rtx-cfd: second-order convection by deferred-correction TVD; MMS order 1.84, cavity closes on Ghia
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First-order upwind's O(h) numerical viscosity was the measured limit on the
whole discretisation: MMS order ~0.9 at Re = 20 against 2.05 in the Stokes
limit. This adds a ConvectionScheme parameter to SimPLE — Upwind (default,
behaviour unchanged), TvdVanAlbada, TvdVanLeer — implemented by deferred
correction: the upwind operator stays implicit, so a_p = sum(a_nb) and
diagonal dominance survive unconditionally, and the limited
high-order-minus-upwind flux difference enters the source explicitly at the
current iterate. At a fixed point the two agree, so the converged answer is
the TVD discretisation. Faces whose far-upwind node lies outside the domain
fall back to pure upwind; wall faces pass no mass, so no correction enters.
Measured by the manufactured solution (van Albada, 16 -> 32 -> 64):
L2 velocity 1.325e-3 4.406e-4 1.232e-4 orders 1.59, 1.84
(upwind) 3.516e-2 1.954e-2 1.038e-2 orders 0.85, 0.91
The error is 27x to 84x below upwind's at equal resolution, the order climbs
toward 2 (the shortfall is limiter clipping plus the boundary fallback, both
of which shrink with h), the pressure error falls at the same rate, and
continuity still holds to solver tolerance in every cell.
On the Re = 100 lid-driven cavity at 65^2 the centreline minimum moves from
-0.1932 (upwind) to -0.2036 against Ghia's -0.2109 — 59% of the remaining
gap closed at equal resolution, converged in 790 iterations — and the vortex
position moves from 0.5000 to 0.4844 toward Ghia's 0.4531. Both new cavity
bounds exclude the upwind values, so falling back to first order fails them.
284 tests, 0 failing.
Co-Authored-By: Claude Fable 5 <[email protected]>
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co-authored by
Claude Fable 5
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@@ -32,7 +32,7 @@ pub use flow_field::FlowField;
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pub use piso::{PisoParameters, PisoResult, PisoSolver};
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#[cfg(feature = "cuda")]
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pub use piso_gpu::PisoGpuSolver;
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pub use simple::{SimpleParameters, SimpleResult, SimpleSolver};
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pub use simple::{ConvectionScheme, SimpleParameters, SimpleResult, SimpleSolver};
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#[cfg(feature = "cuda")]
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pub use simple_gpu::SimpleGpuSolver;
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