V-RAD-01 — in-depth absorption + conduction (sub-surface peak)

Tags: radiation, beer_lambert, convective_bc, coupled

References:

• Lautenberger dissertation (2007) §3.4.2 + Appendix A
• exact/indepth_absorption.jl (re-derivation, PDE-residual self-test)

Problem statement

Lautenberger dissertation §3.4.2 + Appendix A: finite slab δ = 1 cm, in-depth source q₀κe^(−κx) with κ = 1000 m⁻¹ (κδ = 10), convective loss at the irradiated face, insulated back. Exact eigenfunction solution re-derived in exact/indepth_absorption.jl (PDE-residual self-tested).

This is the definitive BEER_LAMBERT + conduction + ConvectiveBC coupling case. The existing Beer–Lambert test checks the absorption profile and energy split WITHOUT conduction; the physics marker here is the SUB-SURFACE temperature peak (the peak sits at the front face at t → 0⁺ and migrates toward the insulated back as t → ∞), which only the coupled problem shows.

Configuration pitfalls encoded below:

• RadiativeFluxBC(flux = q₀, absorptivity = 1.0): the EXPLICIT absorptivity bypasses the Kirchhoff ε_eff rescaling at volumetric injection, so exactly q₀ enters the Beer–Lambert sweep.
• Under BEER_LAMBERT the incident flux contributes zero to the surface Newton balance (deposited volumetrically); convective loss stays at the surface — exactly the exact solution's BC structure. No RadiativeBC is present, so there is no re-radiation term (the exact model has none).
• The component absorption kwarg α is a MASS coefficient [m²/kg]: α = κ/ρ = 1.0 m²/kg gives the target κ = 1000 m⁻¹.
• The transmitted fraction e^(−κδ) ≈ 4.5e-5 of q₀ exits the insulated back in both the exact model and the solver (never deposited): consistent.

k, ρ, c, h, q₀ follow the Gpyro §3.4.1 property set for cross-code comparability of the dissertation figures (report mode).

Quantities of interest (n = 400)

Comparison with other codes

The same case was solved with Gpyro 0.8200 at 101 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 1.995 (L2), expected 2.0.

Solver configuration