rustytorch/crates/specialized/rtx-cfd/tests/embedded3_wall_lipschitz.rs

//! embedded3 item 11b: the wall's smoothness in the interface position.
//! The manufactured sphere is marched to steady state at `M + 1` centres
//! spaced `h/M` apart across one cell along x; at each the load error
//! `E(δ) = F(δ) − F_exact(δ)` (the exact force moves with the sphere and
//! is subtracted) is measured on the scheme's route. The largest jump of
//! `E` between neighbouring positions, relative to the load, and the
//! Lipschitz quotient `|ΔE| / (Δδ |F|)` are reported for both walls.
//! Registered gate (`docs/embedded3_campaign.md` item 11): the cut wall's
//! largest neighbouring jump < 1 % of the load with a bounded quotient.
//!
//! Default run: 8 positions at n = 24 (about two minutes on the host);
//! the gated `#[ignore]` variant sweeps 40.

mod embedded3_sphere;

use embedded3_sphere::{C, exact_force_and_flux, measure};
use rtx_cfd::solvers::incompressible::embedded3::WallScheme;

fn norm(a: [f64; 3]) -> f64 {
    (a[0] * a[0] + a[1] * a[1] + a[2] * a[2]).sqrt()
}

struct Sweep {
    /// Largest neighbouring jump of the load error relative to the load.
    max_jump: f64,
    /// Largest Lipschitz quotient `|ΔE| / (Δδ |F|)` (per unit length).
    max_quotient: f64,
}

fn sweep(n: usize, positions: usize, scheme: WallScheme) -> Sweep {
    let h = 1.0 / n as f64;
    let step = h / positions as f64;
    let mut errors: Vec<[f64; 3]> = Vec::new();
    let mut scale = 0.0_f64;
    for m in 0..=positions {
        let c = (C.0 + m as f64 * step, C.1, C.2);
        let (fe, _) = exact_force_and_flux(c);
        let r = measure(n, scheme, c);
        let e = [
            r.force_surface[0] - fe[0],
            r.force_surface[1] - fe[1],
            r.force_surface[2] - fe[2],
        ];
        scale = scale.max(norm(fe));
        println!(
            "  {scheme:?} δ = {:.4} h: F {:.5?} exact {:.5?} error {:.3e} (rel {:.3e})",
            m as f64 / positions as f64,
            r.force_surface,
            fe,
            norm(e),
            norm(e) / norm(fe)
        );
        errors.push(e);
    }
    let mut max_jump = 0.0_f64;
    for w in errors.windows(2) {
        let d = norm([w[1][0] - w[0][0], w[1][1] - w[0][1], w[1][2] - w[0][2]]);
        max_jump = max_jump.max(d / scale);
    }
    let max_quotient = max_jump / step;
    println!(
        "  {scheme:?}: largest neighbouring jump {:.3e} of the load (spacing {:.3e} = h/{positions}); Lipschitz quotient {:.3e} per unit length",
        max_jump, step, max_quotient
    );
    Sweep {
        max_jump,
        max_quotient,
    }
}

#[test]
fn sphere_load_across_one_cell() {
    let ghost = sweep(24, 8, WallScheme::GhostBinary);
    let cut = sweep(24, 8, WallScheme::CutCell);
    println!(
        "  jumps: ghost {:.3e}, cut {:.3e} ({:.1}x smaller); quotients: ghost {:.3e}, cut {:.3e}",
        ghost.max_jump,
        cut.max_jump,
        ghost.max_jump / cut.max_jump.max(1e-300),
        ghost.max_quotient,
        cut.max_quotient
    );
    assert!(ghost.max_jump.is_finite() && cut.max_jump.is_finite());
}

#[test]
#[ignore = "item 11's gated sweep (40 positions, both walls; tens of minutes on the host)"]
fn sphere_load_lipschitz_gate() {
    let ghost = sweep(24, 40, WallScheme::GhostBinary);
    let cut = sweep(24, 40, WallScheme::CutCell);
    println!(
        "  GATE: cut largest jump {:.3e} of the load (ghost {:.3e}); cut quotient {:.3e} (ghost {:.3e})",
        cut.max_jump, ghost.max_jump, cut.max_quotient, ghost.max_quotient
    );
    assert!(
        cut.max_jump < 0.01,
        "cut-cell jump {:.3e} of the load",
        cut.max_jump
    );
}