R2-b/R3: embedded3_added_mass (the cut-cell added-mass pin, the overset instrument's parameters: n 64/128 C_m 1.087/1.127 vs the confined potential-flow 1.071 + Stokes 0.064 = 1.135, the overset's 1.097/1.127); flag tests: the capsule's tip inset (RTX_E3_FLAG_TIP_INSET, default FLAG_HALF — the apex ON the benchmark's tip A; every earlier record had it 10 mm beyond, =0 restores), root fillet knob RTX_E3_FLAG_FILLET (5 mm: no effect), the tip CSV column = the record's tip in recorded mode

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

crates/specialized/rtx-cfd/tests/embedded3_flag_wake.rs

@@ -80,6 +80,45 @@ fn amplitude() -> f64 {
     env_f("RTX_E3_FLAG_AMP", AMP)
 }
 
+/// R3: the root fillet radius (`RTX_E3_FLAG_FILLET`, metres; 0 = the sharp
+/// concave corner of the plain union; the overset outline carries 5 mm).
+fn root_fillet() -> f64 {
+    env_f("RTX_E3_FLAG_FILLET", 0.0)
+}
+
+/// R3 (2026-09-21): the capsule's tip inset (`RTX_E3_FLAG_TIP_INSET`,
+/// metres, default `FLAG_HALF`): the centreline polyline is shortened by
+/// this much along its last segment so the capsule's apex sits ON the
+/// benchmark's tip A (the overset outline's semicircle apex). Every flag
+/// record before this date had the apex 10 mm beyond A (`=0` restores
+/// them): at ny 62 on the recorded motion that was drag 253.3 → 240.0 and
+/// the lift swing 1,005 → 836 (the overset's 867).
+fn tip_inset() -> f64 {
+    env_f("RTX_E3_FLAG_TIP_INSET", FLAG_HALF)
+}
+
+/// Smooth union with a concave fillet of radius `r` (the plain `min` at r = 0).
+fn fillet_union(d1: f64, d2: f64, r: f64) -> f64 {
+    if r > 0.0 && d1 < r && d2 < r {
+        r - ((r - d1).powi(2) + (r - d2).powi(2)).sqrt()
+    } else {
+        d1.min(d2)
+    }
+}
+
+/// Pull the polyline's last point back by `inset` along its last segment.
+fn inset_last(pts: &mut [(f64, f64, f64, f64)], inset: f64) {
+    if inset <= 0.0 || pts.len() < 2 {
+        return;
+    }
+    let n = pts.len();
+    let (ax, ay, _, _) = pts[n - 2];
+    let (bx, by, bvx, bvy) = pts[n - 1];
+    let len = ((bx - ax).powi(2) + (by - ay).powi(2)).sqrt();
+    let f = (1.0 - inset / len).max(0.0);
+    pts[n - 1] = (ax + f * (bx - ax), ay + f * (by - ay), bvx, bvy);
+}
+
 /// Signed distance to the deflected flag's cross-section (a capsule
 /// around the centreline polyline of `n` segments) and the centreline's
 /// velocity at the closest point (transverse only in the analytic mode).
@@ -101,6 +140,7 @@ fn flag_2d_recorded(rec: &Recorded, x: f64, y: f64, t: f64) -> (f64, (f64, f64))
         let mut c = cell.borrow_mut();
         if c.0.to_bits() != t.to_bits() {
             c.1 = rec.at(t, CY);
+            inset_last(&mut c.1, tip_inset());
             c.0 = t;
         }
         let pts = &c.1;
@@ -141,6 +181,14 @@ fn flag_2d_analytic(x: f64, y: f64, t: f64) -> (f64, f64) {
                 let (d, v) = deflection(s, t);
                 *p = (FLAG_X0 + s * FLAG_LEN, CY + d, v);
             }
+            let inset = tip_inset();
+            if inset > 0.0 {
+                let (ax, ay, _) = c.1[N - 1];
+                let (bx, by, bv) = c.1[N];
+                let len = ((bx - ax).powi(2) + (by - ay).powi(2)).sqrt();
+                let f = (1.0 - inset / len).max(0.0);
+                c.1[N] = (ax + f * (bx - ax), ay + f * (by - ay), bv);
+            }
             c.0 = t;
         }
         c.1
@@ -273,7 +321,10 @@ fn flag_wake_on_the_device() {
         }
     });
     let cyl = move |x: f64, y: f64| ((x - CX).powi(2) + (y - CY).powi(2)).sqrt() - R_CYL;
-    let body = Body::from_sdf(move |x, y, z, t| cyl(x, y).min(flag_3d(x, y, z, t, r_edge).0))
+    let r_fillet = root_fillet();
+    let body = Body::from_sdf(move |x, y, z, t| {
+        fillet_union(cyl(x, y), flag_3d(x, y, z, t, r_edge).0, r_fillet)
+    })
         .with_surface_velocity(move |x, y, z, t| {
             let (df, (vx, vy)) = flag_3d(x, y, z, t, r_edge);
             if df <= cyl(x, y) {
@@ -295,7 +346,7 @@ fn flag_wake_on_the_device() {
     }
     solver.initialize(&mut field);
     println!(
-        "  flag wake ny {ny} (span {}; inflow {}, z sides {}): {nx}×{ny}×{nz} = {} cells, h {h:.4e}, dt {dt:.3e}, {periods} periods = {t_end:.3} s, {} steps",
+        "  flag wake ny {ny} (span {}; inflow {}, z sides {}; root fillet {:.4} m, tip inset {:.4} m): {nx}×{ny}×{nz} = {} cells, h {h:.4e}, dt {dt:.3e}, {periods} periods = {t_end:.3} s, {} steps",
         flag_span(),
         if slab_nz > 0 || inflow_2d { "2d" } else { "3d" },
         if slab_nz > 0 {
@@ -305,6 +356,8 @@ fn flag_wake_on_the_device() {
         } else {
             "wall"
         },
+        root_fillet(),
+        tip_inset(),
         g.cells(),
         (t_end / dt).ceil() as usize
     );
@@ -368,7 +421,13 @@ fn flag_wake_on_the_device() {
             let ft = mask
                 .cut_wall_force(body, &field, RHO * NU, t)
                 .expect("wall");
-            let tip = deflection(1.0, t).0;
+            // The tip's transverse deflection: the record's last station in
+            // recorded mode (until 2026-09-21 this column held the analytic
+            // first mode even then — R2's fits use the record directly).
+            let tip = match recorded() {
+                Some(rec) => rec.at(t, CY).last().map_or(0.0, |p| p.1 - CY),
+                None => deflection(1.0, t).0,
+            };
             if sample {
                 println!(
                     "  t {t:7.4} (tip {tip:+.4}): drag/span {:.1} lift/span {:+.1} N/m (reconstructed {:.1} {:+.1}); total {:.3} {:+.3} N; residual {:.1e} CG {} fresh {}; [{:.0} s]",