embedded3 S2-4: quadratic wall gradient behind Parameters::wall_order (host predictor, operator route, e3_cut.cu; RTX_E3_WALL_ORDER); density pin holds at order 2

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

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

@@ -187,10 +187,28 @@ __device__ double cut_face_update(const E3Params& g, const E3Ptrs& f, const E3Cu
     const double* src = c == 0 ? f.su : (c == 1 ? f.sv : f.sw);
     double source = src[fidx] * v_u;
     double a_w = sqrt(wall[0] * wall[0] + wall[1] * wall[1] + wall[2] * wall[2]);
-    double shear = mu * a_w / distance;
+    /* The wall gradient: one-point (order 1) or quadratic through the next
+       open face away from the body along the wall normal's dominant axis
+       (order 2; the neighbour's old value explicit). */
+    double c1 = 1.0 / distance, shear_explicit = 0.0;
+    if (g.wall_order >= 2 && a_w > 0.0) {
+        double nw[3] = { wall[0] / a_w, wall[1] / a_w, wall[2] / a_w };
+        int d = 0;
+        for (int kk = 1; kk < 3; ++kk) if (fabs(nw[kk]) > fabs(nw[d])) d = kk;
+        int q[3] = { i, j, k };
+        q[d] -= nw[d] > 0.0 ? 1 : -1;
+        int fn = cut_face(g, c, q[0], q[1], q[2]);
+        if (fn >= 0 && cut_ap(m, c)[fn] > 0.0) {
+            double d1 = distance, d2 = d1 + h[d] * fabs(nw[d]);
+            c1 = d2 / (d1 * (d2 - d1));
+            double c2 = -d1 / (d2 * (d2 - d1));
+            shear_explicit = mu * a_w * c2 * (old_c[fn] - ub);
+        }
+    }
+    double shear = mu * a_w * c1;
     double v_eff = fmax(alpha, CUT_INERTIA_FLOOR) * h[c] * area[c];
     double inertia = rho * v_eff / g.dt;
-    return (inertia * u0 - conv + diff + pressure + source + shear * ub) / (inertia + shear);
+    return (inertia * u0 - conv + diff + pressure + source + shear * ub - shear_explicit) / (inertia + shear);
 }
 
 /* The predictor on the open interior faces of component c. */