embedded3 S2-6: the transverse gradient from the face at least 0.2 h off the wall (full neighbours over their own distance along the cut partner's normal) — the first form blew up at DFG ny 61 with the fine floor (coefficient ~ 1/d_f); host = device 7.7e-14 with the closures on; Couette linear exactness kept (<= 0.01 h); RTX_E3_OBLIQUE_N rung knob

Co-Authored-By: Claude Fable 5.1 <[email protected]>

crates/specialized/rtx-cfd/src/kernels/cuda/e3_cut.cu

@@ -16,6 +16,7 @@
 #define CUT_INERTIA_FLOOR 0.1
 #define CUT_DISTANCE_FLOOR 0.05
 #define CUT_DISTANCE_FLOOR_FINE 0.01
+#define CUT_TRANSVERSE_FLOOR 0.2
 
 struct E3Cut {
     const double *a_u, *a_v, *a_w;      /* apertures per face */
@@ -121,18 +122,31 @@ __device__ double cut_transverse(const E3Params& g, const E3Cut& m, int c, int d
     if (!any) return 0.0;
     double alpha_q, apm_q[3], app_q[3], wall_q[3], distance_q;
     cut_cv(g, m, c, q[0], q[1], q[2], fq, &alpha_q, apm_q, app_q, wall_q, &distance_q);
+    /* Explicit, coefficient ~ 1/d_f: the gradient from the faces at least
+       CUT_TRANSVERSE_FLOOR h off the wall — a FULL neighbour too, over its own
+       distance along the cut partner's normal; only when neither is that far,
+       from the cut faces over the floored distance (cut_predictor.rs). */
+    double h_min = fmin(fmin(g.dx, g.dy), g.dz);
+    double d_min = CUT_TRANSVERSE_FLOOR * h_min;
+    double a0 = sqrt(wall[0] * wall[0] + wall[1] * wall[1] + wall[2] * wall[2]);
+    double aq = sqrt(wall_q[0] * wall_q[0] + wall_q[1] * wall_q[1] + wall_q[2] * wall_q[2]);
+    int cut0 = a0 > 0.0 && alpha < 1.0, cutq = aq > 0.0 && alpha_q < 1.0;
+    if (!cut0 && !cutq) return 0.0;
+    double n0[3], nq[3];
+    for (int e = 0; e < 3; ++e) { n0[e] = cut0 ? wall[e] / a0 : 0.0; nq[e] = cutq ? wall_q[e] / aq : 0.0; }
+    if (!cut0) for (int e = 0; e < 3; ++e) n0[e] = nq[e];
+    if (!cutq) for (int e = 0; e < 3; ++e) nq[e] = n0[e];
+    int far = distance >= d_min || distance_q >= d_min;
     double gr[3] = { 0.0, 0.0, 0.0 };
     double count = 0.0;
-    double a0 = sqrt(wall[0] * wall[0] + wall[1] * wall[1] + wall[2] * wall[2]);
+    if (!((far && distance < d_min) || (!far && !cut0))) {
-    if (a0 > 0.0 && alpha < 1.0) {
+        double slope = (u0 - ub) / fmax(distance, d_min);
-        double slope = (u0 - ub) / (distance * a0);
+        for (int e = 0; e < 3; ++e) gr[e] -= slope * n0[e];
-        for (int e = 0; e < 3; ++e) gr[e] -= slope * wall[e];
         count += 1.0;
     }
-    double aq = sqrt(wall_q[0] * wall_q[0] + wall_q[1] * wall_q[1] + wall_q[2] * wall_q[2]);
+    if (!((far && distance_q < d_min) || (!far && !cutq))) {
-    if (aq > 0.0 && alpha_q < 1.0) {
+        double slope = (uq - ubt[fq]) / fmax(distance_q, d_min);
-        double slope = (uq - ubt[fq]) / (distance_q * aq);
+        for (int e = 0; e < 3; ++e) gr[e] -= slope * nq[e];
-        for (int e = 0; e < 3; ++e) gr[e] -= slope * wall_q[e];
         count += 1.0;
     }
     if (count == 0.0) return 0.0;

crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/closure.rs

@@ -5,6 +5,10 @@
 use super::cutwall::CvGeometry;
 use super::wall::Mask;
 
