Omar SobhandClaude Fable 5.1
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Co-Authored-By: Claude Fable 5.1 <[email protected]>
575 lines
20 KiB
Rust
575 lines
20 KiB
Rust
//! embedded3 item 11a: the fresh-cell falsifier of the 2D track
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//! (`embedded_fresh_cell_falsifier.rs`, omni-cortex
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//! `docs/fresh_cell_gcl_campaign.md`) on the 3D solver, per unit span —
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//! the rigid Turek–Hron flag (0.35 × 0.02 m) extruded across a periodic
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//! slab, oscillating transversely in still fluid at the flag's tip speed
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//! (1 m/s peak, 80 mm amplitude) on h = 1/152 at dt = 3.24e-4. Per step:
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//! the load per unit span (the ghost wall's traction route over the
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//! plate's samples; the cut wall's operator route), a far-field pressure
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//! probe, the fluid's kinetic energy, the fresh-cell count.
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//!
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//! Registered gates (`docs/embedded3_campaign.md` item 11):
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//! - GhostBinary reproduces the 2D wall's impulse: energy per flipped
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//! column within 30 % of the 2D 0.048 J/m per flipped cell, spike RMS
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//! exponent in dt ≈ −1 (published −0.8 for the raw volume source);
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//! - CutCell: energy per fresh column ≥ 20× lower, max force spike < 5 %
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//! of ½ρU²L, exponent ∈ [−0.3, 0.3].
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//!
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//! Default run: dt only, both schemes (minutes on the host);
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//! `RTX_E3_FALSIFIER_LADDER=1` runs dt, dt/2, dt/4 and fits the exponent
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//! (the gated variant is `#[ignore]`); `RTX_E3_FALSIFIER_NZ` sets the
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//! span in cells (default 4); `RTX_E3_FALSIFIER_CSV=<dir>` dumps records.
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use rtx_cfd::solvers::incompressible::ConvectionScheme;
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use rtx_cfd::solvers::incompressible::embedded3::{
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Body, Boundaries, Field, Fluid, Grid, Parameters, Side, Solver, WallScheme,
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};
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use std::io::Write as _;
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const RHO: f64 = 1000.0;
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const MU: f64 = 1.0;
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const N: usize = 152;
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const DT_FSI2: f64 = 3.24e-4;
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const HX: f64 = 0.175;
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const HY: f64 = 0.01;
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const AMP: f64 = 0.08;
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const U_PEAK: f64 = 1.0;
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const CX: f64 = 0.5;
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const CY0: f64 = 0.5;
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/// The 2D wall's measured energy per flipped cell (J/m at U = 1, h = 1/152).
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const ENERGY_2D: f64 = 0.048;
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fn span_cells() -> usize {
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std::env::var("RTX_E3_FALSIFIER_NZ")
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.ok()
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.and_then(|v| v.parse().ok())
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.unwrap_or(4)
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}
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fn center_y(t: f64) -> f64 {
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CY0 + AMP * (U_PEAK / AMP * t).sin()
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}
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fn center_v(t: f64) -> f64 {
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U_PEAK * (U_PEAK / AMP * t).cos()
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}
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fn plate_sdf(x: f64, y: f64, yc: f64) -> f64 {
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let qx = (x - CX).abs() - HX;
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let qy = (y - yc).abs() - HY;
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let outside = (qx.max(0.0).powi(2) + qy.max(0.0).powi(2)).sqrt();
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outside + qx.max(qy).min(0.0)
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}
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const R_CIRCLE: f64 = 0.05;
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/// `RTX_E3_FALSIFIER_BODY=circle`: the 2D falsifier's smooth body (a
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/// cylinder of radius 0.05 across the span) instead of the plate.
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fn circle_body() -> bool {
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std::env::var("RTX_E3_FALSIFIER_BODY").is_ok_and(|v| v == "circle")
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}
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/// `RTX_E3_FALSIFIER_BODY=stadium`: the plate with semicircular ends
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/// (radius `HY`): the same length and thickness, a smooth interface for
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/// the cut geometry's linear interpolant.
