Valley realism: transient valley widening/narrowing + deposit (overbank) tracking

[awickert]

Scope

Two coupled pieces of floodplain/valley realism, building on the v3 node-based unified solver (target: v3.1 realism milestone):

1. Transient valley widening / narrowing — valley width B becomes dynamic (B(x, t)) rather than the static set_B.
2. Deposit tracking, incl. overbank — account for where sediment goes: channel-bed gravels vs. overbank/floodplain fines and a storage/stratigraphy layer. Naturally coupled to width change (valley fill vs. the channel thread).

Conservation (sediment budget)

The mass balance the feature must close (integrated Exner, solid volume):

d/dt ∫(1−λ_p)·B·z dx = Q_s,in − Q_s,out + ∫(1−λ_p)·U·B dx − L_fining + ∫(1−λ_p)·z·(dB/dt) dx

The last term — "valley-width storage and release" — is the new physics this issue adds and the term the current solver omits. A compute_sediment_budget() diagnostic (designed) reports channel_storage, overbank_storage, and cumulative_input, with the invariant Δ cumulative_input == Δ(channel_storage + overbank_storage).

Numerical substrate

Builds on volume-first conservation (#18): this work supplies the real valley-geometry V(z) map that the volume-first solver consumes, so dynamic B keeps BDF2 second-order and conservation exact without reintroducing the storage secant.

Related

• Volume-first time integration: conserve stored sediment volume (BDF2-on-V), not elevation #18 (volume-first / BDF2-on-V, the prerequisite foundation).
• Enhancement: solver time-stepping — accuracy vs. Δt, second-order in time, and adaptive stepping #16 (BDF2 second-order time), Enhancement: iterate Picard to convergence (tolerance-based) instead of a fixed niter #17 (iterate Picard to convergence).

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