V-MMS-03 — ALE manufactured solution, prescribed smooth mesh motion

Tags: mms, ale, gcl, order_verification

References:

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

Problem statement

The moving-mesh order-verification companion to V-MMS-01 (and the "hardest and most valuable single test" of the suite plan's Tier 3): non-trivial manufactured fields solved on a mesh compressed to 70 % of its thickness by the prescribed uniform-stretch velocity

w*(z, t) = (ṡ/s)·z, s(t) = 1 − 0.15·(1 − cos(2πt/20)), zi(t) = zi(0)·s(t)

through the Workspace.w_override hook. On a grid point moving with w, the grid time derivative is ∂tT* + w·∂zT; the discrete ALE advection term supplies the w·∂zT part, so the same Eulerian manufactured sources — evaluated at the LIVE cell centers read from the z-block — make T, ξ the exact solution on the moving mesh (see exact/mms.jl header, "ALE"). The error norms therefore measure exactly the moving-mesh transport truncation: ALE advection (van-Leer-limited upwind reconstruction) + lab-frame operators on a nonuniform-in-time mesh.

No reactions: mesh motion is prescribed, not volume-change-driven, so the case isolates GCL/advection from kinetics (V-MMS-01 covers those). The solid field is spatially UNIFORM but time-varying: condensed phases are mesh-bound in this ALE formulation (vsolid = w ⇒ no advection operator, see computealespeciesadvection!), so a z-varying solid target under prescribed non-material motion would have no operator to balance its w·∂zξ* term (constraint documented in exact/mms.jl). The time variation keeps the solid source-injection path active; T and the gas field carry the full space–time structure and exercise the moving-mesh advection.

Expected order: the limiter's slope reconstruction is formally 2nd order on smooth data but clips at extrema (the sin peak crosses the domain), so the observed order sits between 1.5 and 2 — recorded at pin time; a drop below min_order flags a moving-mesh transport regression.

Jacobian: dense FD (jacobian = :fd) — the structured geometry Jacobian assumes reaction-driven mesh velocity (see Workspace.w_override note).

Quantities of interest (n = 128)

QoI	value	exact	error	tolerance	within tol	provenance
L∞ T error on moving mesh, t=10.0 s	0.003857	—	0.003857	0.25	yes	manufactured T* on 30%-compressed mesh
relative L∞ ξ_solid (mesh-bound) error, t=10.0 s	6.205e-12	—	6.205e-12	1e-10	yes	uniform solid: verifies the Lagrangian (no-advection) solid path + source injection
relative L∞ ξ_gas error, t=10.0 s	0.0006197	—	0.0006197	0.006	yes	gas is advected relative to the mesh: moving-mesh transport error channel