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fn stadium_body() -> bool {
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std::env::var("RTX_E3_FALSIFIER_BODY").is_ok_and(|v| v == "stadium")
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}
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fn stadium_sdf(x: f64, y: f64, yc: f64) -> f64 {
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let half = HX - HY;
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let qx = (x - CX).abs().max(half) - half;
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(qx * qx + (y - yc).powi(2)).sqrt() - HY
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}
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fn plate(moving: bool) -> Body {
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let yc = move |t: f64| if moving { center_y(t) } else { CY0 };
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let vc = move |t: f64| if moving { center_v(t) } else { 0.0 };
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if circle_body() {
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return Body::from_sdf(move |x, y, _z, t| {
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((x - CX).powi(2) + (y - yc(t)).powi(2)).sqrt() - R_CIRCLE
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})
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.with_surface_velocity(move |_, _, _, t| (0.0, vc(t), 0.0));
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}
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if stadium_body() {
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return Body::from_sdf(move |x, y, _z, t| stadium_sdf(x, y, yc(t)))
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.with_surface_velocity(move |_, _, _, t| (0.0, vc(t), 0.0));
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}
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Body::from_sdf(move |x, y, _z, t| plate_sdf(x, y, yc(t)))
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.with_surface_velocity(move |_, _, _, t| (0.0, vc(t), 0.0))
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}
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/// The load scale `½ρU²L` of the body (its length across the motion).
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fn load_scale() -> f64 {
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let l = if circle_body() {
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2.0 * R_CIRCLE
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} else {
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2.0 * HX
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};
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0.5 * RHO * U_PEAK * U_PEAK * l
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}
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/// Surface samples of the plate at `t`: `(x, y, z, nx, ny, area)` over the
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/// four edges at spacing `ds` and `nz` z levels.
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fn samples(
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t: f64,
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moving: bool,
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ds: f64,
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nz: usize,
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dz: f64,
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) -> Vec<(f64, f64, f64, f64, f64, f64)> {
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let yc = if moving { center_y(t) } else { CY0 };
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let mut out = Vec::new();
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if circle_body() {
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let n = ((2.0 * std::f64::consts::PI * R_CIRCLE / ds).ceil() as usize).max(8);
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let dth = 2.0 * std::f64::consts::PI / n as f64;
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for k in 0..n {
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let th = (k as f64 + 0.5) * dth;
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let (sn, cs) = th.sin_cos();
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for kz in 0..nz {
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out.push((
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CX + R_CIRCLE * cs,
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yc + R_CIRCLE * sn,
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(kz as f64 + 0.5) * dz,
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cs,
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sn,
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R_CIRCLE * dth * dz,
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));
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}
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}
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return out;
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}
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if stadium_body() {
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let half = HX - HY;
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let n_flat = ((2.0 * half / ds).ceil() as usize).max(1);
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for k in 0..n_flat {
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let x = CX - half + (k as f64 + 0.5) / n_flat as f64 * 2.0 * half;
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for kz in 0..nz {
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let z = (kz as f64 + 0.5) * dz;
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let a = 2.0 * half / n_flat as f64 * dz;
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out.push((x, yc + HY, z, 0.0, 1.0, a));
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out.push((x, yc - HY, z, 0.0, -1.0, a));
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}
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}
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let n_arc = ((std::f64::consts::PI * HY / ds).ceil() as usize).max(4);
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for (cx, sign) in [(CX + half, 1.0), (CX - half, -1.0)] {
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for k in 0..n_arc {
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let th = -std::f64::consts::FRAC_PI_2
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+ (k as f64 + 0.5) / n_arc as f64 * std::f64::consts::PI;
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let (sn, cs) = th.sin_cos();
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let (nx, ny) = (sign * cs, sn);
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for kz in 0..nz {
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out.push((
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cx + HY * nx,
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yc + HY * ny,
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(kz as f64 + 0.5) * dz,
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nx,
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ny,
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std::f64::consts::PI * HY / n_arc as f64 * dz,
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));
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}
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}
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}
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return out;
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}
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let (x0, x1, y0, y1) = (CX - HX, CX + HX, yc - HY, yc + HY);
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let mut edge = |ax: f64, ay: f64, bx: f64, by: f64, nx: f64, ny: f64| {
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let len = ((bx - ax).powi(2) + (by - ay).powi(2)).sqrt();
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let n = ((len / ds).ceil() as usize).max(1);
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for k in 0..n {
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let s = (k as f64 + 0.5) / n as f64;
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for kz in 0..nz {
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out.push((
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ax + s * (bx - ax),
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ay + s * (by - ay),
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(kz as f64 + 0.5) * dz,
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nx,
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ny,
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len / n as f64 * dz,
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));
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}
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}
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};
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edge(x0, y0, x1, y0, 0.0, -1.0);
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edge(x1, y0, x1, y1, 1.0, 0.0);
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edge(x1, y1, x0, y1, 0.0, 1.0);
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edge(x0, y1, x0, y0, -1.0, 0.0);
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out
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}
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struct Record {
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t: f64,
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/// Load per unit span (the scheme's wall route).
