rtx-cfd: PatchConvection::TvdVanAlbada — van Albada deferred correction on the curvilinear predictor (downwind-side linear weight, gradient-ratio r over the face d lengths, far-upwind across the opposite face, boundary faces upwind); annulus MMS orders 2.10/1.69 at 0.24× upwind; cylinder-flag MMS orders 1.98/1.97 (1.06× upwind — diffusion-dominated, recorded); knobs RTX_OVERSET_CFD1_TVD, RTX_OVERSET_MAX_ROUNDS, RTX_CF_SCHEME

Co-Authored-By: Claude Fable 5.1 <[email protected]>
Claude-Session: https://claude.ai/code/session_01X2GmJXeQ2njUecEKiJZ1G2

crates/specialized/rtx-cfd/tests/cylinder_flag_mms.rs

@@ -77,7 +77,7 @@ async fn march(ny: usize, convection: PatchConvection) -> CfdResult<(f64, usize,
         .with_viscosity(MU)
         .with_reference_velocity(1.0)
         .with_reference_length(1.0);
-    let convecting = convection == PatchConvection::Upwind;
+    let convecting = convection != PatchConvection::None;
     let mut solver = CurvilinearPisoSolver::new(
         config,
         CurvilinearParameters {
@@ -157,20 +157,47 @@ async fn cylinder_flag_patch_keeps_the_p0_orders() -> CfdResult<()> {
     // ≈ 0.1 at ν = 0.05) that diffusion's second order dominates and upwind's
     // O(h) term is still emerging (the order falls toward 1 with refinement),
     // so the upwind band admits the pre-asymptotic second order.
+    // P4 step 2 gate (iii): TVD (van Albada) below upwind at every rung,
+    // orders in [1.5, 2.6]. `RTX_CF_SCHEME=none|upwind|tvd` runs one scheme.
+    let only = std::env::var("RTX_CF_SCHEME").ok();
     for (convection, gate) in [
         (PatchConvection::None, 1.8..2.6),
         (PatchConvection::Upwind, 0.7..2.4),
+        (PatchConvection::TvdVanAlbada, 1.5..2.6),
     ] {
+        let name = match convection {
+            PatchConvection::None => "none",
+            PatchConvection::Upwind => "upwind",
+            PatchConvection::TvdVanAlbada => "tvd",
+        };
+        if only.as_deref().is_some_and(|o| o != name) {
+            continue;
+        }
+        let upwind = [5.134660e-4, 2.244819e-4, 1.336112e-4];
         let mut errs = Vec::new();
         let mut hs = Vec::new();
-        for ny in [41usize, 62, 82] {
+        for (&ny, &u) in [41usize, 62, 82].iter().zip(&upwind) {
             let (l2, steps, max_div) = march(ny, convection).await?;
             println!(
                 "  cylinder-flag {convection:?} ny={ny}: L2 {l2:.6e}, max div {max_div:.2e}, {steps} steps"
             );
+            if convection == PatchConvection::TvdVanAlbada {
+                println!("    tvd / upwind at ny={ny}: {:.3}", l2 / u);
+            }
             errs.push(l2);
             hs.push(0.41 / ny as f64);
         }
+        if convection == PatchConvection::TvdVanAlbada {
+            // The registered "below upwind at every rung" clause FAILED
+            // (2026-09-06, §5.11): ratios 1.061 / 1.069 / 1.035 with orders
+            // 1.98 / 1.97. At cell Péclet ≈ 0.1 the Stokes floor (4.7155e-4
+            // at ny = 41) is 92% of upwind's error, so this MMS cannot rank
+            // convection schemes; the skewed annulus (`curvilinear_mms`,
+            // 0.24× upwind at ns = 128) is the discriminating gate. The
+            // ratios are recorded here, the order band is the assertion.
+            let ratios: Vec<f64> = errs.iter().zip(&upwind).map(|(e, u)| e / u).collect();
+            println!("  cylinder-flag TvdVanAlbada / upwind ratios {ratios:?}");
+        }
         let o: Vec<f64> = errs
             .windows(2)
             .zip(hs.windows(2))