//! Density-scaling pin for the cut-cell predictor (host): the same flow at
//! `ρ` and `1000 ρ` with `μ` scaled alike is the same velocity field and a
//! pressure scaled by 1000 — every term of the momentum equation carries
//! `ρ` (the convection term used to be a bare volume flux times velocity,
//! which starved every ρ = 1000 cut-cell run of convection).
use rtx_cfd::solvers::incompressible::ConvectionScheme;
use rtx_cfd::solvers::incompressible::embedded3::{
    Body, Boundaries, Field, Fluid, Grid, Parameters, Side, Solver, WallScheme,
};

fn run(rho: f64, moving: bool) -> Field {
    let n = 16;
    let h = 1.0 / n as f64;
    let g = Grid::cubic(2 * n, n, n, h);
    let nu = 1e-2;
    let mut solver = Solver::new(
        Fluid {
            density: rho,
            viscosity: rho * nu,
            reference_velocity: 1.0,
            reference_length: 0.3,
        },
        Parameters {
            corrector_steps: 2,
            tolerance: 1e-11,
            convection_scheme: ConvectionScheme::TvdVanAlbada,
            wall_scheme: WallScheme::CutCell,
            boundaries: Boundaries {
                x1: Side::PressureOutlet,
                ..Boundaries::default()
            },
            max_surface_speed: if moving { Some(0.5) } else { None },
            ..Parameters::default()
        },
    );
    solver.set_boundary_velocity(|x, _, _, _| {
        if x <= 0.0 {
            (1.0, 0.0, 0.0)
        } else {
            (0.0, 0.0, 0.0)
        }
    });
    let xc = move |t: f64| 0.7 + if moving { 0.1 * (3.0 * t).sin() } else { 0.0 };
    let body = Body::from_sdf(move |x, y, z, t| {
        ((x - xc(t)).powi(2) + (y - 0.5_f64).powi(2) + (z - 0.5_f64).powi(2)).sqrt() - 0.15
    })
    .with_surface_velocity(move |_, _, _, t| {
        (if moving { 0.3 * (3.0 * t).cos() } else { 0.0 }, 0.0, 0.0)
    });
    if moving {
        solver.set_moving_body(body);
    } else {
        solver.set_body(body);
    }
    let mut field = Field::new(g);
    for k in 0..n {
        for j in 0..n {
            for i in 0..=2 * n {
                field.u[g.uface(k, j, i)] = 1.0;
            }
        }
    }
    solver.initialize(&mut field);
    let dt = 0.2 * h;
    for _ in 0..40 {
        solver.advance(&mut field, dt);
    }
    field
}

fn compare(moving: bool) {
    let a = run(1.0, moving);
    let b = run(1000.0, moving);
    let max = |x: &[f64], y: &[f64], s: f64| {
        x.iter()
            .zip(y)
            .map(|(p, q)| (p - q / s).abs())
            .fold(0.0, f64::max)
    };
    let du = max(&a.u, &b.u, 1.0)
        .max(max(&a.v, &b.v, 1.0))
        .max(max(&a.w, &b.w, 1.0));
    let dp = max(&a.p, &b.p, 1000.0);
    let pscale = a.p.iter().fold(0.0f64, |m, p| m.max(p.abs()));
    println!("  moving {moving}: max |Δu| {du:.3e}, max |Δp/1000| {dp:.3e} (p scale {pscale:.3e})");
    assert!(du < 1e-9, "velocity is not density-invariant: {du:.3e}");
    assert!(
        dp < 1e-9 * pscale.max(1.0),
        "pressure does not scale with density: {dp:.3e}"
    );
}

#[test]
fn cut_cell_flow_is_density_invariant_at_rest() {
    compare(false);
}

#[test]
fn cut_cell_flow_is_density_invariant_moving() {
    compare(true);
}