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fy: f64,
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/// Load per unit span by the control-volume route (a box of whole
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/// cells around the body, reading no near-wall value).
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fy_cv: f64,
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fresh: usize,
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skipped: usize,
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p_far: f64,
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/// Kinetic energy per unit span over the fluid cells.
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ke: f64,
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}
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struct Run {
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records: Vec<Record>,
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/// The largest kinetic-energy change per step at a step with fresh
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/// cells (after the impulsive start) over that step's flipped columns
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/// (J/m) — the 2D falsifier's 2.604 J/m over 54 cells = 0.048.
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energy_per_flip: f64,
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seconds: f64,
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}
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fn run(scheme: WallScheme, moving: bool, dt: f64, t_end: f64) -> Run {
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let nz = span_cells();
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let h = 1.0 / N as f64;
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let lz = nz as f64 * h;
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let mut solver = Solver::new(
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Fluid {
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density: RHO,
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viscosity: MU,
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reference_velocity: 1.0,
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reference_length: 2.0 * HY,
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},
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Parameters {
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corrector_steps: 2,
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tolerance: 1e-8,
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convection_scheme: ConvectionScheme::Upwind,
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wall_scheme: scheme,
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boundaries: Boundaries {
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z0: Side::Periodic,
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z1: Side::Periodic,
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..Boundaries::default()
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},
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max_surface_speed: Some(U_PEAK),
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// `RTX_E3_SUBSTEPS`: intermediate geometries for the space-time apertures.
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aperture_substeps: std::env::var("RTX_E3_SUBSTEPS")
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.ok()
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.and_then(|v| v.parse().ok())
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.unwrap_or(0),
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// `RTX_E3_CELL_MEAN=1`: the momentum volume from the two cells' fractions.
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momentum_volume_cell_mean: std::env::var("RTX_E3_CELL_MEAN").is_ok_and(|v| v == "1"),
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..Parameters::default()
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},
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);
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solver.set_boundary_velocity(|_, _, _, _| (0.0, 0.0, 0.0));
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if moving {
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solver.set_moving_body(plate(true));
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} else {
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solver.set_body(plate(false));
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}
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let g = Grid::cubic(N, N, nz, h);
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let mut field = Field::new(g);
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solver.initialize(&mut field);
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let steps = (t_end / dt).round() as usize;
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let mut records = Vec::with_capacity(steps);
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// The 2D definition: the largest |ΔKE| step's energy over that
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// step's flipped columns.
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let mut largest_jump = 0.0_f64;
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let mut energy_per_flip = 0.0_f64;
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let mut ke_prev: Option<f64> = None;
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let start = std::time::Instant::now();
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let (jp, ip, kp) = (
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(0.92 * N as f64) as usize,
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(0.5 * N as f64) as usize,
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nz / 2,
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);
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for step in 0..steps {
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let result = solver.advance(&mut field, dt);
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let t = (step + 1) as f64 * dt;
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let mask = solver.mask().expect("mask");
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let body = solver.body().expect("body");
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let (mut fy, mut skipped) = (0.0, 0usize);
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match scheme {
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WallScheme::GhostBinary => {
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for (x, y, z, nx, ny, area) in samples(t, moving, 0.5 * h, nz, h) {
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match mask.traction_at(body, &field, MU, t, [x, y, z], [nx, ny, 0.0]) {
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Some(tr) => fy += tr[1] * area,
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None => skipped += 1,
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}
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}
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}
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WallScheme::CutCell => {
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fy = mask.cut_wall_force(body, &field, MU, t).expect("cut wall")[1];
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}
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}
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fy /= lz;
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let margin = 8;
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let fy_cv = mask.control_volume_force(
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&field,
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dt,
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RHO,
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MU,
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None,
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(margin, N - margin, margin, N - margin, 0, nz),
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)[1] / lz;
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let p_far = field.p[g.cell(kp, jp, ip)];
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let mut ke = 0.0;
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for k in 0..nz {
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for j in 0..N {
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for i in 0..N {
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let idx = g.cell(k, j, i);
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if mask.is_fluid_cell(idx) {
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let uc = 0.5 * (field.u[g.uface(k, j, i)] + field.u[g.uface(k, j, i + 1)]);
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let vc = 0.5 * (field.v[g.vface(k, j, i)] + field.v[g.vface(k, j + 1, i)]);
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let wc = 0.5 * (field.w[g.wface(k, j, i)] + field.w[g.wface(k + 1, j, i)]);
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ke += 0.5 * RHO * (uc * uc + vc * vc + wc * wc) * h * h * h * mask.vol(idx);
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}
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}
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}
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}
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ke /= lz;
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if let Some(prev) = ke_prev {
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if step > 30 && result.fresh_cells > 0 && (ke - prev).abs() > largest_jump {
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largest_jump = (ke - prev).abs();
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// The plate's event is its row (the 2D divided by the row's
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// 54 cells); the circle's is the step's fresh columns.
