Thermal Simulation

This example shows thermal simulation of material deposition on a plate.

The example is composed of the following files:

• demo_316_short.info: the input file
• demo_316_short_scan_path.txt: the scan path of the heat source

It can be run using ./adamantine -i demo_316_short.info.

Understanding the input file

An adamantine INFO file is organized into named blocks. A block starts with a name followed by braces, and each line inside the braces sets one input. For example, geometry { ... } is the geometry block, while geometry { length } would refer to the length input inside that block. Text after a semicolon is a comment and is ignored by the program. Values written with e notation are scientific notation: for example, 10e-3 means 0.010, or 10 millimeters when the unit is meters.

The complete list of inputs and their accepted values is available in the input-file reference. This explanation focuses on what each value does in this particular example.

The sections below follow the order in the input file. Together they answer four basic questions: what is being simulated, what material and heat source are used, how the equations are advanced in time, and what files are written.

1. Geometry

geometry
{
  import_mesh false
  dim 3
  length 10e-3
  height 2.0e-3
  width 10e-3
  length_divisions 50
  height_divisions 8
  width_divisions 50
  material_deposition true
  material_deposition_method scan_paths
  deposition_length 0.0003
  deposition_height 0.0002
  deposition_width 0.0003
  deposition_lead_time 0.0005
  material_height 0.75e-3
}

The geometry block defines the computational domain and how material is initially placed in it.

• import_mesh false tells adamantine to generate a regular mesh from the dimensions below. If this were true, the block would instead need a mesh filename and mesh format.
• dim 3 selects a three-dimensional simulation. Therefore all three domain dimensions and all three division counts are used.
• length 10e-3, height 2.0e-3, and width 10e-3 make a box that is 10 mm long, 2 mm high, and 10 mm wide. The input-file units for these values are meters.
• length_divisions 50, height_divisions 8, and width_divisions 50 split the box into 50, 8, and 50 cell layers in the corresponding directions. More divisions generally give a finer spatial resolution, but also increase the computational cost. These are cell counts, not physical lengths.
• material_deposition true enables adding material while the simulation is running. This is what makes the example a deposition process rather than a heat source moving over a permanently filled block.
• material_deposition_method scan_paths says that deposition is controlled by the beam scan path. The alternative method reads deposition information from a separate material-deposition file.
• deposition_length 0.0003, deposition_width 0.0003, and deposition_height 0.0002 define the size of each material-deposition box: 0.3 mm along the scan direction, 0.3 mm across the scan direction, and 0.2 mm vertically. deposition_width is used because this is a 3D problem.
• deposition_lead_time 0.0005 means that material is added 0.5 ms before the heat source reaches the corresponding scan location. The lead time gives the newly deposited material a spatial and temporal relationship to the moving beam.
• material_height 0.75e-3 says that the initial material occupies the part of the domain below 0.75 mm. The region above that height starts empty and can be filled by the deposition process.

There is no use_powder input in this block, so it keeps its default value of false. The example therefore does not turn on the separate initial-powder layer option described in the input-file reference.

2. Boundary

boundary
{
  type convective,radiative
}

The boundary block describes how heat crosses the external boundary of the domain. The comma-separated value selects two boundary mechanisms at once:

• convective models heat exchanged with the surrounding environment through convection. The convection coefficient and ambient temperature come from the material block below.
• radiative models thermal radiation from the surface to the environment. Its strength depends on the emissivity and the surrounding radiation temperature.

Because no boundary_X or printed_surface sub-block is supplied, the same general boundary selection is used rather than assigning different boundary types to particular face IDs or to the printed surface.

3. Physics

physics
{
  thermal true
  mechanical false
}

This block selects the equations that adamantine solves.

• thermal true enables the transient heat equation, so the temperature field changes as the beam moves and as heat diffuses through the material.
• mechanical false disables the mechanical calculation. The example does not compute displacement, stress, or strain.

Since only the thermal flag is enabled, this is a purely thermal simulation. If both flags were true, adamantine would solve a coupled thermo-mechanical problem.

4. Refinement

refinement
{
  n_refinements 0
  time_steps_between_refinement 2000000000
}

The refinement block controls adaptive mesh refinement near the heat-source paths.

• n_refinements 0 requests no additional refinement levels. The generated mesh is therefore used at its original resolution.
• time_steps_between_refinement 2000000000 is the interval at which the refinement procedure would be considered. It is intentionally enormous for this example, so refinement is effectively disabled even aside from the zero refinement levels.

