V-HC-01 — semi-infinite solid, convective surface BC (erfc)

Tags: heat_conduction, convective_bc, surface_newton

References:

• Carslaw & Jaeger (1959), Conduction of Heat in Solids, §2.7
• Lautenberger dissertation (2007) §3.4.1 (parameters)
• FDS Verification Guide ht3d_slab; ThermaKin (FSS 9:1141) Eq. 25

Problem statement

The one verification case shared by all three reference codes (FDS ht3d_slab, Gpyro §3.4.1, ThermaKin Eq. 25), in Gpyro's variant: constant absorbed radiant flux q″ = 25 kW/m² plus convective exchange h = 20 W/m²K with T∞ = T₀ = 300 K; k = 0.2 W/(m·K), ρ = 1000 kg/m³, c = 1400 J/(kg·K), so profiles at t = 30/60/90/180 s are directly comparable to the dissertation figures.

Because the combined surface BC is linear in Ts, absorbed-flux + convection is exactly convection toward T∞eff = T∞ + q″/h = 1550 K, and the Carslaw & Jaeger §2.7 erfc solution (exact/semi_infinite.jl) applies unchanged.

Coverage beyond the existing Dirichlet erf test: HeatFluxBC + ConvectiveBC enter the surface Newton solve, so the surface temperature is an unknown coupled to the interior — the place surface-BC bugs live.

Domain: L = 5 cm ≫ thermal penetration (erfc(η) ≈ 3e-12 at the back face at t = 180 s), so the finite slab is semi-infinite to well below the QoI tolerances; the back-face-rise QoI enforces this assumption explicitly.

Quantities of interest (n = 500)

Comparison with other codes

The same case was solved with FDS 6.11.0 at 133 cells (Δx≈0.38 mm) and Gpyro 0.8200 at 500 nodes (Δz=0.1 mm); decks, outputs, and run provenance are committed under test/verification/reference/. Each code's error against the same exact solution is drawn below on a log scale, muted gray behind this solver's series — the signed linear-scale panel above shows where the error lives, this one compares magnitudes across codes.

Wall times at every ladder rung against the reference runs. Resolutions and simulated spans differ where noted (details in reference/timings.csv), so cross-code timings are indicative rather than a controlled benchmark; rungs at a matched resolution are directly comparable.

Solution overlays including the other codes' points: Tprofilesvs_codes, surfaceThistoryvscodes.

Convergence

Observed order 1.993 (L2), expected 2.0.

Solver configuration