engine: flow-past sample, air past an L-bracket on the floor

file.sample flow-past: air at 25 mm/s past the upright L-bracket in a box of
2.5 mm lattice cells (Re 83), inlet, outlet, a no-slip floor and slip walls;
the fluid step reports the force on each named face. Its test holds the
drag coefficient on the upright's frontal area between 1 and 3.5 (2.3) and
the lattice's mass change under 1 %. No picture: the viewport does not draw
flow results yet (M12).

Part of #164 (its streamlines wait for a flow display in the viewport)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

crates/engine/src/cmd/forms.rs

@@ -809,7 +809,7 @@ pub const RECOVERY_LIST: &[Field] = &[path("dir", "Folder", false).hint("the rec
 pub const RECOVER: &[Field] = &[text("id", "Autosave").req(), path("dir", "Folder", false).hint("the recovery folder")];
 pub const RECOVERY_DISCARD: &[Field] = &[text("id", "Autosave"), flag("all", "All"), path("dir", "Folder", false).hint("the recovery folder")];
 pub const SAMPLE: &[Field] =
-    &[choice("name", "Sample", &[("cantilever", "Cantilever"), ("impact", "Impact"), ("parts", "Parts"), ("drop-test", "Drop test"), ("rubber-seal", "Rubber seal")]).req().def("\"cantilever\"")];
+    &[choice("name", "Sample", &[("cantilever", "Cantilever"), ("impact", "Impact"), ("parts", "Parts"), ("drop-test", "Drop test"), ("rubber-seal", "Rubber seal"), ("flow-past", "Flow past a bracket")]).req().def("\"cantilever\"")];
 pub const COUNT: &[Field] = &[int("count", "Count", 1, 1_000_000).def("1")];
 
 pub const DECK: &[Field] = &[

crates/engine/src/sample.rs

@@ -68,6 +68,13 @@ pub const SAMPLES: &[Sample] = &[
         design: None,
         script: |_| rubber_seal(),
     },
+    Sample {
+        name: "flow-past",
+        label: "Flow Past a Bracket",
+        about: "Air flowing past an L-bracket on the floor: lattice Boltzmann flow and the force on each face",
+        design: Some(UPRIGHT_BRACKET),
+        script: |_| flow_past(),
+    },
 ];
 
 /// The sample called `name`.
@@ -333,6 +340,33 @@ pub fn rubber_seal() -> Value {
     Value::Array(steps)
 }
 
+/// The flow sample's free-stream speed, mm/s.
+pub const FLOW_SPEED: f64 = 25.0;
+/// Air at 20 °C: density (t/mm³) and dynamic viscosity (MPa s).
+const AIR: [f64; 2] = [1.2e-12, 1.8e-11];
+
+/// Air at [`FLOW_SPEED`] past [`UPRIGHT_BRACKET`] standing on the floor, the upright's back face
+/// to the wind: a 240 × 120 × 100 mm box of 2.5 mm cells (184 320), a uniform inlet at x_min, an
+/// outlet at zero pressure at x_max, a no-slip floor and slip walls at the sides and top. Reynolds
+/// number ρ U h / μ = 83 on the upright's 50 mm height: laminar, a steady wake. Step `Flow` (16 s,
+/// about 6.7 flow-throughs; ten frames) reports the force on each named face of the bracket.
+pub fn flow_past() -> Value {
+    let [density, viscosity] = AIR;
+    json!([
+        {"command": "model.units", "params": {"system": "mm-t-s-N-MPa"}},
+        {"command": "model.material.create", "params": {"name": "Air", "density": density, "fluid": {"type": "newtonian", "viscosity": viscosity}}},
+        {"command": "model.fluid_domain.create", "params": {
+            "name": "Wind", "material": "Air", "min": [-60, -40, 0], "max": [180, 80, 100], "spacing": 2.5,
+            "faces": {
+                "x_min": {"type": "velocity", "velocity": [FLOW_SPEED, 0, 0]}, "x_max": {"type": "pressure", "pressure": 0},
+                "y_min": {"type": "slip"}, "y_max": {"type": "slip"}, "z_min": {"type": "wall"}, "z_max": {"type": "slip"}
+            },
+            "obstacles": ["Bracket"], "initial_velocity": [FLOW_SPEED, 0, 0]
+        }},
+        {"command": "model.step.create", "params": {"name": "Flow", "procedure": {"type": "fluid", "domain": "Wind", "end_time": 16, "frames": 10}}},
+    ])
+}
+
 /// Six times the signed volume of the tetrahedron `p[0..4]` (positive when p3 lies on the side
 /// p0 → p1 → p2 turns counter-clockwise around).
 fn signed_volume(p: &[[f64; 3]]) -> f64 {
@@ -448,6 +482,29 @@ mod tests {
         assert!(stiffer > 1.05 && stiffer < 2.5, "bonded {bonded} N, frictionless {free} N");
     }
 
