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

//! embedded3 gates 9a and 10: 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 (item 9) and the apertured cut-cell wall (item
//! 10). The velocity error falls at the scheme's order, every fluid cell
//! is divergence-free (apertured, with the porous surface's flux, on the
//! cut wall), 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). Item 10's gate: the cut wall's errors
//! are at most the binary wall's at every n, its loads within 10 % at the
//! finest rung.

mod embedded3_sphere;

use embedded3_sphere::{C, Measurement, 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()
}

/// The velocity errors and the two routes' relative force errors per rung.
struct Ladder {
    errors: Vec<f64>,
    surface: Vec<f64>,
    cv: Vec<f64>,
}

fn ladder(resolutions: &[usize], scheme: WallScheme) -> Ladder {
    let (fe, m) = exact_force_and_flux(C);
    let f_scale = norm(fe);
    let fcv = [fe[0] - m[0], fe[1] - m[1], fe[2] - m[2]];
    println!(
        "  {scheme:?}: 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, scheme, C)).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:?}"
    );
    Ladder {
        errors,
        surface: se,
        cv: ce,
    }
}

/// Item 10's comparison: the cut wall's velocity error at most the binary
/// wall's at every rung; both routes within `load_bound` at the finest.
fn compare(resolutions: &[usize], load_bound: f64) {
    let ghost = ladder(resolutions, WallScheme::GhostBinary);
    let cut = ladder(resolutions, WallScheme::CutCell);
    for (k, &n) in resolutions.iter().enumerate() {
        println!(
            "  n = {n:3}  L2 u ghost {:.4e} cut {:.4e}  (ratio {:.3})",
            ghost.errors[k],
            cut.errors[k],
            cut.errors[k] / ghost.errors[k]
        );
        assert!(
            cut.errors[k] <= ghost.errors[k],
            "cut-cell error above the binary wall's at n = {n}"
        );
    }
    let last = resolutions.len() - 1;
    assert!(
        cut.surface[last] < load_bound && cut.cv[last] < load_bound,
        "cut-cell loads at the finest rung: surface {:.3e}, control volume {:.3e} (bound {load_bound})",
        cut.surface[last],
        cut.cv[last]
    );
}

#[test]
fn embedded_sphere_recovers_the_manufactured_solution() {
    ladder(&[12, 24], WallScheme::GhostBinary);
}

#[test]
fn cut_cell_wall_recovers_the_manufactured_solution() {
    compare(&[12, 24], 0.2);
}

#[test]
#[ignore = "the three-rung ladder to n = 48 (minutes on the host)"]
fn embedded_sphere_three_rungs() {
    ladder(&[12, 24, 48], WallScheme::GhostBinary);
}

#[test]
#[ignore = "item 10's finest rung: the cut wall's loads within 10 % at n = 48"]
fn cut_cell_three_rungs() {
    compare(&[12, 24, 48], 0.1);
}