# Example 03: Non-linear run with temperature-dependent properties
#
# Thermal conductivity, density and specific heat vary with temperature
# (solid and liquid polynomial branches blended by the liquid fraction), making
# the diffusion problem non-linear. Each time step is solved with a Picard
# iteration and a global property correction (Green's first identity).
#
# The domain is small with a fine z-grid so the thin mushy zone is resolved. 
# Runtime is on the order of minutes.
#
# Run: uv run python simulations/main.py simulations/examples/03_nonlinear_tdep.yaml

simulation:
  name: "nonlinear_tdep"
  backend: "cpu"              
  duration:
    value: 2.0e-4
    unit: "s"
  dt:
    value: 4.0e-6
    unit: "s"
  update_interval: 1

  # Non-linear solve controls.
  max_picard_iter: 80         # Picard iteration cap per step. 
  picard_omega: 0.31          # relaxation factor; 0.31 converges here, higher does not.
                              # This value has to be tuned for each case as it is problem dependent.

  # picard_tol: 1.0e-4        # convergence tolerance (optional; default 1e-4).

domain:
  size:
    value: [0.5e-3, 0.3e-3, 0.12e-3]  # [Lx, Ly, Lz] in m (0.5 x 0.3 x 0.12 mm) — small box.
    unit: "m"
  mesh:
    value: [100, 60, 96]              # dz ~ 1.25 um resolves the mushy zone.
    unit: ""

# OPTIONAL moving fine-mesh that resolves the sharp mushy-zone gradients
# under the beam. Omit the whole `fine_mesh` parameters to evaluate latent heat on
# the coarse main grid (the default: lower memory, faster, coarser mushy zone).
fine_mesh:
  refinement: 2                          # Fine cells per coarse cell, per axis.
  box_size: [0.2e-3, 0.15e-3, 0.04e-3]   # [Lx_box, Ly_box, Lz_box] in m.

material:
  name: "316L"
  # Temperature-dependent reference 316L properties. Each branch is an expression
  # of T in standard Python. The solid and liquid branches are blended across
  # the mushy zone by the liquid fraction f_l(T). 
  #
  # `reference` (REQUIRED for each T-dependent property) is the constant reference
  # property k_bar, rho_bar, Cp_bar, determines the fluctuation k'=k(T)-k̄.
  # Recommendation:
  # the average of the property's two extrema over [T0, T_boil] — centering it
  # matters for convergence. Omitting will raise an error.
  k:
    solid: "9.248 + 0.01571 * T"
    liquid: "12.41 + 0.003279 * T"
    reference: 24.5075              # ½(min k + max k) over [T0, T_boil]
    unit: "W/(m.K)"
  rho:
    solid: "8084.2 - 0.42086 * T - 3.8942e-5 * T**2"
    liquid: "7432.7 + 0.039338 * T - 1.8007e-4 * T**2"
    reference: 6896.2365           # ½(min rho + max rho) over [T0, T_boil]
    unit: "kg/m^3"
  Cp:
    solid: "458.98 + 0.1328 * T"
    liquid: "769.86"                # constant branch (a bare-number string)
    reference: 633.8752            # ½(min Cp + max Cp) over [T0, T_boil]
    unit: "J/(kg.K)"
  L_f:
    value: 2.677e5
    unit: "J/kg"
  T_solidus:
    value: 1674.15
    unit: "K"
  T_liquidus:
    value: 1697.15
    unit: "K"
  T0:
    value: 293.0
    unit: "K"
  h_conv_bottom:
    value: 3000.0
    unit: "W/(m2.K)"
  DeltaH_LV:
    value: 7.416e6
    unit: "J/kg"
  R_v:
    value: 150.774
    unit: "J/(kg.K)"
  Pa:
    value: 101325.0
    unit: "Pa"
  T_boil:
    value: 3090.0
    unit: "K"

laser:
  radius:
    value: 30.0e-6
    unit: "m"
  absorptivity: 0.30
  power_nominal:
    value: 24.0
    unit: "W"
  path:
    type: "gcode"
    file: "example03_track.gcode"   # v_scan = 0.15 m/s, starts mid-domain (x = 0.3 mm).

io:
  run_tag: "nonlinear_tdep"
  output_interval: null
  outputs: [full_volume]
  at_end: [full_volume, slices, profiles]
  profiles_locations:
    - 'laser'
  slice_planes:
    - name: "longitudinal_section"
      normal: "y"              # plane x-z: longitudinal melt-pool section.
      width: 0.16e-3
      height: 0.035e-3
      isotherms:
        - ["T_s", 1674.15]