V-MMS-02 — ALE free-stream preservation under prescribed mesh motion

Tags: mms, ale, gcl, free_stream

References:

• Thomas & Lombard, AIAA J. 17 (1979) — geometric conservation law
• docs/VerificationSuitePlan_2026-07-06.md Tier 3 (ALE-MMS deliverable)

Problem statement

The sharpest possible discrete-GCL assert: spatially uniform T, ξ with no reactions and zero-flux manufactured BCs, while the mesh is compressed to 70 % of its initial thickness through the Workspace.w_override hook with the uniform-stretch velocity

w*(z, t) = (ṡ/s)·z, s(t) = 1 − 0.15·(1 − cos(2πt/20)), z_bottom pinned

(node trajectories zi(t) = zi(0)·s(t) exactly). A uniform state must stay uniform to machine precision on the moving mesh: the ALE advection of a constant field must vanish discretely (limiter slope ≡ 0), the dilation correction is zero (θ reaction-driven, no reactions), and the conductive/ species fluxes are zero. Any drift is a moving-mesh transport defect that smooth-field order studies (V-MMS-03) can hide inside their truncation error.

The node-motion ODE żi = w*(zi,t) is integrated by the same stiff integrator, so the top-cell-center trajectory doubles as an exactness check on the prescribed-motion path (temporal tolerance only).

Jacobian: colored/dense FD (jacobian = :fd) — the structured geometry Jacobian assumes reaction-driven mesh velocity and does not model the override (documented on Workspace.w_override).

Quantities of interest (n = 20)

Solver configuration