rtx-cfd embedded3 item 9: wall.rs (binary ghost mask: three face families, trilinear stencil with periodic-z wrap, z-weighted least-squares ghost fit, flux compatibility correction; slip walls allowed as touched sides) + loads.rs (surface-stress route with probes, control-volume route with full-span z faces skipped); the step wired (body/mask, predicates, anchor, ghost re-imposition). Gates HELD: CFD1 ny 41 nz 1 CV 15.6156 / surface 15.7126 both to 1e-6 of the 2D record; nz 4 periodic CV 1.1e-6 / surface 4.2e-4; sphere MMS order 0.89, div 1e-8, ghost correction 1.0e-4 → 2.0e-5, both load routes' errors falling (0.153 → 0.115 surface, 0.214 → 0.139 CV)

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

crates/specialized/rtx-cfd/tests/embedded3_embedded_mms.rs

@@ -0,0 +1,301 @@
+//! embedded3 gate 9a: the manufactured solution with an embedded sphere
+//! (centre (0.6, 0.45, 0.5), r 0.2, off-centre so the exact force is not
+//! zero by symmetry) carrying the exact field as its surface velocity, on
+//! the binary ghost wall. The velocity error falls at the scheme's order,
+//! every fluid cell is divergence-free, the compatibility correction
+//! shrinks, and both load routes converge to the exact surface integral of
+//! the manufactured stress (the control-volume route measures F − M with M
+//! the momentum flux through the porous manufactured surface).
+
+use rtx_cfd::solvers::incompressible::ConvectionScheme;
+use rtx_cfd::solvers::incompressible::embedded3::{Body, Field, Fluid, Grid, Parameters, Solver};
+use std::f64::consts::PI;
+
+const RHO: f64 = 1.0;
+const MU: f64 = 0.05;
+const C: (f64, f64, f64) = (0.6, 0.45, 0.5);
+const R: f64 = 0.2;
+
+fn u3(x: f64, y: f64, z: f64) -> f64 {
+    (PI * x).sin() * (PI * y).cos() * (PI * z).cos()
+}
+fn v3(x: f64, y: f64, z: f64) -> f64 {
+    (PI * x).cos() * (PI * y).sin() * (PI * z).cos()
+}
+fn w3(x: f64, y: f64, z: f64) -> f64 {
+    -2.0 * (PI * x).cos() * (PI * y).cos() * (PI * z).sin()
+}
+fn p3(x: f64, y: f64, z: f64) -> f64 {
+    (PI * x).sin() * (PI * y).sin() * (PI * z).sin()
+}
+/// The velocity gradient ∂u_i/∂x_j and the pressure gradient.
+fn grads(x: f64, y: f64, z: f64) -> ([[f64; 3]; 3], [f64; 3]) {
+    let (sx, cx) = (PI * x).sin_cos();
+    let (sy, cy) = (PI * y).sin_cos();
+    let (sz, cz) = (PI * z).sin_cos();
+    (
+        [
+            [PI * cx * cy * cz, -PI * sx * sy * cz, -PI * sx * cy * sz],
+            [-PI * sx * sy * cz, PI * cx * cy * cz, -PI * cx * sy * sz],
+            [
+                2.0 * PI * sx * cy * sz,
+                2.0 * PI * cx * sy * sz,
+                -2.0 * PI * cx * cy * cz,
+            ],
+        ],
+        [PI * cx * sy * sz, PI * sx * cy * sz, PI * sx * sy * cz],
+    )
+}
+fn source3(x: f64, y: f64, z: f64) -> (f64, f64, f64) {
+    let (g, gp) = grads(x, y, z);
+    let u = [u3(x, y, z), v3(x, y, z), w3(x, y, z)];
+    let lap = -3.0 * PI * PI;
+    let conv = |i: usize| u[0] * g[i][0] + u[1] * g[i][1] + u[2] * g[i][2];
+    (
+        RHO * conv(0) + gp[0] - MU * lap * u[0],
+        RHO * conv(1) + gp[1] - MU * lap * u[1],
+        RHO * conv(2) + gp[2] - MU * lap * u[2],
+    )
+}
+fn boundary3(x: f64, y: f64, z: f64) -> (f64, f64, f64) {
+    let u = if x <= 0.0 || x >= 1.0 {
+        0.0
+    } else {
+        u3(x, y, z)
+    };
+    let v = if y <= 0.0 || y >= 1.0 {
+        0.0
+    } else {
+        v3(x, y, z)
+    };
+    let w = if z <= 0.0 || z >= 1.0 {
+        0.0
+    } else {
+        w3(x, y, z)
+    };
+    (u, v, w)
+}
+
+/// Exact force `∮ (−p I + μ(∇u + ∇uᵀ)) n dA` and momentum flux `∮ ρ u (u·n) dA`
+/// over the sphere by a fine Fibonacci quadrature.
