V-GT-01 — Gaussian gas-pulse diffusion (plane source)

Tags: gas_transport, fickian, mass_conservation

References:

• J. Crank, The Mathematics of Diffusion (plane-source solution)
• Stoliarov & Lyon, FSS 9:1141 (2008), gas-transport verification

Problem statement

Pure Fickian transport of gas released inside the solid (Crank/ThermaKin plane source). Instead of approximating a delta function, the initial condition is a finite-width Gaussian — itself an exact solution — so the comparison is IC-discretization-free:

ξ(z,t) = M_tot/√(2πσ²(t)) · exp(−(z−z₀)²/(2σ²(t))), σ²(t) = σ₀² + 2dt

Setup notes:

• All permeabilities are 0 ⇒ has_darcy_flow is false ⇒ the residual takes the pure-diffusion path (compute_gas_fluxes!), whose kernel −(λ/T)·Δ(ξT)/Δz reduces exactly to Fick's law with diffusivity λ at uniform T (adiabatic faces + no sources keep T uniform to machine).
• λ = d is set on BOTH components: PARALLEL mixing is volume-fraction weighted, so equal per-component λ makes λ_eff ≡ d independent of composition (otherwise the pulse would see a composition-dependent d).
• Default ImpermeableBC on both faces: mass is conserved to machine precision; the sealed-boundary image-source correction to the infinite- domain reference is ≤ e^(−11.7) ≈ 8e-6 of the peak at tend (domain half-width = 4.9σ(tend)) — below the discretization error.

QoIs: profile L∞ (relative to the evolving peak), total-mass conservation, and the parameter-free variance growth law Var(t) = σ₀² + 2dt.

Quantities of interest (n = 640)

Convergence

Observed order 2.012 (L2), expected 2.0.

Solver configuration