embedded3 flag wake: RTX_E3_FLAG_DEPTH — the duct's z extent as a knob (default H); the inflow paraboloid, the flag's centring and the full/free tag follow it (the wide-duct exploration: the benchmark-span flag with free ends in a 0.82 m duct)

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

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

@@ -212,21 +212,29 @@ fn flag_2d_analytic(x: f64, y: f64, t: f64) -> (f64, f64) {
     (best - FLAG_HALF, v_best)
 }
 
-/// The flag's span: `RTX_E3_FLAG_SPAN` (default 0.2); at the channel's
+/// The flag's span: `RTX_E3_FLAG_SPAN` (default 0.2); at the duct's
-/// full width the flag is the 2D geometry extruded (S2-3b).
+/// full depth the flag is the 2D geometry extruded (S2-3b).
 fn flag_span() -> f64 {
     env_f("RTX_E3_FLAG_SPAN", FLAG_SPAN)
 }
 
+/// The duct's depth (the z extent): `RTX_E3_FLAG_DEPTH` (default H, the
+/// square duct). A wider duct than the flag's span (2026-09-22, the
+/// "wide span" exploration) puts a finite-span plate in free flow between
+/// the side walls — not the benchmark's geometry.
+fn duct_depth() -> f64 {
+    env_f("RTX_E3_FLAG_DEPTH", H)
+}
+
 /// The flag in 3D: the extruded capsule cut to the span with edges
 /// rounded to radius `r` (no cut at the full width).
 fn flag_3d(x: f64, y: f64, z: f64, t: f64, r: f64) -> (f64, (f64, f64)) {
     let (d2, v) = flag_2d(x, y, t);
     let span = flag_span();
-    if span >= H {
+    if span >= duct_depth() {
         return (d2, v);
     }
-    let zc = 0.5 * H;
+    let zc = 0.5 * duct_depth();
     let q1 = d2 + r;
     let q2 = (z - zc).abs() - 0.5 * span + r;
     let outside = (q1.max(0.0).powi(2) + q2.max(0.0).powi(2)).sqrt();
@@ -234,7 +242,8 @@ fn flag_3d(x: f64, y: f64, z: f64, t: f64, r: f64) -> (f64, (f64, f64)) {
 }
 
 fn inflow(y: f64, z: f64) -> f64 {
-    16.0 * U_M * y * z * (H - y) * (H - z) / (H * H * H * H)
+    let d = duct_depth();
+    16.0 * U_M * y * z * (H - y) * (d - z) / (H * H * d * d)
 }
 
 #[test]
@@ -247,7 +256,11 @@ fn flag_wake_on_the_device() {
     // `RTX_E3_FLAG_NZ=4`: a thin slab periodic in z with the 2D inflow (Ū = 1) — the
     // flag as a 2D problem, minutes per rung: the instrument for the load routes' parts.
     let slab_nz = env_f("RTX_E3_FLAG_NZ", 0.0) as usize;
-    let nz = if slab_nz > 0 { slab_nz } else { ny };
+    let nz = if slab_nz > 0 {
+        slab_nz
+    } else {
+        (duct_depth() / h).round() as usize
+    };
     // S2-9b: the 3D run with the slab's 2D inflow (uniform in z) and/or slip
     // side walls — the decomposition of the 3D-over-slab drag.
     let inflow_2d = std::env::var("RTX_E3_FLAG_INFLOW").is_ok_and(|v| v == "2d");
@@ -491,7 +504,7 @@ fn flag_wake_on_the_device() {
                 }
             }
             if phase_due {
-                let tag = if flag_span() >= H { "full" } else { "free" };
+                let tag = if flag_span() >= duct_depth() { "full" } else { "free" };
                 let path = std::path::Path::new(vtk_dir.as_ref().unwrap())
                     .join(format!("flag_{tag}_ny{ny}_phase{next_phase:02}.vtk"));
                 write_vtk(&path, &field, Some(mask)).expect("vtk");