embedded3 S2-7b: the moving-wall forms on the device — the ub table at the open part's centroid foot (RTX_E3_WALL_FOOT=centroid, table only), the solid exchange's wall velocity at the axis feet (RTX_E3_WALL_EXCHANGE=axisfoot: per-face six-entry foot table, bit 12 in e3_cut.cu), the true-normal wall flux through the shared host table (RTX_E3_WALL_FLUX=true); refusals lifted (conv sides stay host-only); host = device green on the sphere (varying surface velocity), the cylinder and the moving circle with each knob and all three

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

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

@@ -30,6 +30,7 @@ struct E3Cut {
     double *cell_flux;                  /* scratch per cell */
     const double *s_u, *s_v, *s_w;      /* open-part centroid shifts per face, 3 interleaved (S2-5) */
     const double *vn_u, *vn_v, *vn_w;   /* the wall's normal velocity into the fluid per face (A3-i) */
+    const double *foot_u, *foot_v, *foot_w; /* the wall velocity at the axis feet per face, 6 interleaved (S2-7b: [2d + side]) */
 };
 
 /* f(xi) = xi / (1 - exp(-xi)), f(0) = 1 exactly (closure.rs advancing_factor). */
@@ -206,6 +207,9 @@ __device__ double cut_face_update(const E3Params& g, const E3Ptrs& f, const E3Cu
     int cp[3] = { i, j, k };               /* cell plus */
     const double* ubt = c == 0 ? m.ub_u : (c == 1 ? m.ub_v : m.ub_w);
     double ub = fast ? 0.0 : ubt[fidx];
+    /* bit 12 of wall_order: the solid exchange takes the wall velocity at the axis foot (S2-7b) */
+    const double* ft = c == 0 ? m.foot_u : (c == 1 ? m.foot_v : m.foot_w);
+    const int axis_foot = (g.wall_order & 4096) != 0;
     /* face position */
     double x[3];
     #pragma unroll
@@ -318,7 +322,7 @@ __device__ double cut_face_update(const E3Params& g, const E3Ptrs& f, const E3Cu
                 diff += mu * g_minus * a_d * cut_transverse(g, m, c, d, fidx, f_dn1, qn, -1.0, u0, ub, alpha, wall, distance, dn1, sh, ubt) / dl;
             }
         }
-        if (solid_up) { double kx = mu * g_plus * a_d / delta_x; wall_implicit += kx; wall_rhs += kx * up1; }
+        if (solid_up) { double kx = mu * g_plus * a_d / delta_x; wall_implicit += kx; wall_rhs += kx * (axis_foot ? ft[6 * fidx + 2 * d + 1] : up1); }
         /* fast: dl == h exactly, kx == +0.0 exactly, so the else branch below is (X + 0.0) * (up1 - u0) == X * (up1 - u0) */
         else if (fast && f_up1 >= 0 && centroid) diff += (mu * g_plus * a_d / h[d]) * (up1 - u0);
         else if (f_up1 >= 0 && centroid) {
@@ -330,7 +334,7 @@ __device__ double cut_face_update(const E3Params& g, const E3Ptrs& f, const E3Cu
         }
         else if (f_up1 >= 0) diff += mu * g_plus * a_d * (up1 - u0) / h[d];
         else if (sides[d][1] == SIDE_VELOCITY) diff += mu * g_plus * a_d * (beyond_p - u0) / (0.5 * h[d]);
-        if (solid_dn) { double kx = mu * g_minus * a_d / delta_x; wall_implicit += kx; wall_rhs += kx * dn1; }
+        if (solid_dn) { double kx = mu * g_minus * a_d / delta_x; wall_implicit += kx; wall_rhs += kx * (axis_foot ? ft[6 * fidx + 2 * d] : dn1); }
         else if (fast && f_dn1 >= 0 && centroid) diff -= (mu * g_minus * a_d / h[d]) * (u0 - dn1);
         else if (f_dn1 >= 0 && centroid) {
             double dl = h[d] - (sh[3 * f_dn1 + d] - sh[3 * fidx + d]);