rtx-cfd: ALE on a moving tensor-product grid, DGCL-exact by construction

The first brick of the Turek-Hron frontier: PISO (explicit conservative
predictor + SOR projection) generalised to a staggered grid whose x- and
y-lines move arbitrarily each step while the domain boundary stays fixed.

The discretisation choice that carries everything: time-averaged face
areas (A^n + A^{n+1})/2 in both the fluid fluxes and the face-swept
volumes. For tensor-product motion the discrete geometric conservation
law then holds as an algebraic identity, so uniform flow is a
machine-precision fixed point, not a truncation-order one:

- DGCL test: uniform (0.7, -0.4) on a 16x12 grid with interior lines
  wiggling out of phase, 400 steps: max deviation 7.9e-15 (~35 ulp).
  Negative control with end-of-step areas (per-step cell error exactly
  dw*dh/V, the cross term the identity absorbs): 1.5e-2 - a 1e12
  separation, so the test can fail.
- Degeneracy: zero motion on a uniform grid vs fixed-grid PISO over
  Taylor-Green steps: max difference 2.2e-16 - one ulp - pinning every
  geometric generalisation to the verified implementation.
- Physics under motion: Taylor-Green on the wiggling mesh, L2 error
  2.42e-2 -> 1.07e-2 (n=16 -> 32, order 1.17); moving-mesh error at
  n=32 sits below the fixed-mesh 1.1532e-2 (PISO's published value to
  four digits); energy decay unchanged by the motion.

One trap documented in the test: the projection's inner-stop floor
(0.1 * tolerance * reference_flux) at an engineering tolerance lets a
one-sweep partial p' accumulate into p, whose gradient perturbs the
velocities at ~1e-11 with the geometry blameless. The DGCL run must use
a rounding-level tolerance because machine-precision preservation is the
claim under test. Measured: 3.6e-11 at tol 1e-9, 7.9e-15 at 1e-13.

Incompressibility needs no mesh-velocity term: subtracting the GCL from
moving-cell mass conservation leaves plain div(u) = 0 on the current
geometry, so the projection is the fixed-grid one with non-uniform
coefficients.

292 rtx-cfd tests green (288 + 4).

Co-Authored-By: Claude Fable 5 <[email protected]>

crates/specialized/rtx-cfd/src/solvers/incompressible/mod.rs

@@ -9,6 +9,8 @@ use crate::{CfdConfig, CfdError, CfdResult};
 // use nalgebra::{DMatrix, DVector};
 // use std::collections::HashMap;
 
+/// ALE solver on a moving tensor-product staggered grid
+pub mod ale;
 /// Boundary conditions
 pub mod boundary_conditions;
 /// Flow field data structures
@@ -25,6 +27,7 @@ pub mod simple;
 pub mod simple_gpu;
 
 // Re-export main types
+pub use ale::{AleField, AleParameters, AlePisoSolver, AleResult, SweptFaceRule};
 pub use boundary_conditions::{
     BoundaryCondition, BoundaryConditions, BoundaryLocation, BoundaryType,
 };