embedded3 S2-5: the cut wall sat ½(1−α)h inside the body — cross diffusion over the open-part centroid spacing (RTX_E3_DIFFUSION_CENTROID; host + e3_cut.cu, shift tables, point-implicit excess); flat-wall effective-position instrument; DFG 2D-1 ladder tests (device + host); knobs tried and refuted along the way (oblique distance, axis exchange, centroid pressure gradient)

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

crates/specialized/rtx-cfd/tests/embedded3_wall_position.rs

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+//! S2-5 instrument: where does the cut wall sit? Poiseuille flow along z
+//! (periodic, body force `f`) between an EMBEDDED flat wall at `y = y_w`
+//! (cut at a chosen fraction θ of a cell) and the domain's top wall. The
+//! flow rate per unit width is `f (H − y_w)³ / (12 μ)`, so the measured
+//! rate gives the effective wall position `y_eff`; the offset
+//! `(y_eff − y_w)/h` must vanish at second order and is the number the
+//! DFG ladder reads as an effective radius ≈ 0.2 h short.
+use rtx_cfd::solvers::incompressible::ConvectionScheme;
+use rtx_cfd::solvers::incompressible::embedded3::{
+    Body, Boundaries, Field, Fluid, Grid, Parameters, Side, Solver, WallScheme,
+};
+
+const MU: f64 = 0.1;
+const F: f64 = 1.0;
+const HY: f64 = 1.0;
+
+fn offset(ny: usize, theta: f64) -> (f64, Vec<(f64, f64, f64)>) {
+    let h = HY / ny as f64;
+    let (nx, nz) = (3 * ny, 2);
+    let y_w = (ny as f64 / 4.0).floor() * h + theta * h;
+    let exact = move |y: f64| {
+        if y > y_w {
+            F / (2.0 * MU) * (y - y_w) * (HY - y)
+        } else {
+            0.0
+        }
+    };
+    let mut solver = Solver::new(
+        Fluid {
+            density: 1.0,
+            viscosity: MU,
+            reference_velocity: 1.0,
+            reference_length: 1.0,
+        },
+        Parameters {
+            corrector_steps: 2,
+            tolerance: 1e-10,
+            convection_scheme: ConvectionScheme::Upwind,
+            wall_scheme: WallScheme::CutCell,
+            boundaries: Boundaries {
+                z0: Side::Periodic,
+                z1: Side::Periodic,
+                ..Boundaries::default()
+            },
+            ..Parameters::default()
+        },
+    );
+    solver.set_boundary_velocity(move |_x, y, _z, _t| (0.0, 0.0, exact(y)));
+    solver.set_momentum_source(|_, _, _, _| (0.0, 0.0, F));
+    solver.set_body(Body::from_sdf(move |_x, y, _z, _t| y - y_w));
+    let g = Grid::cubic(nx, ny, nz, h);
+    let mut field = Field::new(g);
+    for k in 0..=nz {
+        for j in 0..ny {
+            for i in 0..nx {
+                if k < nz || true {
+                    let idx = g.wface(k.min(nz), j, i);
+                    field.w[idx] = exact((j as f64 + 0.5) * h);
+                }
+            }
+        }
+    }
+    solver.initialize(&mut field);
+    let dt = 0.5 * h * h / (6.0 * MU);
+    let steps = (3.0 / dt).ceil() as usize;
+    for _ in 0..steps {
+        solver.advance(&mut field, dt);
+    }
+    let mask = solver.mask().expect("mask");
+    let i = nx / 2;
+    let mut q = 0.0;
+    let mut profile = Vec::new();
+    for j in 0..ny {
+        let f = g.wface(0, j, i);
+        let a = mask.a_w(f);
+        q += a * field.w[f] * h;
+        let y = (j as f64 + 0.5) * h;
+        if a > 0.0 && profile.len() < 4 {
+            profile.push((a, field.w[f], exact(y)));
+        }
+    }
+    let y_eff = HY - (12.0 * MU * q / F).cbrt();
+    ((y_eff - y_w) / h, profile)
+}
+
+#[test]
+#[ignore = "S2-5 instrument: the cut wall's effective position on a flat wall (a minute on the host)"]
+fn flat_wall_effective_position() {
+    for ny in [16usize, 32] {
+        for theta in [0.05, 0.25, 0.5, 0.75, 0.95] {
+            let (off, profile) = offset(ny, theta);
+            let p: Vec<String> = profile
+                .iter()
+                .map(|(a, w, e)| format!("α {a:.2} w {w:.5} (exact at the face centre {e:.5})"))
+                .collect();
+            println!(
+                "  ny {ny} θ {theta:.2}: effective wall offset {off:+.4} h (positive = the wall sits inside the fluid); first open faces: {}",
+                p.join("; ")
+            );
+        }
+    }
+}