S2-9: the flag on the recorded FSI2 kinematics — fsi2_overset_dump_centreline (rtx-fsi) exports the saved instants' wetted-node d/ḋ as a centreline per knot (clamp + 70 columns); tests/embedded3_flag_kinematics (cubic Hermite through the knots with their velocities, t = 0 at RTX_E3_FLAG_KIN_T0, a 0.5 s ramp from the undeflected line, arc-length interpolation along the stations) drives both the 3D/slab flag (RTX_E3_FLAG_KINEMATICS, both in-plane surface-velocity components, the record's period) and the 2D reference; the analytic paths unchanged (same tuples)

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

crates/specialized/rtx-fsi/tests/turek_hron_fsi2_overset.rs

@@ -649,3 +649,71 @@ fn fsi2_overset_prescribed_motion() {
         mean(&|w| w.3[2])
     );
 }
+
+/// S2-9: the recorded FSI2 kinematics as a CENTRELINE per instant for the
+/// 3D flag (`RTX_FSI2O_REPLAY=dir`, `RTX_FSI2O_NY`, `RTX_FSI2O_CENTRELINE_CSV=out`):
+/// per knot, t and per station (the clamp, then each bottom/top column
+/// root → tip) the deformed midpoint (x, y) and its velocity (vx, vy).
+#[test]
+#[ignore = "S2-9 export: needs RTX_FSI2O_REPLAY (the saved instants)"]
+fn fsi2_overset_dump_centreline() {
+    use fsi2_harness::overset::OversetFluid;
+    use fsi2_harness::replay::Replay;
+    use std::io::Write as _;
+    let Ok(replay_dir) = std::env::var("RTX_FSI2O_REPLAY") else {
+        println!("  RTX_FSI2O_REPLAY unset");
+        return;
+    };
+    let out = std::env::var("RTX_FSI2O_CENTRELINE_CSV").expect("RTX_FSI2O_CENTRELINE_CSV");
+    let ny: usize = std::env::var("RTX_FSI2O_NY").ok().and_then(|v| v.parse().ok()).unwrap_or(62);
+    let case = case_from_env("FSI2O", FSI2);
+    let fluid = OversetFluid::build_case(case, ny, 35, 100, 3).expect("overset fluid");
+    let itf = &fluid.interface;
+    let replay = Replay::load(&replay_dir);
+    let n = 2 * itf.wetted.len();
+    assert_eq!(replay.d[0].len(), n, "the instants' d does not match this interface");
+    // Columns root → tip: bottom is root → tip, top is tip → root.
+    let cols: Vec<(usize, usize)> = itf
+        .bottom
+        .iter()
+        .copied()
+        .zip(itf.top.iter().rev().copied())
+        .collect();
+    for &(b, t) in &cols {
+        assert!((itf.reference[b].0 - itf.reference[t].0).abs() < 1e-9, "bottom / top columns disagree");
+    }
+    let mut f = std::fs::File::create(&out).expect("csv");
+    write!(f, "t").unwrap();
+    for i in 0..=cols.len() {
+        write!(f, ",x{i},y{i},vx{i},vy{i}").unwrap();
+    }
+    writeln!(f).unwrap();
+    let clamp = (fsi2_harness::FLAG_X0, 0.5 * (fsi2_harness::FLAG_Y0 + fsi2_harness::FLAG_Y1));
+    for (k, &tk) in replay.times.iter().enumerate() {
+        let (d, dd) = (&replay.d[k], &replay.dd[k]);
+        write!(f, "{tk:.6}").unwrap();
+        write!(f, ",{:.9},{:.9},0,0", clamp.0, clamp.1).unwrap();
+        for &(b, t) in &cols {
+            let (xb, yb) = (itf.reference[b].0 + d[2 * b], itf.reference[b].1 + d[2 * b + 1]);
+            let (xt, yt) = (itf.reference[t].0 + d[2 * t], itf.reference[t].1 + d[2 * t + 1]);
+            let (vxb, vyb, vxt, vyt) = (dd[2 * b], dd[2 * b + 1], dd[2 * t], dd[2 * t + 1]);
+            write!(
+                f,
+                ",{:.9},{:.9},{:.9},{:.9}",
+                0.5 * (xb + xt),
+                0.5 * (yb + yt),
+                0.5 * (vxb + vxt),
+                0.5 * (vyb + vyt)
+            )
+            .unwrap();
+        }
+        writeln!(f).unwrap();
+    }
+    println!(
+        "  centreline: {} instants over [{:.4}, {:.4}] s, {} stations → {out}",
+        replay.times.len(),
+        replay.times[0],
+        replay.times.last().unwrap(),
+        cols.len() + 1
+    );
+}