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Realtime Fluid Simulation: Projection

The core of most real-time fluid simulators, like the one in EmberGen, are based on the "Stable Fluids" algorithm by Jos Stam, which to my knowledge was first presented at SIGGRAPH '99. This is a post about one part of this algorithm that's often underestimated: Projection

MG4_F32.mp4

Stable Fluids

The Stable Fluids algorithm solves a subset of the famous "Navier Stokes equations", which describe how fluids interact and move. In particular, it typically solves what's called the "incompressible Euler equations", where viscous forces are often ignored.

	1) Clone and build WebKit

	git clone https://github.com/WebKit/WebKit.git WebKit
	cd WebKit
	Tools/Scripts/build-webkit -cmakeargs="-DENABLE_WEBGPU_BY_DEFAULT=1" --debug


	2) Run your app

	__XPC_METAL_CAPTURE_ENABLED=1 Tools/Scripts/run-minibrowser --debug --url http://localhost:5000/index.html#/loaders/gsplat

	// This is Twigl's "geekest mode" so the code runs inside a "main" function.
	// FC.xy is fragcoord
	// r.xy is resolution
	// t is time (in seconds I think)
	// o.rgba is output color

	// This is the original code, before any readability improvements:
	/*

	#define X(S,D)I=ivec3(S);D=fract(float(I.x^I.y^I.z)*PI

	const {hexToHsluv, hsluvToHex} = require('hsluv')

	const interpolate = (a1, a2) => x => a1.map((c, i) => c + (a2[i] - c) * x)
	const range = steps => Array.from({length: steps + 1}, (_, i) => i / steps)

	const stopsToHsluv = (start, end) => {
	const hStart = hexToHsluv(start)
	const hEnd = hexToHsluv(end)

	const throughZero = Math.abs(hStart[0] - hEnd[0]) > 180

	#! /bin/bash
	# This command converts audio according to the specifications listed in the Spark docs:
	# https://sparkar.facebook.com/ar-studio/learn/documentation/docs/audio
	# mono m4a, 44.1kHz sample rate, 16-bit-depth resolution
	# Usage:
	# convert-audio.sh myaudio.mp3 converted.m4a
	# Notes:
	# Always use m4a for output file type
	# Change "64k" to a higher value to improve bitrate/quality. e.g. 96k 128k 192k

	function walk(node) {
	// I stole this function from here:
	// http://is.gd/mwZp7E

	var child, next;

	var tagName = node.tagName ? node.tagName.toLowerCase() : "";
	if (tagName == 'input' \|\| tagName == 'textarea') {
	return;
	}

	copy() {
	try {
	if ((navigator as any).clipboard) {
	(navigator as any).clipboard.writeText(this.couponCode);
	} else if ((window as any).clipboardData) { // IE
	(window as any).clipboardData.setData('text', this.couponCode);
	} else { // other browsers, iOS, Mac OS
	this.copyToClipboard(this.inputEl.nativeElement);
	}
	this.tooltipText = 'Copied to Clipboard.'; // copy succeed.

	//////////////////////////////////////////////////////////////////////////
	//////////////////////////////////////////////////////////////////////////
	//////////////////////////////////////////////////////////////////////////
	// Plexus
	// Collab by Ben Ursu & Dan Cronin \| Afrosquared
	// Spark AR Studio
	// Instagram \| https://www.instagram.com/a/r/?effect_id=2029175904053487