//! P5-3's added-mass pin (`docs/overset_metal_campaign.md`, the replay-to-
//! replay reading): the composite's UNSTEADY pressure response on the
//! moving patch against potential theory.
//!
//! A no-slip circular cylinder of radius `r` on an O-grid patch translates
//! through a closed box of still fluid, `x_c(t) = A sin ωt`, the patch
//! carried with it every step (`set_patch_mesh`, the A-P2 moving path)
//! and the wall carrying the exact velocity. The in-phase force is the
//! added-mass reaction, `F = −m_a ẍ` with `m_a = ρ π r²` (unbounded
//! potential flow), plus Stokes's viscous correction `4 / √(π β)` with
//! `β = r² ω / ν` and a small blockage term for the box. The FSI2
//! ladder's motion-fixed lift response is ~1.4× the reference's at every
//! h and dt (2026-09-09); nothing rigid (CFD1–3, all within 1 %) can see
//! the unsteady scale, this can. Registered before the run: `C_m` in
//! [1.0, 1.25] at n = 64 means the unsteady scale is right and the
//! discrepancy is the wake's; `C_m ≥ 1.4` locates it here.
//!
//! `RTX_OVERSET_N` (64), `RTX_OVERSET_AM_PERIODS` (4).

use rtx_cfd::mesh::patch_gen::annulus_skewed;
use rtx_cfd::mesh::{PatchMesh, PatchSide};
use rtx_cfd::solvers::incompressible::{
    CurvilinearParameters, CurvilinearPisoSolver, EmbeddedParameters, EmbeddedPisoSolver,
    FlowField, NormalDiffusion, OversetField, OversetParameters, OversetPisoSolver, PatchField,
    PoissonSolverKind,
};
use rtx_cfd::{CfdConfig, CfdResult};
use std::f64::consts::PI;

const RHO: f64 = 1.0;
const NU: f64 = 5e-5;
const R: f64 = 0.1;
const R_OUT: f64 = 0.25;
const CX: f64 = 0.5;
const CY: f64 = 0.5;
const AMP: f64 = 0.005;
const OMEGA: f64 = 2.0 * PI;

fn patch_at(n: usize, x: f64) -> CfdResult<PatchMesh> {
    annulus_skewed([CX + x, CY], R, R_OUT, 9 * n / 4, n / 4, 0.0, 3.0)
}

fn env_usize(k: &str, d: usize) -> usize {
    std::env::var(k)
        .ok()
        .and_then(|v| v.parse().ok())
        .unwrap_or(d)
}

#[tokio::test]
async fn oscillating_cylinder_added_mass_on_the_moving_patch() -> CfdResult<()> {
    let n = env_usize("RTX_OVERSET_N", 64);
    let periods = env_usize("RTX_OVERSET_AM_PERIODS", 4);
    let h = 1.0 / n as f64;
    let config = CfdConfig::new()
        .with_density(RHO)
        .with_viscosity(RHO * NU)
        .with_reference_velocity(AMP * OMEGA)
        .with_reference_length(2.0 * R);
    let mut background = EmbeddedPisoSolver::new(
        config.clone(),
        EmbeddedParameters {
            corrector_steps: 2,
            tolerance: 1e-8,
            poisson_solver: PoissonSolverKind::Multigrid,
            ..EmbeddedParameters::default()
        },
    )?;
    background.set_boundary_velocity(|_, _, _| (0.0, 0.0));
    let mut patch = CurvilinearPisoSolver::new(
        config,
        CurvilinearParameters {
            tolerance: 1e-6,
            normal_diffusion: NormalDiffusion::LineImplicit,
            ..CurvilinearParameters::default()
        },
        patch_at(n, 0.0)?,
    )?;
    // The wall's exact velocity: the patch's clock is the end of the step.
    patch.set_side_velocity(PatchSide::Inner, |_, _, t| {
        (AMP * OMEGA * (OMEGA * t).cos(), 0.0)
    });
    let mut patch_field = PatchField::new(patch.mesh());
    patch.initialize(&mut patch_field, |_, _| (0.0, 0.0));
    let bg_field = FlowField::new(n, n, h, h)?;
    let params = OversetParameters {
        stall_rounds: 0,
        ..OversetParameters::default()
    };
    let mut solver = OversetPisoSolver::new(background, patch, (n, n, h, h), params)?;
    let mut field = OversetField {
        background: bg_field,
        patch: patch_field,
    };
    solver.initialize(&mut field)?;

