Moving Geometry (Space-Time Slabs)

Moving models:

• MovingDiffusionModelMono
• MovingDiffusionModelDiph

use per-step space-time slab assembly over [t^n, t^{n+1}].

Geometry Path

For each step:

1. evaluate phase level-set(s) at t^n and t^{n+1} for V^n, V^{n+1},
2. build a 2-time-node SpaceTimeCartesianGrid,
3. compute geometric moments in space-time,
4. reduce slab moments back to space operators/capacity.

Temporal Treatment

For moving assemblies:

• slab/mass terms use V^n, V^{n+1} and Ψ masks,
• diffusivity-weighted operator blocks are sampled at t^n + θΔt,
• source data are end-state for :BE,
• source data are θ-blended between t^n and t^{n+1} for θ < 1,
• interface scalar/flux coefficients and values follow the same rule.

Interface Sampling Convention

Spatial interface sampling remains at slab C_γ.

When blending in time (θ < 1), both t^n and t^{n+1} evaluations are taken at that same slab C_γ sample set.

API

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

solve_unsteady!(model::MovingDiffusionModel..., ...) dispatches to the same moving solver.