+/// The distance floor inside the explicit transverse gradient (S2-6), in
+/// units of the smallest spacing.
+pub(in crate::solvers::incompressible::embedded3) const TRANSVERSE_DISTANCE_FLOOR: f64 = 0.2;
+
 impl Mask {
     /// The shift of a face's open-part centroid from the face centre:
     /// `½h(1 − α)` along the wall normal's in-plane part, away from the

crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/step/cut_predictor.rs

@@ -11,6 +11,8 @@
 //! carries the inertia floor.
 
 use super::{Side, Solver};
+use crate::solvers::incompressible::embedded3::closure::TRANSVERSE_DISTANCE_FLOOR;
+use crate::solvers::incompressible::embedded3::cutwall::CvGeometry;
 use crate::solvers::incompressible::embedded3::cutwall::INERTIA_FLOOR;
 use crate::solvers::incompressible::embedded3::field::Field;
 use crate::solvers::incompressible::simple::ConvectionScheme;
@@ -202,6 +204,7 @@ impl Solver {
             // the own direction); the two-point difference then carries
             // `∇u · Δs_⊥`, removed with the cut faces' own wall-normal
             // gradients `(u − U_b)/d_f` (old values: explicit).
+            let h_min = h[0].min(h[1]).min(h[2]);
             let transverse = |q: [i64; 3], uq: f64, sign: f64| -> f64 {
                 let sq = mask.face_shift(c, q);
                 let mut ds = [0.0; 3];
@@ -215,20 +218,37 @@ impl Solver {
                 }
                 let cvq = mask.cv_geometry(c, q);
                 let ubq = mask.surface_velocity_at(body, lat.face_position(c, q), c, t_old);
-                let mut g = [0.0; 3];
+                // Explicit, with a coefficient ∝ 1/d_f: take the gradient from
-                let mut count = 0.0;
+                // the faces at least TRANSVERSE_DISTANCE_FLOOR h off the wall —
-                for (cvk, uk, ubk) in [(&cv, u0, ub), (&cvq, uq, ubq)] {
+                // a FULL neighbour too, over its own distance along the cut
+                // partner's normal (a linear field gives the same gradient on
+                // every one of them); only when neither is that far, from the
+                // cut faces over the floored distance.
+                let d_min = TRANSVERSE_DISTANCE_FLOOR * h_min;
+                let unit = |cvk: &CvGeometry| {
                     let a = (cvk.wall[0] * cvk.wall[0]
                         + cvk.wall[1] * cvk.wall[1]
                         + cvk.wall[2] * cvk.wall[2])
                         .sqrt();
-                    if a > 0.0 && cvk.alpha < 1.0 {
+                    (a > 0.0 && cvk.alpha < 1.0)
-                        let slope = (uk - ubk) / (cvk.distance * a);
+                        .then(|| [cvk.wall[0] / a, cvk.wall[1] / a, cvk.wall[2] / a])
-                        for e2 in 0..3 {
+                };
-                            g[e2] -= slope * cvk.wall[e2];
+                let (n0, nq) = (unit(&cv), unit(&cvq));
-                        }
+                let faces = [(&cv, u0, ub, n0.or(nq)), (&cvq, uq, ubq, nq.or(n0))];
-                        count += 1.0;
+                let far = faces.iter().any(|f| f.3.is_some() && f.0.distance >= d_min);
+                let mut g = [0.0; 3];
+                let mut count = 0.0;
+                for (cvk, uk, ubk, normal) in faces {
+                    let Some(nk) = normal else { continue };
+                    let is_cut = unit(cvk).is_some();
+                    if far && cvk.distance < d_min || !far && !is_cut {
+                        continue;
                     }
+                    let slope = (uk - ubk) / cvk.distance.max(d_min);
+                    for e2 in 0..3 {
+                        g[e2] -= slope * nk[e2];
+                    }
+                    count += 1.0;
                 }
                 if count == 0.0 {
                     return 0.0;