//! The discrete geometric conservation law (DGCL) test for the ALE solver.
//!
//! **Uniform flow must stay exactly uniform on an arbitrarily moving mesh.**
//! A constant velocity field with a constant pressure is an exact solution of
//! the incompressible Navier–Stokes equations regardless of how the mesh
//! moves underneath it; an ALE discretisation preserves it if and only if its
//! discrete volume increments equal the sums of its discrete face-swept
//! volumes — the DGCL (Thomas & Lombard 1979; Farhat, Geuzaine & Grandmont
//! 2001). Nothing about the physics is exercised, so any deviation is pure
//! geometric inconsistency, and it shows up at machine precision rather than
//! at truncation order.
//!
//! For tensor-product mesh motion the trapezoidal face rule is exactly
//! conservative:
//!
//! ```text
//!   dx1*dy1 - dx0*dy0  =  (dx1-dx0)*(dy0+dy1)/2 + (dy1-dy0)*(dx0+dx1)/2
//! ```
//!
//! an algebraic identity, so with time-averaged face areas in both the fluid
//! fluxes and the swept volumes the uniform state is a fixed point of the
//! update to rounding error. The negative control replaces the averaged areas
//! with end-of-step areas — the "obvious" choice that looks consistent and is
//! first-order accurate — and per step each cell then picks up a relative
//! error of exactly `dw*dh/V` (the cross term the identity above absorbs).
//! That control failing loudly is what proves this test can fail.

use rtx_cfd::solvers::incompressible::ale::{
    AleField, AleParameters, AlePisoSolver, SweptFaceRule,
};
use rtx_cfd::{CfdConfig, CfdResult};
use std::f64::consts::PI;

const U_UNIFORM: f64 = 0.7;
const V_UNIFORM: f64 = -0.4;
const LX: f64 = 1.0;
const LY: f64 = 0.75;
const NX: usize = 16;
const NY: usize = 12;

/// Interior mesh-line motion: smooth, boundary-fixed, with different lines
/// moving out of phase (the `phase * xi` term) and incommensurate frequencies
/// in the two directions, so no symmetry can hide a conservation defect.
/// The displacement gradient stays below 1 (`amp * (pi + phase) < 1` in the
/// normalised coordinate), so mesh lines never cross.
fn moved_x(xi: f64, t: f64) -> f64 {
    let s = xi / LX;
    xi + 0.06 * LX * (PI * s).sin() * (2.9 * t + 3.0 * s).sin()
}

fn moved_y(yj: f64, t: f64) -> f64 {
    let s = yj / LY;
    yj + 0.06 * LY * (PI * s).sin() * (4.3 * t + 2.0 * s).sin()
}

fn reference_x() -> Vec<f64> {
    (0..=NX).map(|i| LX * i as f64 / NX as f64).collect()
}

fn reference_y() -> Vec<f64> {
    (0..=NY).map(|j| LY * j as f64 / NY as f64).collect()
}

/// March uniform flow on the wiggling mesh and return the largest deviation
/// from uniformity, over every velocity unknown and every step, plus the
/// largest final pressure magnitude.
async fn max_deviation(rule: SweptFaceRule, steps: usize, dt: f64) -> CfdResult<(f64, f64)> {
    let config = CfdConfig::new()
        .with_density(1.0)
        .with_viscosity(0.05)
        .with_reference_velocity(1.0)
        .with_reference_length(1.0);
    // The tolerance must sit at the rounding floor, not at an engineering
    // level: the projection's inner stop is floored at
    // `0.1 * tolerance * reference_flux`, and with a 1e-9 tolerance the SOR
    // quits after one sweep on the eps-level sources this test produces,
    // leaving a partial p' that accumulates into p (~3e-9 over 400 steps)
    // and whose gradient re-perturbs the velocities at ~1e-11 — five orders
    // above rounding, with the geometry entirely blameless. Measured before
    // and after: 3.6e-11 at tolerance 1e-9, rounding-level at 1e-13.
    let params = AleParameters {
        corrector_steps: 2,
        tolerance: 1e-13,
        swept_face_rule: rule,
        ..AleParameters::default()
    };
    let mut solver = AlePisoSolver::new(config, params)?;
    solver.set_boundary_velocity(|_x, _y, _t| (U_UNIFORM, V_UNIFORM));

    let mut field = AleField::new(reference_x(), reference_y())?;
    field.u.fill(U_UNIFORM);
    field.v.fill(V_UNIFORM);
    field.p.fill(0.0);

    let (rx, ry) = (reference_x(), reference_y());
    let mut worst: f64 = 0.0;
    for step in 0..steps {
        let t_new = (step + 1) as f64 * dt;
        let new_x: Vec<f64> = rx.iter().map(|&xi| moved_x(xi, t_new)).collect();
        let new_y: Vec<f64> = ry.iter().map(|&yj| moved_y(yj, t_new)).collect();
        solver.advance(&mut field, &new_x, &new_y, dt).await?;

        for value in field.u.iter() {
            worst = worst.max((value - U_UNIFORM).abs());
        }
        for value in field.v.iter() {
            worst = worst.max((value - V_UNIFORM).abs());
        }
    }

    let max_p = field.p.iter().fold(0.0f64, |m, &p| m.max(p.abs()));
    Ok((worst, max_p))
}

#[tokio::test]
async fn uniform_flow_stays_exactly_uniform_on_an_arbitrarily_moving_mesh() -> CfdResult<()> {
    let (worst, max_p) = max_deviation(SweptFaceRule::Trapezoidal, 400, 1e-3).await?;
    println!("  DGCL: max |u - U| over 400 steps = {worst:.3e}, final max |p| = {max_p:.3e}");

    // Machine precision relative to the velocity scale — not truncation
    // order. 400 steps of rounding accumulate to ~1e-13 at worst.
    let scale = U_UNIFORM.abs().max(V_UNIFORM.abs());
    assert!(
        worst < 1e-11 * scale,
        "DGCL violated: uniform flow deviated by {worst:.3e} on the moving mesh"
    );
    // With a uniform field the projection source is exactly zero, so the
    // pressure must never move off its initial constant.
    assert!(max_p < 1e-11, "pressure moved off constant: {max_p:.3e}");
    Ok(())
}

#[tokio::test]
async fn end_of_step_face_areas_violate_the_gcl_visibly() -> CfdResult<()> {
    // The control: identical run, but fluxes and swept volumes use the
    // end-of-step face areas. Each cell's update then multiplies the uniform
    // state by (1 + dw*dh/V) per step — a defect this test must see and the
    // conservative rule must not have.
    let (worst, _) = max_deviation(SweptFaceRule::EndOfStep, 400, 1e-3).await?;
    println!("  GCL-violating control: max |u - U| over 400 steps = {worst:.3e}");

    let scale = U_UNIFORM.abs().max(V_UNIFORM.abs());
    assert!(
        worst > 1e-6 * scale,
        "the GCL-violating rule deviated only {worst:.3e} — the DGCL test \
         has lost its teeth (motion too tame, or the rule is not actually \
         reaching the fluxes)"
    );
    Ok(())
}