    // Step: the patch's smallest edge against the explicit limits, and the
    // wall's own displacement per step well under a cell.
    let mut hp = f64::INFINITY;
    for c in 0..solver.patch().mesh().cell_count() {
        for (f, _) in solver.patch().mesh().cell_faces(c) {
            let d = solver.patch().mesh().faces()[f].d;
            hp = hp.min((d[0] * d[0] + d[1] * d[1]).sqrt());
        }
    }
    let period = 2.0 * PI / OMEGA;
    let dt_raw = 0.4 * (hp * hp / (4.0 * NU)).min(h).min(0.2 * hp / (AMP * OMEGA));
    let steps_per_period = (period / dt_raw).ceil() as usize;
    let dt = period / steps_per_period as f64;
    let beta = R * R * OMEGA / NU;
    println!(
        "  n = {n}, h = {h:.4}, patch inner edge {hp:.4}, dt = {dt:.3e} ({steps_per_period} per period), A/r = {:.3}, KC = {:.3}, β = {beta:.0}: Stokes C_m ≈ {:.3}",
        AMP / R,
        2.0 * PI * AMP / R,
        1.0 + 4.0 / (PI * beta).sqrt()
    );

    let mut samples: Vec<(f64, f64, f64, f64)> = Vec::new();
    let mut rounds_total = 0usize;
    let mut reclass_total = 0usize;
    let start = std::time::Instant::now();
    for step in 0..periods * steps_per_period {
        let t_new = (step + 1) as f64 * dt;
        solver.set_patch_mesh(patch_at(n, AMP * (OMEGA * t_new).sin())?)?;
        let r = solver.advance(&mut field, dt).await?;
        rounds_total += r.rounds.iter().sum::<usize>();
        reclass_total += r.reclassified_cells;
        let load = solver
            .patch()
            .surface_force(&field.patch, PatchSide::Inner, solver.time());
        let f = load.total();
        samples.push((t_new, f[0], load.pressure[0], load.viscous[0]));
        if (step + 1) % steps_per_period == 0 {
            println!(
                "    period {}: F_x at the end {:+.4e} (pressure {:+.4e}, viscous {:+.4e}), rounds {:.2}/step, reclassified {:.1}/step, {:.0} s",
                (step + 1) / steps_per_period,
                f[0],
                load.pressure[0],
                load.viscous[0],
                rounds_total as f64 / (step + 1) as f64,
                reclass_total as f64 / (step + 1) as f64,
                start.elapsed().as_secs_f64()
            );
        }
    }
    // Least squares over the last two periods: F = a sin ωt + b cos ωt (+ c).
    // ẍ = −A ω² sin ωt, so the added-mass reaction −m_a ẍ = m_a A ω² sin ωt:
    // C_m = a / (ρ π r² A ω²). ẋ = A ω cos ωt, so b = −c_d A ω (damping).
    let fit = |col: usize| -> (f64, f64, f64) {
        let last: Vec<&(f64, f64, f64, f64)> = samples
            .iter()
            .filter(|s| s.0 > (periods as f64 - 2.0) * period - 1e-12)
            .collect();
        let g = |s: &(f64, f64, f64, f64)| match col {
            1 => s.1,
            2 => s.2,
            _ => s.3,
        };
        // Normal equations for [sin, cos, 1].
        let mut m = [[0.0f64; 3]; 3];
        let mut rhs = [0.0f64; 3];
        for s in &last {
            let b = [(OMEGA * s.0).sin(), (OMEGA * s.0).cos(), 1.0];
            for i in 0..3 {
                rhs[i] += b[i] * g(s);
                for j in 0..3 {
                    m[i][j] += b[i] * b[j];
                }
            }
        }
        // 3×3 solve by Cramer's rule.
        let det = |a: [[f64; 3]; 3]| {
            a[0][0] * (a[1][1] * a[2][2] - a[1][2] * a[2][1])
                - a[0][1] * (a[1][0] * a[2][2] - a[1][2] * a[2][0])
                + a[0][2] * (a[1][0] * a[2][1] - a[1][1] * a[2][0])
        };
        let d = det(m);
        let mut sol = [0.0; 3];
        for k in 0..3 {
            let mut mk = m;
            for i in 0..3 {
                mk[i][k] = rhs[i];
            }
            sol[k] = det(mk) / d;
        }
        (sol[0], sol[1], sol[2])
    };
    let (a, b, c) = fit(1);
    let (ap, bp, _) = fit(2);
    let (av, bv, _) = fit(3);
    let m_a = RHO * PI * R * R;
    let cm = a / (m_a * AMP * OMEGA * OMEGA);
    let cm_p = ap / (m_a * AMP * OMEGA * OMEGA);
    let cm_v = av / (m_a * AMP * OMEGA * OMEGA);
    let damping = -b / (AMP * OMEGA);
    println!(
        "  ADDED MASS n = {n}: C_m = {cm:.4} (pressure {cm_p:.4} + viscous {cm_v:.4}) against 1 + Stokes {:.3}; damping coefficient {damping:.4e} (pressure {:+.3e}, viscous {:+.3e}) [N·s/m per m]; mean force {c:+.3e}; {} steps in {:.0} s",
        1.0 + 4.0 / (PI * beta).sqrt(),
        -bp / (AMP * OMEGA),
        -bv / (AMP * OMEGA),
        samples.len(),
        start.elapsed().as_secs_f64()
    );
    assert!(cm.is_finite(), "non-finite added-mass coefficient");
    Ok(())
}