Fluid simulation · kimi-k3

Let me build a fluid simulation. I'll do a CPU-based semi-Lagrangian solver on a coarse grid (e.g., 150x100), rendered to canvas via ImageData upscaled, or via drawing to a small offscreen canvas and drawImage scaled up. Simple approach:

- Grid velocity u,v and dye r,g,b fields.
- Each frame: advect velocity semi-Lagrangian, add dissipation, advect dye, maybe a simple pressure projection (a few Jacobi iterations) for swirling. Semi-Lagrangian without projection gives smeared flow; projection with ~10-20 iterations at 128x80 is fine.

Resolution: SIM=128 cells wide. 1200x800 -> grid 120x80. Jacobi 20 iterations * 120*80*~4 ops — fine.

Pointer drag injects velocity in drag direction and dye with current color.

Render: create ImageData of grid size, fill from dye, putImageData to offscreen canvas, then drawImage scaled with smoothing.

Controls: color input, pause/resume button, clear button.

Let me write it.

Grid: W=144, H=96 maybe. dt fixed. Steps per frame: 1. Jacobi iterations ~20. That's 144*96=13824 cells * 20 iterations = 276k ops, fine.

Implementation details:
- Float32Arrays: u, v, u0, v0, r,g,b, r0... p, div.
- advect(field, u, v, dt, dissipation): bilinear sample at x - dt*u.
- project: compute divergence, jacobi solve p, subtract gradient.
- Boundary: set edges zero.

Splat on drag: radius in grid coords, add velocity = drag vector scaled, add dye color scaled.

Seed: on load, do a few splats with random colors/directions, plus maybe some vortex.

Pause: stop stepping but still render.

Write index.html, then test with browser: screenshot, drag, screenshot after release, clear, drag again.

Let me write the code carefully.

Render: dye values 0..1, multiply 255. Maybe additive-ish. Background dark. Also can render velocity slightly? Keep it dye only.

Auto-run? On load seed and let it run.

Code:

```js
const N = ... aspect: canvas size = window. grid W=Math.round(160*aspect ratio scaling). Fix cell count: let simScale; choose gridW=160, gridH=Math.round(160*h/w).
```

Use gridW=160; gridH = max(24, round(160*H/W)).

Splat function:

```js
function splat(x, y, dx, dy, color, radius){
  // x,y in grid coords
  const r2 = radius*radius;
  const x0=Math.max(1,Math.floor(x-radius)), x1=Math.min(W-2,Math.ceil(x+radius));
  ...
  for cells: const d2=(i-x)^2+(j-y)^2; if d2<r2: fall=Math.exp(-d2/r2*4)...
  u += dx*fall; dye += color*fall
}
```

Pointer handling: convert client coords to grid coords; dx = (x - lastX) in grid units per event; scale velocity by some factor, clamp.

dt: semi-Lagrangian with dt in grid-cell units ~1.0 per step.

Projection: standard.

Boundary handling: set b=0 velocity zero at borders; advection clamps sample coords to [0.5, W-1.5].

Let me write it. Also cap devicePixelRatio for rendering? Rendering is small ImageData + scaled drawImage, cheap. Canvas CSS fullscreen; set canvas.width=innerWidth etc. Actually for upscaling, draw to offscreen canvas at grid size then drawImage to main canvas scaled to full — smoothing gives nice blur.

Also add slight fade of dye (multiply 0.995) so it dissipates.

Test with browser tool: reload, screenshot, drag, screenshot, clear click, drag, screenshot. Console inspect.

Write the file.

Seed visible. Now drag test.

Dye follows the drag and head is curled — momentum persists. Let me wait a moment after release and screenshot to check swirling continues, then drag in another direction.

Motion continues after release (dye keeps moving and curling, dissipating gradually). Good. Now change color? The color input — hard to set via click. I can just drag in another direction with same color; or set color via JS isn't available in tools. Clicking color input opens native picker; skip — test Clear and fresh drag. Also test Pause.

Clear works — canvas empty. Now drag in another direction (diagonal up) and check fresh flow, then pause test.

Fresh flow starts after clear, in the new direction. Now test Pause — click Pause, then verify motion stops (two screenshots identical). Then resume. Also test color selector — clicking input[type=color] opens a native picker that I can't easily interact with; skip interactive verification, the handler reads colorInput.value on each splat which is straightforward.

Button toggled to "Resume", sim paused (dye frozen). Resume it to leave in running state. Then done. Also confirm clicking resume works.

All checks pass. Console has only an iframe sandbox warning (harness-related, not from our code). Done — report.