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/solvers/incompressible/embedded3/step/cut_predictor.rs

@@ -226,7 +226,10 @@ impl Solver {
         });
         let a_w =
             (cv.wall[0] * cv.wall[0] + cv.wall[1] * cv.wall[1] + cv.wall[2] * cv.wall[2]).sqrt();
-        let shear = mu * a_w / cv.distance;
+        let (c1, c2, nb) = mask.wall_gradient(c, p, &cv);
+        let shear = mu * a_w * c1;
+        // The explicit part of the quadratic wall gradient (order 2).
+        let shear_explicit = nb.map_or(0.0, |f| mu * a_w * c2 * (old[c][f] - ub));
         let fraction = if self.params.momentum_volume_cell_mean {
             let vol = |q: [i64; 3]| lat.cell(q).map_or(cv.alpha, |ci| mask.vol(ci));
             0.5 * (vol(cell_minus) + vol(cell_plus))
@@ -235,8 +238,8 @@ impl Solver {
         };
         let v_eff = fraction.max(INERTIA_FLOOR) * h[c] * area[c];
         let inertia = rho * v_eff / dt;
-        let u_star =
-            (inertia * u0 - conv + diff + pressure + source + shear * ub) / (inertia + shear);
+        let u_star = (inertia * u0 - conv + diff + pressure + source + shear * ub - shear_explicit)
+            / (inertia + shear);
         let v_alpha = fraction * h[c] * area[c];
         (u_star, rho * (v_eff - v_alpha) * (u_star - u0) / dt)
     }

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

@@ -78,7 +78,7 @@ struct E3Params {
     bz0: i32,
     bz1: i32,
     scheme: i32,
-    pad: i32,
+    wall_order: i32,
     dx: f64,
     dy: f64,
     dz: f64,
@@ -284,7 +284,7 @@ impl DeviceStep {
             bz0: side_code(b.z0),
             bz1: side_code(b.z1),
             scheme: scheme_code(self.solver.params.convection_scheme),
-            pad: 0,
+            wall_order: i32::from(self.solver.params.wall_order),
             dx: g.dx,
             dy: g.dy,
             dz: g.dz,

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

@@ -91,6 +91,11 @@ pub struct Parameters {
     /// inertia of the fluid half of its volume instead of a tenth of a
     /// cell against O(1) fluxes).
     pub momentum_volume_cell_mean: bool,
+    /// The cut wall's shear closure: 1 = one-point `μ A_w (u_f − U_b)/d_f`
+    /// (the recorded form), 2 = the quadratic wall gradient through the
+    /// next open face along the wall normal's dominant axis (S2-4).
+    /// `Parameters::default()` reads `RTX_E3_WALL_ORDER` (default 1).
+    pub wall_order: u8,
 }
 
 impl Default for Parameters {
@@ -107,6 +112,10 @@ impl Default for Parameters {
             max_surface_speed: None,
             aperture_substeps: 0,
             momentum_volume_cell_mean: false,
+            wall_order: std::env::var("RTX_E3_WALL_ORDER")
+                .ok()
+                .and_then(|v| v.parse().ok())
+                .unwrap_or(1),
         }
     }
 }
@@ -231,6 +240,7 @@ impl Solver {
         .map(|mut m| {
             m.scheme = self.params.convection_scheme;
             m.density = self.fluid.density;
+            m.wall_order = self.params.wall_order;
             m
         })
         .expect("embedded mask")