+fn exact_force_and_flux() -> ([f64; 3], [f64; 3]) {
+    let n = 200_000;
+    let golden = PI * (3.0 - 5.0_f64.sqrt());
+    let (mut f, mut m) = ([0.0; 3], [0.0; 3]);
+    let da = 4.0 * PI * R * R / n as f64;
+    for k in 0..n {
+        let zz = 1.0 - 2.0 * (k as f64 + 0.5) / n as f64;
+        let rr = (1.0 - zz * zz).sqrt();
+        let th = golden * k as f64;
+        let nrm = [rr * th.cos(), rr * th.sin(), zz];
+        let (x, y, z) = (C.0 + R * nrm[0], C.1 + R * nrm[1], C.2 + R * nrm[2]);
+        let (g, _) = grads(x, y, z);
+        let p = p3(x, y, z);
+        let u = [u3(x, y, z), v3(x, y, z), w3(x, y, z)];
+        let un = u[0] * nrm[0] + u[1] * nrm[1] + u[2] * nrm[2];
+        for i in 0..3 {
+            let mut t = -p * nrm[i];
+            for j in 0..3 {
+                t += MU * (g[i][j] + g[j][i]) * nrm[j];
+            }
+            f[i] += t * da;
+            m[i] += RHO * u[i] * un * da;
+        }
+    }
+    (f, m)
+}
+
+struct Measurement {
+    l2_velocity: f64,
+    max_div: f64,
+    ghost_correction: f64,
+    force_surface: [f64; 3],
+    skipped: usize,
+    force_cv: [f64; 3],
+}
+
+fn measure(n: usize) -> Measurement {
+    let h = 1.0 / n as f64;
+    let dt = 0.4 * (h * h / (4.0 * MU / RHO)).min(h);
+    let mut solver = Solver::new(
+        Fluid {
+            density: RHO,
+            viscosity: MU,
+            reference_velocity: 1.0,
+            reference_length: 1.0,
+        },
+        Parameters {
+            corrector_steps: 2,
+            tolerance: 1e-8,
+            convection_scheme: ConvectionScheme::Upwind,
+            ..Parameters::default()
+        },
+    );
+    solver.set_momentum_source(|x, y, z, _t| source3(x, y, z));
+    solver.set_boundary_velocity(|x, y, z, _t| boundary3(x, y, z));
+    solver.set_body(
+        Body::sphere(|_t| C, R)
+            .with_surface_velocity(|x, y, z, _t| (u3(x, y, z), v3(x, y, z), w3(x, y, z))),
+    );
+    let g = Grid::cubic(n, n, n, h);
+    let mut f = Field::new(g);
+    solver.initialize(&mut f);
+    for _ in 0..200_000 {
+        let (bu, bv, bw) = (f.u.clone(), f.v.clone(), f.w.clone());
+        solver.advance(&mut f, dt);
+        let mut change = 0.0_f64;
+        for (a, b) in
+            f.u.iter()
+                .zip(&bu)
+                .chain(f.v.iter().zip(&bv))
+                .chain(f.w.iter().zip(&bw))
+        {
+            change = change.max((a - b).abs());
+        }
+        if change / dt < 1e-6 {
+            break;
+        }
+    }
+    let mask = solver.mask().expect("mask");
+    use rtx_cfd::solvers::incompressible::embedded3::FaceKind;
+    let (mut sq, mut vol) = (0.0, 0.0);
+    let dv = h * h * h;
+    for k in 0..n {
+        for j in 0..n {
+            for i in 1..n {
+                if mask.u_kind(g.uface(k, j, i)) == FaceKind::Fluid {
+                    let e = f.u[g.uface(k, j, i)]
+                        - u3(i as f64 * h, (j as f64 + 0.5) * h, (k as f64 + 0.5) * h);
+                    sq += e * e * dv;
+                    vol += dv;
+                }
+            }
+        }
+        for j in 1..n {
+            for i in 0..n {
+                if mask.v_kind(g.vface(k, j, i)) == FaceKind::Fluid {
+                    let e = f.v[g.vface(k, j, i)]
+                        - v3((i as f64 + 0.5) * h, j as f64 * h, (k as f64 + 0.5) * h);
+                    sq += e * e * dv;
+                    vol += dv;
+                }
+            }
+        }
+    }
+    for k in 1..n {
+        for j in 0..n {
+            for i in 0..n {
+                if mask.w_kind(g.wface(k, j, i)) == FaceKind::Fluid {
+                    let e = f.w[g.wface(k, j, i)]