5. Materials

materials
{
  n_materials 1
  property_format polynomial
  material_0
  {
    ...
  }
}

The materials block supplies the physical properties used by the heat equation.

• n_materials 1 declares one material definition, named material_0. The number in the name is zero-based: the first material is material 0.
• property_format polynomial says how temperature-dependent properties are represented. A property is interpreted as polynomial coefficients, starting with the coefficient of T^0. Because the values in this example are single numbers, they represent constant properties rather than properties that vary with temperature.

The material_0 block contains three possible material states:

material_0
{
  solid { ... }
  powder { ... }
  liquid { ... }
  solidus 1675
  liquidus 1708
  latent_heat 290000
  radiation_temperature_infty 300
  convection_temperature_infty 300
}

The state blocks allow adamantine to use different properties before melting, while material is powder, and after melting. The phase-change temperatures are in kelvins:

• solidus 1675 is the temperature below which the material is treated as solid.
• liquidus 1708 is the temperature above which it is treated as liquid.
• Between the solidus and liquidus temperatures, the material is in the transition interval. latent_heat 290000 supplies the energy per kilogram associated with melting.

The environmental temperatures are both 300 K:

• radiation_temperature_infty 300 is the surrounding temperature used by the radiative boundary condition.
• convection_temperature_infty 300 is the surrounding temperature used by the convective boundary condition.

The global initial_temperature and new_material_temperature inputs are omitted, so both keep their documented default of 300 K. This means that the initial material and material added during deposition start at the same ambient temperature unless another input changes them.

Solid properties

solid
{
  density 7904
  specific_heat 714
  thermal_conductivity_x 31.4
  thermal_conductivity_y 31.4
  thermal_conductivity_z 31.4
  convection_heat_transfer_coef 100
  emissivity 0.15
}

The solid has density 7904 kg/m^3, specific heat 714 J/(K*kg), and thermal conductivity 31.4 W/(m*K) in each direction. Equal conductivity in all directions makes this material thermally isotropic. The convection heat transfer coefficient is 100 W/(m^2*K), and the surface emissivity is 0.15. Those last two values are used by the boundary conditions selected above.

Powder properties

powder
{
  specific_heat 714
  density 7904
  thermal_conductivity_x 0.314
  thermal_conductivity_y 0.314
  thermal_conductivity_z 0.314
  convection_heat_transfer_coef 100
  emissivity 0.15
}

The powder uses the same density and specific heat as the solid, but its thermal conductivity is 0.314 W/(m*K) in every direction, one hundredth of the solid value. This represents the poorer heat conduction of a loose powder region. The powder state is defined for the material model, although this input does not enable the separate use_powder initial-layer option.

Liquid properties

liquid
{
  specific_heat 847
  density 7904
  thermal_conductivity_x 37.3
  thermal_conductivity_y 37.3
  thermal_conductivity_z 37.3
  convection_heat_transfer_coef 100
  emissivity 0.15
}

The liquid has density 7904 kg/m^3, specific heat 847 J/(K*kg), and thermal conductivity 37.3 W/(m*K) in each direction. As with the other states, convection and radiation use a coefficient of 100 W/(m^2*K) and an emissivity of 0.15.

Mechanical material properties such as Lamé parameters, thermal expansion, plastic modulus, and elastic limit are not included because the physics block turns mechanics off.

6. Heat source

sources
{
  n_beams 1
  beam_0
  {
    type goldak
    depth 0.5e-3
    diameter 0.6e-3
    scan_path_file demo_316_short_scan_path.txt
    scan_path_file_format segment
    absorption_efficiency 0.3
    max_power 400.0
  }
}

The sources block describes the moving heat input.

• n_beams 1 creates one heat source, named beam_0.
• type goldak selects the Goldak heat-source model, which is the laser-like source used in this example.
• depth 0.5e-3 limits the source’s maximum penetration depth to 0.5 mm.
• diameter 0.6e-3 gives the source a diameter of 0.6 mm.
• scan_path_file demo_316_short_scan_path.txt points to the file that tells the source where to start and how to move. The file must be available from the directory in which adamantine is run.
• scan_path_file_format segment tells adamantine to interpret that file as a sequence of path segments. This is different from the event-series format.
• absorption_efficiency 0.3 says that 30% of the beam power is absorbed by the object and contributes heat; the rest is not deposited as thermal input.
• max_power 400.0 sets the beam’s maximum power to 400 W.