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let columns = if circle_body() {
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result.fresh_cells as f64 / nz as f64
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} else {
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(2.0 * HX / h).round()
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};
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energy_per_flip = largest_jump / columns;
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}
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}
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ke_prev = Some(ke);
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records.push(Record {
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t,
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fy,
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fy_cv,
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fresh: result.fresh_cells,
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skipped,
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p_far,
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ke,
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});
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}
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Run {
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records,
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energy_per_flip,
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seconds: start.elapsed().as_secs_f64(),
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}
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}
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/// Spike series: the load minus its 21-step running median.
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fn spikes(f: &[f64]) -> Vec<f64> {
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let w = 10usize;
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(0..f.len())
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.map(|k| {
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let lo = k.saturating_sub(w);
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let hi = (k + w + 1).min(f.len());
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let mut win: Vec<f64> = f[lo..hi].to_vec();
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win.sort_by(|a, b| a.partial_cmp(b).unwrap());
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f[k] - win[win.len() / 2]
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})
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.collect()
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}
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struct Stats {
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rms_force: f64,
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rms_spike: f64,
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max_spike: f64,
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rms_spike_cv: f64,
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max_spike_cv: f64,
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rms_pfar_spike: f64,
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max_pfar_spike: f64,
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max_ke_jump: f64,
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fresh_total: usize,
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skipped_max: usize,
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}
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fn stats(records: &[Record], t_lo: f64, t_hi: f64) -> Stats {
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let fy: Vec<f64> = records.iter().map(|r| r.fy).collect();
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let sp = spikes(&fy);
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let fcv: Vec<f64> = records.iter().map(|r| r.fy_cv).collect();