+                        - w3((i as f64 + 0.5) * h, (j as f64 + 0.5) * h, k as f64 * h);
+                    sq += e * e * dv;
+                    vol += dv;
+                }
+            }
+        }
+    }
+    let mut max_div = 0.0_f64;
+    for k in 0..n {
+        for j in 0..n {
+            for i in 0..n {
+                if mask.is_fluid_cell(g.cell(k, j, i)) {
+                    let div = (f.u[g.uface(k, j, i + 1)] - f.u[g.uface(k, j, i)]) / h
+                        + (f.v[g.vface(k, j + 1, i)] - f.v[g.vface(k, j, i)]) / h
+                        + (f.w[g.wface(k + 1, j, i)] - f.w[g.wface(k, j, i)]) / h;
+                    max_div = max_div.max(div.abs());
+                }
+            }
+        }
+    }
+    let body = solver.body().expect("body");
+    let surface = mask.surface_force(body, &f, MU, solver.time(), 0.5 * h);
+    let (i0, i1) = (n / 8, n - n / 8);
+    let src = |x: f64, y: f64, z: f64| source3(x, y, z);
+    let force_cv = mask.control_volume_force(&f, dt, RHO, MU, Some(&src), (i0, i1, i0, i1, i0, i1));
+    Measurement {
+        l2_velocity: (sq / vol).sqrt(),
+        max_div,
+        ghost_correction: solver.ghost_correction().abs(),
+        force_surface: surface.f,
+        skipped: surface.skipped,
+        force_cv,
+    }
+}
+
+fn norm(a: [f64; 3]) -> f64 {
+    (a[0] * a[0] + a[1] * a[1] + a[2] * a[2]).sqrt()
+}
+
+fn ladder(resolutions: &[usize]) {
+    let (fe, m) = exact_force_and_flux();
+    let f_scale = norm(fe);
+    let fcv = [fe[0] - m[0], fe[1] - m[1], fe[2] - m[2]];
+    println!(
+        "  exact force {fe:.5?}; momentum flux {m:.5?}; the control-volume route measures {fcv:.5?}"
+    );
+    let ms: Vec<Measurement> = resolutions.iter().map(|&n| measure(n)).collect();
+    let errors: Vec<f64> = ms.iter().map(|x| x.l2_velocity).collect();
+    let mut se = Vec::new();
+    let mut ce = Vec::new();
+    for (k, (mm, &n)) in ms.iter().zip(resolutions).enumerate() {
+        let rate = if k == 0 {
+            "    -".to_string()
+        } else {
+            format!("{:5.2}", (errors[k - 1] / errors[k]).log2())
+        };
+        let s = norm([
+            mm.force_surface[0] - fe[0],
+            mm.force_surface[1] - fe[1],
+            mm.force_surface[2] - fe[2],
+        ]) / f_scale;
+        let c = norm([
+            mm.force_cv[0] - fcv[0],
+            mm.force_cv[1] - fcv[1],
+            mm.force_cv[2] - fcv[2],
+        ]) / f_scale;
+        println!(
+            "  n = {n:3}  L2 u {:.4e} (order {rate})  max div {:.2e}  ghost corr {:.2e}  F_surface {:.4?} rel {s:.3e} (skipped {})  F_cv {:.4?} rel {c:.3e}",
+            mm.l2_velocity,
+            mm.max_div,
+            mm.ghost_correction,
+            mm.force_surface,
+            mm.skipped,
+            mm.force_cv
+        );
+        se.push(s);
+        ce.push(c);
+    }
+    assert!(
+        errors.windows(2).all(|w| w[1] < w[0]),
+        "errors not monotone {errors:?}"
+    );
+    for w in errors.windows(2) {
+        let rate = (w[0] / w[1]).log2();
+        assert!(
+            rate > 0.75 && rate < 2.3,
+            "order {rate:.3} outside [0.75, 2.3]"
+        );
+    }
+    for mm in &ms {
+        assert!(mm.max_div < 1e-5, "max div {:.3e}", mm.max_div);
+    }
+    assert!(
+        se.windows(2).all(|w| w[1] < w[0]),
+        "surface-route error not falling {se:?}"
+    );
+    assert!(
+        ce.windows(2).all(|w| w[1] < w[0]),
+        "control-volume-route error not falling {ce:?}"
+    );
+}
+
+#[test]
+fn embedded_sphere_recovers_the_manufactured_solution() {
+    ladder(&[12, 24]);
+}
+
+#[test]
+#[ignore = "the three-rung ladder to n = 48 (minutes on the host)"]
+fn embedded_sphere_three_rungs() {
+    ladder(&[12, 24, 48]);
+}