embedded3 S2-7b A1: the moving wall's mass flux from the body's true normal at the wall foot (RTX_E3_WALL_FLUX=true, host prototype, device refuses it) — the wall flux of a rotating cylinder 5e-3 → 1e-9 of ΩR h², the rotating wall's cut-cell pressure error 0.33 → 0.11 (n 16) / 0.30 → 0.09 (n 32) of ρ(ΩR)², full cells second order; the rotating wall's offset unchanged (−0.02 h)

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

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

@@ -223,6 +223,7 @@ impl Mask {
             wall_order2_centroid: false,
             wall_exchange_foot: false,
             conv_sides_exact: false,
+            wall_flux_true_normal: false,
             grad_weights: None,
             diffusion_centroid: false,
             face_shifts: None,
@@ -699,6 +700,18 @@ impl Mask {
             (j as f64 + 0.5) * g.dy,
             (k as f64 + 0.5) * g.dz,
         ];
+        // S2-7b A1: the flux through the TRUE surface at the wall foot —
+        // `A_w (u_b · n)` with n the body's own normal into the body.
+        if self.wall_flux_true_normal {
+            let (s, n) = self.interpolant_distance_and_normal(cut, x);
+            let foot = [x[0] - s * n[0], x[1] - s * n[1], x[2] - s * n[2]];
+            let v = body.surface_velocity(foot[0], foot[1], foot[2], t);
+            let eps = 1e-6 * g.dx.min(g.dy).min(g.dz);
+            let (n1, n2, n3) = body.normal(foot[0], foot[1], foot[2], t, eps);
+            let a_w = (w[0] * w[0] + w[1] * w[1] + w[2] * w[2]).sqrt();
+            // `normal` points out of the solid: into the body is its negative.
+            return -a_w * (v.0 * n1 + v.1 * n2 + v.2 * n3);
+        }
         let mut flux = 0.0;
         for (c, wc) in w.iter().enumerate() {
             flux += self.surface_velocity_at(body, x, c, t) * wc;

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

@@ -178,7 +178,9 @@ impl DeviceStep {
             "the order-2 second point at the neighbour's centroid (S2-7) is a host prototype: the device kernels do not carry it"
         );
         assert!(
-            !solver.params.wall_exchange_foot && !solver.params.conv_sides_exact,
+            !solver.params.wall_exchange_foot
+                && !solver.params.conv_sides_exact
+                && !solver.params.wall_flux_true_normal,
             "the axis-foot exchange / exact convective sides (S2-7b) are host prototypes: the device kernels do not carry them"
         );
         assert!(

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

@@ -174,6 +174,13 @@ pub struct Parameters {
     /// faces across, the cell-centre planes along) instead of the averages
     /// of whole-face fluxes. `RTX_E3_CONV_SIDES=exact`; the device refuses it.
     pub conv_sides_exact: bool,
+    /// HOST PROTOTYPE (S2-7b, A1): a moving wall's mass flux from the body's
+    /// TRUE normal at the wall foot, `A_w (u_b · n_true)` (zero for a
+    /// tangentially moving wall), instead of `u_b · W_c` with the
+    /// interpolant's facet vector, which pumps `U_b h/R` through every facet
+    /// of a rotating or flexing wall. `RTX_E3_WALL_FLUX=true`; the device
+    /// refuses it.
+    pub wall_flux_true_normal: bool,
     /// S2-5: the cross-direction diffusion between two faces over the
     /// distance between their OPEN-PART CENTROIDS (a cut face's velocity
     /// is its open part's mean, ½h(1 − α) off the face centre along the
@@ -218,6 +225,7 @@ impl Default for Parameters {
             wall_exchange_axis: std::env::var("RTX_E3_WALL_EXCHANGE").map_or(true, |v| v != "h"),
             wall_exchange_foot: std::env::var("RTX_E3_WALL_EXCHANGE").is_ok_and(|v| v == "axisfoot"),
             conv_sides_exact: std::env::var("RTX_E3_CONV_SIDES").is_ok_and(|v| v == "exact"),
+            wall_flux_true_normal: std::env::var("RTX_E3_WALL_FLUX").is_ok_and(|v| v == "true"),
             pressure_centroid: std::env::var("RTX_E3_PRESSURE_CENTROID").is_ok_and(|v| v == "1"),
             momentum_volume_tiled: std::env::var("RTX_E3_MOMENTUM_VOLUME")
                 .is_ok_and(|v| v == "tiled"),
@@ -366,6 +374,7 @@ impl Solver {
             m.wall_order2_centroid = self.params.wall_order2_centroid;
             m.wall_exchange_foot = self.params.wall_exchange_foot;
             m.conv_sides_exact = self.params.conv_sides_exact;
+            m.wall_flux_true_normal = self.params.wall_flux_true_normal;
             m.diffusion_centroid = self.params.diffusion_centroid;
             if self.params.diffusion_centroid {
                 m.compute_face_shifts();

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

@@ -118,6 +118,7 @@ pub struct Mask {
     /// exchange; the convective sides from the sides' own apertures.
     pub(super) wall_exchange_foot: bool,
     pub(super) conv_sides_exact: bool,
+    pub(super) wall_flux_true_normal: bool,
     /// The centroid prototype's pressure-gradient weights per u / v / w face.
     /// The centroid-distance cross diffusion (S2-5).
     pub(super) diffusion_centroid: bool,
@@ -548,6 +549,7 @@ impl Mask {
             wall_order2_centroid: false,
             wall_exchange_foot: false,
             conv_sides_exact: false,
+            wall_flux_true_normal: false,
             grad_weights: None,
             diffusion_centroid: false,
             face_shifts: None,