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let spc = spikes(&fcv);
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let pf: Vec<f64> = records.iter().map(|r| r.p_far).collect();
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let spf = spikes(&pf);
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let idx: Vec<usize> = (0..records.len())
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.filter(|&k| records[k].t >= t_lo && records[k].t <= t_hi)
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.collect();
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let rms = |v: &dyn Fn(usize) -> f64| {
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(idx.iter().map(|&k| v(k) * v(k)).sum::<f64>() / idx.len().max(1) as f64).sqrt()
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};
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Stats {
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rms_force: rms(&|k| fy[k]),
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rms_spike: rms(&|k| sp[k]),
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max_spike: idx.iter().map(|&k| sp[k].abs()).fold(0.0, f64::max),
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rms_spike_cv: rms(&|k| spc[k]),
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max_spike_cv: idx.iter().map(|&k| spc[k].abs()).fold(0.0, f64::max),
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rms_pfar_spike: rms(&|k| spf[k]),
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max_pfar_spike: idx.iter().map(|&k| spf[k].abs()).fold(0.0, f64::max),
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max_ke_jump: idx
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.iter()
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.filter(|&&k| k > 0)
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.map(|&k| (records[k].ke - records[k - 1].ke).abs())
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.fold(0.0, f64::max),
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fresh_total: idx.iter().map(|&k| records[k].fresh).sum(),
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skipped_max: idx.iter().map(|&k| records[k].skipped).max().unwrap_or(0),
|
||
}
|
||
}
|
||
|
||
fn dump(dir: &str, name: &str, records: &[Record]) {
|
||
let path = std::path::Path::new(dir).join(format!("{name}.csv"));
|
||
let mut f = std::fs::File::create(path).expect("csv");
|
||
writeln!(f, "t,fy,fy_cv,fresh,skipped,p_far,ke").unwrap();
|
||
for r in records {
|
||
writeln!(
|
||
f,
|
||
"{:.6},{:.6e},{:.6e},{},{},{:.6e},{:.6e}",
|
||
r.t, r.fy, r.fy_cv, r.fresh, r.skipped, r.p_far, r.ke
|
||
)
|
||
.unwrap();
|
||
}
|
||
}
|
||
|
||
struct Verdict {
|
||
energy_per_flip: f64,
|
||
max_spike: f64,
|
||
exponent: Option<f64>,
|
||
}
|
||
|
||
fn falsify(scheme: WallScheme, ladder: bool) -> Verdict {
|
||
let csv_dir = std::env::var("RTX_E3_FALSIFIER_CSV").ok();
|
||
let period = 2.0 * std::f64::consts::PI * AMP / U_PEAK;
|
||
let t_end = 0.3 * period;
|
||
let (t_lo, t_hi) = (0.02 * period, 0.28 * period);
|
||
let rest = run(scheme, false, DT_FSI2, t_end);
|
||
let s0 = stats(&rest.records, t_lo, t_hi);
|
||
println!(
|
||
" {scheme:?} plate AT REST, dt {DT_FSI2:.2e} ({:.0} s): rms force {:.3e}, rms spike {:.3e}, max spike {:.3e}, fresh {}, skipped max {}",
|
||
rest.seconds, s0.rms_force, s0.rms_spike, s0.max_spike, s0.fresh_total, s0.skipped_max
|
||
);
|
||
if let Some(d) = &csv_dir {
|
||
dump(d, &format!("{scheme:?}_rest"), &rest.records);
|
||
}
|
||
let dts: Vec<f64> = if ladder {
|
||
vec![DT_FSI2, DT_FSI2 / 2.0, DT_FSI2 / 4.0]
|
||
} else {
|
||
vec![DT_FSI2]
|
||
};
|
||
let mut points = Vec::new();
|
||
let mut energy = 0.0_f64;
|
||
let mut max_spike = 0.0_f64;
|
||
for &dt in &dts {
|
||
let r = run(scheme, true, dt, t_end);
|
||
let s = stats(&r.records, t_lo, t_hi);
|
||
println!(
|
||
" {scheme:?} plate MOVING, dt {dt:.3e} ({} steps, {:.0} s): rms force {:.3e}, rms spike {:.3e} ({:.1}x rest), max spike {:.3e} N/m ({:.2e} of ½ρU²L), fresh cells {} ({:.2}/step), skipped max {}",
