Moving Geometry (Space-Time Slabs)

Moving advection-diffusion models:

• MovingAdvDiffModelMono
• MovingAdvDiffModelDiph

compose moving diffusion from PenguinDiffusion with moving advection from PenguinTransport.

Assembly Composition

Per step on [t^n, t^{n+1}]:

1. PenguinDiffusion.assemble_unsteady_*_moving! builds slab geometry terms, moving mass/GCL part, and diffusion/interface contributions.
2. PenguinTransportDiffusion evaluates advection at t^n + \theta \Delta t.
3. Moving advection blocks are appended:
   • conv_bulk = sum(opsA.C)
   • conv_iface = 0.5 * sum(opsA.K)
4. Outer transport BCs are applied.
5. Active-row identity constraints are re-applied.

Relative Interface Velocity

For moving interfaces, advection uses:

\[u_{\gamma,\mathrm{rel}} = u_\gamma - w_\gamma\]

where wγ is the interface velocity sampled at γ points.

API

sol = solve_unsteady_moving!(model, u0, (t0, tf); dt=Δt, scheme=:BE, method=:direct)

Accepted scheme values:

• :BE (θ=1)
• :CN (θ=1/2)
• numeric θ with 0 ≤ θ ≤ 1

Regression Coverage

• Static-geometry recovery (wγ=0, time-independent body) against fixed models.
• Zero-advection reduction against moving diffusion.
• MMS convergence for moving mono (no interface) and moving diphasic (translating planar interface).