embedded3 S2-7b: the curved instrument's per-wall operator probe (curved_operator_probe) and RTX_E3_CURVED_SCHEME; host prototype RTX_E3_WALL_FOOT=centroid (the shear closure's wall velocity at the foot from the open part's CENTROID, not the face centre — on a rotating wall the two feet are ½h(1−α) apart: rigid-mode probe residual 4.5× smaller, the rotating wall's offset −0.022 → ±0.002 h, its cut pressure zeroth → first order); default off, device refuses it

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

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

@@ -224,6 +224,7 @@ impl Mask {
             wall_exchange_foot: false,
             conv_sides_exact: false,
             wall_flux_true_normal: false,
+            wall_foot_centroid: false,
             grad_weights: None,
             diffusion_centroid: false,
             face_shifts: None,

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

@@ -120,12 +120,21 @@ impl Solver {
         let ec = e(c);
         let cell_minus = add(p, ec, -1);
         let cell_plus = p;
-        let ub = mask.surface_velocity_at(body, x, c, t_old);
+        let shift0 = mask.face_shift(c, p);
+        // S2-7b: the wall velocity at the foot from the open part's centroid.
+        let foot_of = |q: [i64; 3], xq: [f64; 3]| -> [f64; 3] {
+            if mask.wall_foot_centroid {
+                let sq = mask.face_shift(c, q);
+                [xq[0] + sq[0], xq[1] + sq[1], xq[2] + sq[2]]
+            } else {
+                xq
+            }
+        };
+        let ub = mask.surface_velocity_at(body, foot_of(p, x), c, t_old);
 
         let mut mass_out = 0.0;
         let mut conv = 0.0;
         let mut diff = 0.0;
-        let shift0 = mask.face_shift(c, p);
         // The implicit exchange with solid neighbour faces (S2-5).
         let (mut wall_implicit, mut wall_rhs) = (0.0, 0.0);
         for d in 0..3 {
@@ -251,7 +260,7 @@ impl Solver {
                     return 0.0;
                 }
                 let cvq = mask.cv_geometry(c, q);
-                let ubq = mask.surface_velocity_at(body, lat.face_position(c, q), c, t_old);
+                let ubq = mask.surface_velocity_at(body, foot_of(q, lat.face_position(c, q)), c, t_old);
                 // Explicit, with a coefficient ∝ 1/d_f: take the gradient from
                 // the faces at least TRANSVERSE_DISTANCE_FLOOR h off the wall —
                 // a FULL neighbour too, over its own distance along the cut

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

@@ -180,7 +180,8 @@ impl DeviceStep {
         assert!(
             !solver.params.wall_exchange_foot
                 && !solver.params.conv_sides_exact
-                && !solver.params.wall_flux_true_normal,
+                && !solver.params.wall_flux_true_normal
+                && !solver.params.wall_foot_centroid,
             "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

@@ -181,6 +181,13 @@ pub struct Parameters {
     /// of a rotating or flexing wall. `RTX_E3_WALL_FLUX=true`; the device
     /// refuses it.
     pub wall_flux_true_normal: bool,
+    /// HOST PROTOTYPE (S2-7b, moving walls): the shear closure's wall velocity
+    /// at the foot of the normal from the face's open-part CENTROID (where
+    /// its value lives) instead of from the face centre — the two feet are
+    /// ½h(1 − α) apart along the wall, an O(Ωh) velocity error over d_f on a
+    /// rotating or flexing wall (zero on a wall at rest or in translation).
+    /// `RTX_E3_WALL_FOOT=centroid`; the device refuses it.
+    pub wall_foot_centroid: 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
@@ -226,6 +233,7 @@ impl Default for Parameters {
             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"),
+            wall_foot_centroid: std::env::var("RTX_E3_WALL_FOOT").is_ok_and(|v| v == "centroid"),
             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"),
@@ -375,6 +383,7 @@ impl Solver {
             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.wall_foot_centroid = self.params.wall_foot_centroid;
             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

@@ -119,6 +119,7 @@ pub struct Mask {
     pub(super) wall_exchange_foot: bool,
     pub(super) conv_sides_exact: bool,
     pub(super) wall_flux_true_normal: bool,
+    pub(super) wall_foot_centroid: 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,
@@ -550,6 +551,7 @@ impl Mask {
             wall_exchange_foot: false,
             conv_sides_exact: false,
             wall_flux_true_normal: false,
+            wall_foot_centroid: false,
             grad_weights: None,
             diffusion_centroid: false,
             face_shifts: None,