+    #[test]
+    fn the_flow_sample_opens_ready_to_solve() {
+        let s = open("flow-past");
+        assert_eq!(s.model.fluid_domains().len(), 1);
+    }
+
+    /// The drag on the bracket, as a coefficient on the upright's frontal area (40 × 50 mm), is
+    /// that of a bluff plate standing on a wall at a Reynolds number of 83, raised by the 17 %
+    /// blockage of the box: between 1 and 3.5 (a flat plate broadside to the flow is about 1.2 at
+    /// high Reynolds number and rises as it falls). The lattice conserves mass.
+    #[test]
+    #[ignore = "heavy: cargo xtask test --heavy (CI heavy job)"]
+    fn the_flow_past_the_bracket_has_a_bluff_body_drag() {
+        let mut s = open("flow-past");
+        let r = s.execute("solve.run", &json!({})).unwrap();
+        let r = &r["steps"][0]["summary"];
+        let drag: f64 = r["forces"].as_array().unwrap().iter().filter(|f| f["body"] == "Bracket").map(|f| f["mean"][0].as_f64().unwrap()).sum();
+        let [density, _] = AIR;
+        let cd = drag / (0.5 * density * FLOW_SPEED * FLOW_SPEED * 40.0 * 50.0);
+        assert!(cd > 1.0 && cd < 3.5, "Cd {cd}: {r}");
+        assert!(r["mass"]["relative_change"].as_f64().unwrap().abs() < 0.01, "{r}");
+    }
+
     #[test]
     fn the_drop_test_opens_ready_to_solve() {
         let s = open("drop-test");

docs/examples.md

@@ -46,3 +46,24 @@ P = 2 (λ − λ⁻²)(C10 + C01/λ) per original area: 3 430 N against 3 466 N
 the bulge makes it stiffer (shape factor 0.5): 6 518 N, held between 1.05 and 2.5 times the
 frictionless force. The groove and the plates are prescribed displacements today; with implicit
 contact (#161) the ring will be pressed by contact against a groove.
+
+## Flow past a bracket (`flow-past`)
+
+Air (ρ = 1.2 kg/m³, μ = 1.8 × 10⁻⁵ Pa s) at 25 mm/s past the same L-bracket standing on the
+floor, the upright's back to the wind. A 240 × 120 × 100 mm box of 2.5 mm cells (184 320),
+uniform inlet, outlet at zero pressure, a no-slip floor and slip walls at the sides and top;
+D3Q19 lattice Boltzmann (TRT) for 16 s, about 6.7 flow-throughs, ten frames. Reynolds number
+83 on the upright's 50 mm height: laminar, a steady wake. About 10 s.
+
+**Look at:** the step's report (`solve.fluid`, or Results after Solve): the force on every
+named face of the bracket and on each side of the box, final and time-averaged, and the mass
+history; `solve.probe` with `points` gives the velocity and pressure in any cell, and with
+`forces` each face's force history.
+
+**Check:** the drag on the bracket, as a coefficient on the upright's frontal area
+(40 × 50 mm), is 2.3 — a bluff plate standing on a wall at low Reynolds number in a box it
+blocks by 17 %, held between 1 and 3.5 (a flat plate broadside to the flow is about 1.2 at high
+Reynolds number and rises as it falls); the lattice's mass changes by less than 1 %.
+
+There is no picture yet: the viewport does not draw flow results (velocity slices and
+streamlines are planned in M12), so this example is numbers only for now.