rtx-cfd: solver_metric_force carries the scheme's limited face correction with the predictor's far-upwind choice, so the flux form is the solver's under TVD too (CFD2 ny = 41: three boxes spread 1.8 N/m → 5e-13; the upwind-only form read 120.2 for a solver box of 126.0)

Co-Authored-By: Claude Fable 5.1 <[email protected]>
Claude-Session: https://claude.ai/code/session_0116sg1Qz1gMv9hdcKP1XUam

crates/specialized/rtx-cfd/src/solvers/incompressible/overset/residual.rs

@@ -385,7 +385,8 @@ impl OversetPisoSolver {
 impl OversetPisoSolver {
     /// The force on everything inside the box `(i0, i1, j0, j1)` (cell
     /// index bounds, as `EmbeddedMask::control_volume_force`) in the
-    /// SOLVER'S OWN flux form: the predictor's upwind convective flux,
+    /// SOLVER'S OWN flux form: the predictor's convective flux (upwind
+    /// plus the scheme's limited correction),
     /// its diffusive flux and the cell pressure, on the momentum control
     /// volumes' faces that make up the box boundary (u volumes `i0 + 1
     /// ..= i1` × `j0 .. j1`, v volumes `i0 .. i1` × `j0 + 1 ..= j1`),
@@ -409,29 +410,65 @@ impl OversetPisoSolver {
         let mu = self.background.config().viscosity;
         let bg = &field.background;
         let (u, v, p) = (&bg.u_old, &bg.v_old, &bg.p);
-        let upwind = |f: f64, up: f64, down: f64| if f >= 0.0 { up } else { down };
+        // The predictor's face value: upwind plus the scheme's limited
+        // correction with the same far-upwind choice (`u_rhs`), so the
+        // flux form is the solver's under upwind AND under TVD.
+        let scheme = self.background.parameters().convection_scheme;
+        let face = |f: f64, far_up: Option<f64>, up: f64, down: f64, far_dn: Option<f64>| {
+            if f >= 0.0 {
+                up + scheme.face_correction(far_up, up, down)
+            } else {
+                down + scheme.face_correction(far_dn, down, up)
+            }
+        };
         // Outward x-momentum flux through the u-volume face at cell i's
         // centre (n = +x), per unit length.
         let phi_u_x = |j: usize, i: usize| {
             let ue = 0.5 * (u[(j, i)] + u[(j, i + 1)]);
-            rho * ue * upwind(ue, u[(j, i)], u[(j, i + 1)]) - mu * (u[(j, i + 1)] - u[(j, i)]) / dx
+            let uf = face(
-                + p[(j, i)]
+                ue,
+                (i >= 1).then(|| u[(j, i - 1)]),
+                u[(j, i)],
+                u[(j, i + 1)],
+                (i + 2 <= nx).then(|| u[(j, i + 2)]),
+            );
+            rho * ue * uf - mu * (u[(j, i + 1)] - u[(j, i)]) / dx + p[(j, i)]
         };
         // Through the u-volume face at v-face row j (n = +y), for u face i.
         let phi_u_y = |j: usize, i: usize| {
             let vn = 0.5 * (v[(j, i - 1)] + v[(j, i)]);
-            rho * vn * upwind(vn, u[(j - 1, i)], u[(j, i)]) - mu * (u[(j, i)] - u[(j - 1, i)]) / dy
+            let uf = face(
+                vn,
+                (j >= 2).then(|| u[(j - 2, i)]),
+                u[(j - 1, i)],
+                u[(j, i)],
+                (j + 1 < ny).then(|| u[(j + 1, i)]),
+            );
+            rho * vn * uf - mu * (u[(j, i)] - u[(j - 1, i)]) / dy
         };
         // y-momentum: through the v-volume face at cell j's centre (n = +y).
         let phi_v_y = |j: usize, i: usize| {
             let vn = 0.5 * (v[(j, i)] + v[(j + 1, i)]);
-            rho * vn * upwind(vn, v[(j, i)], v[(j + 1, i)]) - mu * (v[(j + 1, i)] - v[(j, i)]) / dy
+            let vf = face(
-                + p[(j, i)]
+                vn,
+                (j >= 1).then(|| v[(j - 1, i)]),
+                v[(j, i)],
+                v[(j + 1, i)],
+                (j + 2 <= ny).then(|| v[(j + 2, i)]),
+            );
+            rho * vn * vf - mu * (v[(j + 1, i)] - v[(j, i)]) / dy + p[(j, i)]
         };
         // Through the v-volume face at u-face column i (n = +x), for v face j.
         let phi_v_x = |j: usize, i: usize| {
             let ue = 0.5 * (u[(j - 1, i)] + u[(j, i)]);
-            rho * ue * upwind(ue, v[(j, i - 1)], v[(j, i)]) - mu * (v[(j, i)] - v[(j, i - 1)]) / dx
+            let vf = face(
+                ue,
+                (i >= 2).then(|| v[(j, i - 2)]),
+                v[(j, i - 1)],
+                v[(j, i)],
+                (i + 1 < nx).then(|| v[(j, i + 1)]),
+            );
+            rho * ue * vf - mu * (v[(j, i)] - v[(j, i - 1)]) / dx
         };
         let vol = dx * dy;
         let (mut out_x, mut out_y) = (0.0, 0.0);