_time = 0.0
  end_time = 57036
  dt = ${dt} # ms
  dtmin = 1e-6

  auto_advance = true # cut time-step when subapp fails

  error_on_dtmin = false
[]

[Outputs]
  file_base = 'output/Thermal'
  csv = true
  [exodus]
    type = Exodus
    file_base = 'output/Exodus/Thermal'
    time_step_interval = 1
  []
[]

[Postprocessors]
  [bead_max_temperature]
    type = ElementExtremeValue
    variable = temp
    value_type = max
    block = '2'
    outputs = 'csv'
  []
  [bead_min_temperature]
    type = ElementExtremeValue
    variable = temp
    value_type = min
    block = '2'
    outputs = 'csv'
  []
  [bead_volume]
    type = VolumePostprocessor
    block = '2'
    outputs = 'csv console'
  []
  [bead_x_coord_max]
    type = ElementExtremeValue
    variable = x_coord
    value_type = max
    block = '2'
    outputs = 'csv console'
  []
  [bead_x_coord_min]
    type = ElementExtremeValue
    variable = x_coord
    value_type = min
    block = '2'
    outputs = 'csv'
  []
  [bead_y_coord_max]
    type = ElementExtremeValue
    variable = y_coord
    value_type = max
    block = '2'
    outputs = 'csv console'
  []
  [bead_y_coord_min]
    type = ElementExtremeValue
    variable = y_coord
    value_type = min
    block = '2'
    outputs = 'csv console'
  []
  [bead_z_coord_max]
    type = ElementExtremeValue
    variable = z_coord
    value_type = max
    block = '2'
    outputs = 'csv console'
  []
[]

(test/tests/gaussian_heat_source/gaussian_heat_source.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 0.5
    zmin = 0
    zmax = 0.1
    nx = 10
    ny = 5
    nz = 1
  []
[]

[Variables]
  [temp]
  []
[]

[ICs]
  [temp_substrate]
    type = ConstantIC
    variable = temp
    value = 300
  []
[]

[Kernels]
  [time]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat_conduct]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = thermal_conductivity
  []
  [heatsource]
    type = ADMatHeatSource
    material_property = volumetric_heat
    variable = temp
    scalar = 1
  []
[]

[Functions]
  [heat_source_x]
    type = ParsedFunction
    expression = '0.05*t'
  []
  [heat_source_y]
    type = ParsedFunction
    expression = 0.25
  []
  [heat_source_z]
    type = ParsedFunction
    expression = 0.1
  []
[]

[BCs]
  [temp_bottom_fix]
    type = ADDirichletBC
    variable = temp
    boundary = back
    value = 300
  []
[]

[Materials]
  [volumetric_heat]
    type = ADFunctionPathGaussianHeatSource
    r = 0.2
    power = 0.3
    efficiency = 0.3
    factor = 2
    function_x = heat_source_x
    function_y = heat_source_y
    function_z = heat_source_z
    heat_source_type = 'mixed'
    threshold_length = 0.1
  []
  [density]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 7609e-9
  []
  [heat]
    type = ADHeatConductionMaterial
    specific_heat_temperature_function = 500
    thermal_conductivity_temperature_function = 25e-6
    temp = temp
  []
[]

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

[Executioner]
  type = Transient

  automatic_scaling = true

  solve_type = 'PJFNK'

  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 10
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8

  start_time = 0.0
  end_time = 20
  dt = 1
  dtmin = 1e-4
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [avg_temp]
    type = ElementAverageValue
    variable = temp
  []
  [max_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
  []
  [min_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = min
  []
[]

(test/tests/gaussian_heat_source/gaussian_heat_source_vary_r.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 0.5
    zmin = 0
    zmax = 0.1
    nx = 10
    ny = 5
    nz = 1
  []
[]

[Variables]
  [temp]
  []
[]

[ICs]
  [temp_substrate]
    type = ConstantIC
    variable = temp
    value = 300
  []
[]

[Kernels]
  [time]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat_conduct]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = thermal_conductivity
  []
  [heatsource]
    type = ADMatHeatSource
    material_property = volumetric_heat
    variable = temp
    scalar = 1
  []
[]

[Functions]
  [heat_source_x]
    type = ParsedFunction
    expression = '0.05*t'
  []
  [heat_source_y]
    type = ParsedFunction
    expression = 0.25
  []
  [heat_source_z]
    type = ParsedFunction
    expression = 0.1
  []
[]

[BCs]
  [temp_bottom_fix]
    type = ADDirichletBC
    variable = temp
    boundary = back
    value = 300
  []
[]

[Materials]
  [volumetric_heat]
    type = ADFunctionPathGaussianHeatSource
    r = '0.2 0.3 0.1'
    power = 0.3
    efficiency = 0.3
    factor = 2
    function_x = heat_source_x
    function_y = heat_source_y
    function_z = heat_source_z
    heat_source_type = 'mixed'
    threshold_length = 0.1
  []
  [density]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 7609e-9
  []
  [heat]
    type = ADHeatConductionMaterial
    specific_heat_temperature_function = 500
    thermal_conductivity_temperature_function = 25e-6
    temp = temp
  []
[]

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

[Executioner]
  type = Transient

  automatic_scaling = true

  solve_type = 'PJFNK'

  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 10
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8

  start_time = 0.0
  end_time = 20
  dt = 1
  dtmin = 1e-4
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [avg_temp]
    type = ElementAverageValue
    variable = temp
  []
  [max_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
  []
  [min_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = min
  []
[]

(test/tests/function_path_gaussian_heat_source/func_path_gaussian_heat_source.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 0.5
    zmin = 0
    zmax = 0.1
    nx = 10
    ny = 5
    nz = 1
  []
[]

[Variables]
  [temp]
  []
[]

[ICs]
  [temp_substrate]
    type = ConstantIC
    variable = temp
    value = 300
  []
[]

[Kernels]
  [time]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat_conduct]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = thermal_conductivity
  []
  [heatsource]
    type = ADMatHeatSource
    material_property = volumetric_heat
    variable = temp
    scalar = 1
  []
[]

[Functions]
  [heat_source_x]
    type = ParsedFunction
    expression = '0.05*t'
  []
  [heat_source_y]
    type = ParsedFunction
    expression = 0.25
  []
  [heat_source_z]
    type = ParsedFunction
    expression = 0.1
  []
[]

[BCs]
  [temp_bottom_fix]
    type = ADDirichletBC
    variable = temp
    boundary = back
    value = 300
  []
[]

[Materials]
  [volumetric_heat]
    type = ADFunctionPathGaussianHeatSource
    r = 0.2
    power = 0.3
    efficiency = 0.3
    factor = 2
    function_x = heat_source_x
    function_y = heat_source_y
    function_z = heat_source_z
    heat_source_type = 'mixed'
    threshold_length = 0.1
  []
  [density]
    type = ADGenericConstantMaterial
    prop_names = 'density'
    prop_values = 7609e-9
  []
  [heat]
    type = ADHeatConductionMaterial
    specific_heat_temperature_function = 500
    thermal_conductivity_temperature_function = 25e-6
    temp = temp
  []
[]

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

[Executioner]
  type = Transient

  automatic_scaling = true

  solve_type = 'PJFNK'

  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'preonly lu       superlu_dist'

  line_search = 'none'

  l_max_its = 20
  nl_max_its = 10
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8

  start_time = 0.0
  end_time = 20
  dt = 1
  dtmin = 1e-4
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  [avg_temp]
    type = ElementAverageValue
    variable = temp
  []
  [max_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
  []
  [min_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = min
  []
[]

Input Parameters
Input Files
References