|
||
r.records.len(),
|
||
r.seconds,
|
||
s.rms_force,
|
||
s.rms_spike,
|
||
s.rms_spike / s0.rms_spike.max(1e-300),
|
||
s.max_spike,
|
||
s.max_spike / load_scale(),
|
||
s.fresh_total,
|
||
s.fresh_total as f64 / r.records.len() as f64,
|
||
s.skipped_max
|
||
);
|
||
println!(
|
||
" control-volume route: rms spike {:.3e}, max spike {:.3e} N/m ({:.2e} of ½ρU²L)",
|
||
s.rms_spike_cv,
|
||
s.max_spike_cv,
|
||
s.max_spike_cv / load_scale()
|
||
);
|
||
println!(
|
||
" far probe p(0.5, 0.92): rms spike {:.3e}, max spike {:.3e}; max |ΔKE| per step {:.3e} J/m; energy per flipped column {:.3e} J/m ({:.2} of the 2D wall's {ENERGY_2D})",
|
||
s.rms_pfar_spike,
|
||
s.max_pfar_spike,
|
||
s.max_ke_jump,
|
||
r.energy_per_flip,
|
||
r.energy_per_flip / ENERGY_2D
|
||
);
|
||
if let Some(d) = &csv_dir {
|
||
dump(d, &format!("{scheme:?}_moving_dt{dt:.3e}"), &r.records);
|
||
}
|
||
assert!(s.rms_force.is_finite() && s.rms_spike.is_finite());
|
||
if dt == DT_FSI2 {
|
||
energy = r.energy_per_flip;
|
||
max_spike = s.max_spike;
|
||
}
|
||
points.push((dt, s.rms_spike));
|
||
}
|
||
let exponent = (points.len() >= 2).then(|| {
|
||
let xs: Vec<f64> = points.iter().map(|p| p.0.ln()).collect();
|
||
let ys: Vec<f64> = points.iter().map(|p| p.1.ln()).collect();
|
||
let mx = xs.iter().sum::<f64>() / xs.len() as f64;
|
||
let my = ys.iter().sum::<f64>() / ys.len() as f64;
|
||
let num: f64 = xs.iter().zip(&ys).map(|(x, y)| (x - mx) * (y - my)).sum();
|
||
let den: f64 = xs.iter().map(|x| (x - mx).powi(2)).sum();
|
||
let e = num / den;
|
||
println!(
|
||
" {scheme:?}: spike RMS ~ (dt)^{e:.2} across {} time steps",
|
||
points.len()
|
||
);
|
||
e
|
||
});
|
||
Verdict {
|
||
energy_per_flip: energy,
|
||
max_spike,
|
||
exponent,
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn oscillating_plate_both_walls() {
|
||
let ladder = std::env::var("RTX_E3_FALSIFIER_LADDER").is_ok();
|
||
println!(
|
||
" body: {}",
|
||
if circle_body() {
|
||
"circle R 0.05"
|
||
} else if stadium_body() {
|
||
"stadium 0.35 x 0.02 (semicircular ends)"
|
||
} else {
|
||
"plate 0.35 x 0.02"
|
||
}
|
||
);
|
||
let ghost = falsify(WallScheme::GhostBinary, ladder);
|
||
let cut = falsify(WallScheme::CutCell, ladder);
|
||
println!(
|
||
" energy per flipped column: ghost {:.3e}, cut {:.3e} (ratio {:.1}x); max spike: ghost {:.3e}, cut {:.3e} N/m",
|
||
ghost.energy_per_flip,
|
||
cut.energy_per_flip,
|
||
ghost.energy_per_flip / cut.energy_per_flip.max(1e-300),
|
||
ghost.max_spike,
|
||
cut.max_spike
|
||
);
|
||
assert!(
|
||
ghost.energy_per_flip > 0.0,
|
||
"the binary wall must flip cells"
|
||
);
|
||
}
|
||
|
||
/// The registered gates on the dt ladder.
|
||
#[test]
|
||
#[ignore = "item 11's gated ladder (dt, dt/2, dt/4 on both walls; tens of minutes on the host)"]
|
||
fn oscillating_plate_gates() {
|
||
let ghost = falsify(WallScheme::GhostBinary, true);
|
||
let cut = falsify(WallScheme::CutCell, true);
|
||
let ratio = ghost.energy_per_flip / cut.energy_per_flip.max(1e-300);
|
||
println!(
|
||
" GATES: ghost energy per flipped column {:.3e} ({:.2} of 2D), exponent {:.2}; cut energy {:.3e} ({:.1}x lower), max spike {:.3e} N/m ({:.2e} of ½ρU²L), exponent {:.2}",
|
||
ghost.energy_per_flip,
|
||
ghost.energy_per_flip / ENERGY_2D,
|
||
ghost.exponent.unwrap(),
|
||
cut.energy_per_flip,
|
||
ratio,
|
||
cut.max_spike,
|
||
cut.max_spike / load_scale(),
|
||
cut.exponent.unwrap()
|
||
);
|
||
let g2d = ghost.energy_per_flip / ENERGY_2D;
|
||
assert!(
|
||
(0.7..=1.3).contains(&g2d),
|
||
"ghost energy per flip {g2d:.2} of 2D"
|
||
);
|
||
assert!(ratio >= 20.0, "cut energy only {ratio:.1}x lower");
|
||
assert!(
|
||
cut.max_spike < 0.05 * load_scale(),
|
||
"cut max spike {:.3e}",
|
||
cut.max_spike
|
||
);
|
||
let e = cut.exponent.unwrap();
|
||
assert!((-0.3..=0.3).contains(&e), "cut exponent {e:.2}");
|
||
}
|