7. Time stepping

time_stepping
{
  method forward_euler
  duration 0.004
  time_step 0.6e-4
}

This block controls how the transient thermal equation is advanced.

• method forward_euler selects the first-order explicit Forward Euler time integration method.
• duration 0.004 runs the simulation for 0.004 s, or 4 ms, unless the run is stopped earlier for another reason.
• time_step 0.6e-4 uses a time step of 0.00006 s, or 60 microseconds. The time step must be small enough for the chosen mesh, material properties, and explicit integration method to remain stable.

The scan path does not determine the duration here because scan_path_for_duration is omitted and therefore keeps its default value of false.

8. Output

post_processor
{
  filename_prefix output
  time_steps_between_output 10
}

The post_processor block controls field output.

• filename_prefix output makes generated output files start with the prefix output.
• time_steps_between_output 10 writes the temperature and other requested fields every ten simulation time steps instead of after every step. This reduces the number of output files and the amount of disk space used.

No additional output refinement is requested, so output uses the default additional refinement level of zero.

9. Thermal discretization

discretization
{
  thermal
  {
    fe_degree 3
    quadrature gauss
  }
}

The discretization block describes how the thermal field is represented on the mesh.

• fe_degree 3 uses third-degree finite-element basis functions. Higher degree can represent smoother spatial variation within each cell, but generally costs more to solve.
• quadrature gauss uses Gauss quadrature to evaluate the integrals needed by the finite-element method. gauss is also the default, so this line makes the choice explicit.

There is no mechanical discretization block because mechanical physics is disabled.

10. Profiling

profiling
{
  timer false
  caliper "spot(profile.mpi),loop-report,runtime-report"
}

The profiling block is about measuring program performance, not changing the physics.

• timer false disables adamantine’s built-in timing output.
• caliper ... provides a Caliper configuration string. If Caliper profiling is enabled in the build and activated by the run environment, this string requests spot profiling, loop reporting, and runtime reporting.

11. Memory space

memory_space host

host tells the Kokkos-backed parts of the program to use host memory, which corresponds to the CPU in this example. The alternative device value is used when adamantine has been built with GPU support and the calculation should run in device memory.

Putting the configuration together

In plain language, this file asks adamantine to simulate a 3D, 10 mm by 10 mm by 2 mm domain whose initial material fills the bottom 0.75 mm. A single Goldak heat source moves along the segments in the scan-path file. The model tracks heat transfer, melting, latent heat, convection, and radiation, while material is added ahead of the moving source. The calculation uses an unrefined, third-degree finite-element mesh, advances for 4 ms with 60 microsecond Forward Euler steps, and writes fields every ten steps.

Below are snapshots of the temperature at different times:

Temperature at t = 0s

Temperature at t = 6e-4s

Temperature at t = 12e-4s

Temperature at t = 18e-4s

Temperature at t = 24e-4s

Temperature at t = 30e-4s

Demo316 AMR

This example is similar to the previous one but it uses adaptive mesh refinement (AMR).

The example is composed of the following files:

• demo_316_short_amr.info: the input file
• demo_316_short_scan_path_amr.txt: the scan path of the heat source

It can be run using ./adamantine -i demo_316_short_amr.info.

The main difference with the previous example concerns the refinement input:

refinement
{
  n_refinements 1                 ; Number of time the cells on the paths of the beams are refined.
  time_steps_between_refinement 5 ; Number of time steps after which the refinement process is performed.
  coarsen_after_beam true         ; The cells are coarsen once the beam has passed
}

The other differences are:

• the domain size is reduced and the number of cells is reduced accordingly
• the time step is increased from 6e-5 s to 1e-4 s
• the order of the finite element is decrease from 3 to 2

Demo316 anisotropic

This is similar to Demo316 but the thermal conductivity of the material is anisotropic. The conductivity in the deposition direction is increased.

This example is composed of the following files:

• demo_316_short_anisotropic.info: the input file
• demo_316_short_scan_path.txt: the scan path of the heat source

It can be run using ./adamantine -i demo_316_short_anisotropic.info.

The differences with Demo316 are:

• the domain is reduced
• the boundary conditions are changed from convective and radiative to adiabatic
• the thermal conductivity in the deposition direction, x, is increased for the solid, liquid, and powder phases. This is not physical but it is done to test the anisotropic capabilities of adamantine
• the duration of the simulation is reduced from 4e-3 s to 1e-4 s
• the time step is reduced from 6e-5 s to 1e-5 s
• the order of the finite element is decrease from 3 to 2