rustytorch/crates/specialized/rtx-cfd/tests/embedded3_cut_geometry.rs

//! embedded3 gate 8: the cut geometry. A sphere and a z-cylinder on
//! n = 16 / 32 / 64: the fluid volume and the wall area converge at second
//! order; the wall closure Σ_c A_w n_w vanishes to rounding for a body
//! inside the box; a continuity sweep of the sphere's centre across one
//! cell (200 positions): bounded difference quotient of every aperture and
//! volume, no jump > 1e-3 between neighbouring positions; and the
//! translating sphere's discrete volume change per step, MEASURED (the
//! plan's "to rounding" clause is checked, not assumed).

use rtx_cfd::solvers::incompressible::embedded3::{Body, CutGeometry, Grid};
use std::f64::consts::PI;

fn cube(n: usize) -> Grid {
    let h = 1.0 / n as f64;
    Grid {
        nx: n,
        ny: n,
        nz: n,
        dx: h,
        dy: h,
        dz: h,
    }
}

#[test]
fn volume_and_area_converge_at_second_order_and_the_wall_closes() {
    let r: f64 = 0.3;
    let sphere_v = 4.0 / 3.0 * PI * r.powi(3);
    let sphere_a = 4.0 * PI * r * r;
    let cyl_v = PI * r * r * 1.0;
    let cyl_a = 2.0 * PI * r * 1.0;
    for (name, exact_v, exact_a, body) in [
        (
            "sphere",
            1.0 - sphere_v,
            sphere_a,
            Body::sphere(|_t| (0.5, 0.5, 0.5), r),
        ),
        (
            "z-cylinder",
            1.0 - cyl_v,
            cyl_a,
            Body::cylinder_z(0.5, 0.5, r),
        ),
    ] {
        let mut ev = Vec::new();
        let mut ea = Vec::new();
        for n in [16usize, 32, 64] {
            let g = CutGeometry::build(&body, cube(n), 0.0);
            let v = g.fluid_volume();
            let (a, closure) = g.wall_area_and_closure();
            let closure_norm =
                (closure[0].powi(2) + closure[1].powi(2) + closure[2].powi(2)).sqrt();
            ev.push((v - exact_v).abs());
            ea.push((a - exact_a).abs());
            println!(
                "  {name} n {n}: fluid volume {v:.8} (exact {exact_v:.8}, err {:.2e}); wall area {a:.6} (exact {exact_a:.6}, err {:.2e}); closure |Σ A_w n_w| {closure_norm:.2e}",
                ev.last().unwrap(),
                ea.last().unwrap()
            );
            // The z-cylinder touches the z walls: its closure includes the
            // end caps' missing area only through the cell walls, so the
            // closure holds for the sphere; for the cylinder the z component
            // is the two caps (equal and opposite) and x, y close.
            if name == "sphere" {
                assert!(
                    closure_norm < 1e-12,
                    "{name} n {n}: closure {closure_norm:.3e}"
                );
            } else {
                assert!(
                    closure[0].abs() < 1e-12 && closure[1].abs() < 1e-12,
                    "{name} n {n}: closure x/y {closure:?}"
                );
            }
        }
        for (label, e) in [("volume", &ev), ("area", &ea)] {
            for w in e.windows(2) {
                let order = (w[0] / w[1]).log2();
                println!("  {name} {label} order {order:.2}");
                assert!(order > 1.5, "{name} {label}: order {order:.2} below second");
            }
        }
    }
}

/// Continuity in the body position. A face aperture where the interface is
/// tangent to the face changes at a rate of order `r / h` per cell width of
/// shift (the cap's area grows linearly in the shift, on a face of area
/// h²), so an O(1) Lipschitz bound is the wrong premise; the discriminating
/// test is that the largest change between neighbouring positions falls in
/// proportion when the sweep is refined tenfold — a discontinuity would not.
fn sweep(positions: usize) -> f64 {
    let n = 16;
    let g = cube(n);
    let h = g.dx;
    let r: f64 = 0.3;
    let mut prev: Option<CutGeometry> = None;
    let mut worst_jump = 0.0_f64;
    for s in 0..=positions {
        let shift = h * s as f64 / positions as f64;
        let body = Body::sphere(
            move |_t| (0.5 + shift, 0.5 + 0.37 * shift, 0.5 + 0.11 * shift),
            r,
        );
        let cut = CutGeometry::build(&body, g, 0.0);
        if let Some(p) = &prev {
            let jump = |a: &[f64], b: &[f64]| {
                a.iter()
                    .zip(b)
                    .fold(0.0_f64, |m, (x, y)| m.max((x - y).abs()))
            };
            let j = jump(&cut.a_u, &p.a_u)
                .max(jump(&cut.a_v, &p.a_v))
                .max(jump(&cut.a_w, &p.a_w))
                .max(jump(&cut.vol, &p.vol));
            worst_jump = worst_jump.max(j);
        }
        prev = Some(cut);
    }
    worst_jump
}

#[test]
fn apertures_and_volumes_are_continuous_in_the_body_position() {
    let j200 = sweep(200);
    let j2000 = sweep(2000);
    let ratio = j2000 / j200;
    println!(
        "  sphere over one cell: largest neighbour change {j200:.3e} at 200 positions, {j2000:.3e} at 2000 (ratio {ratio:.3}; 0.1 = Lipschitz, 1 = a jump)"
    );
    assert!(
        ratio < 0.2,
        "the largest change does not fall with the sweep resolution (ratio {ratio:.3}): a discontinuity"
    );
    assert!(
        ratio > 0.05,
        "ratio {ratio:.3} below the Lipschitz expectation — check the sweep"
    );
}

#[test]
fn the_translating_sphere_volume_change_is_measured() {
    let n = 32;
    let g = cube(n);
    let r: f64 = 0.3;
    let dt = 1e-3;
    let speed = 1.0; // one cell width in n·dt... 0.03125 m per 31 steps
    let mut worst_rel = 0.0_f64;
    let mut prev = CutGeometry::build(
        &Body::sphere(move |t| (0.5 + speed * t, 0.5, 0.5), r),
        g,
        0.0,
    );
    let swept_per_step = PI * r * r * speed * dt; // the sphere's cross-section swept
    for s in 1..=31 {
        let t = s as f64 * dt;
        let cut = CutGeometry::build(&Body::sphere(move |t| (0.5 + speed * t, 0.5, 0.5), r), g, t);
        let dv = cut.fluid_volume() - prev.fluid_volume();
        worst_rel = worst_rel.max(dv.abs() / swept_per_step);
        prev = cut;
    }
    let body_v = 4.0 / 3.0 * PI * r.powi(3);
    println!(
        "  translating sphere n {n}: largest |Σ ΔV_c| per step = {worst_rel:.3e} of the swept cross-section volume per step ({:.2e} of the body volume)",
        worst_rel * swept_per_step / body_v
    );
    // Recorded; the compatibility of the moving-body projection is decided
    // on this number (the plan's clause "to rounding" is not true for the
    // piecewise-linear interpolant — the cut cells' volume error moves with
    // the body).
}