文于止墨

欧拉流体模拟

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由

文止墨
于 , , , ,

关于著作权详情，请参照代码开头注释。

演示界面请看这里

HTML
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<!DOCTYPE html>
<html>
	<meta name="viewport" content="width=device-width, initial-scale=1.0">

	<head>
		<title>Euler Fluid</title>
		<style>
			body {
				font-family: verdana; 
				font-size: 15px;
			}			
			.button {
				background-color: #606060;
				border: none;
				color: white;
				padding: 10px 10px;
				font-size: 16px;
				margin: 4px 2px;
				cursor: pointer;
			}
			.slider {
				-webkit-appearance: none;
                appearance: none;
				width: 80px;
				height: 6px;
				border-radius: 5px;
				background: #d3d3d3;
				outline: none;
				opacity: 0.7;
				-webkit-transition: .2s;
				transition: opacity .2s;
			}
		</style>
	</head>
	
<body>

	<button class="button" onclick="setupScene(1)">Wind Tunnel</button>
	<button class="button" onclick="setupScene(3)">Hires Tunnel</button>
	<button class="button" onclick="setupScene(0)">Tank</button>
	<button class="button" onclick="setupScene(2)">Paint</button>
	<input type = "checkbox" id = "streamButton" onclick = "scene.showStreamlines = !scene.showStreamlines">Streamlines
	<input type = "checkbox" id = "velocityButton" onclick = "scene.showVelocities = !scene.showVelocities">Velocities
	<input type = "checkbox" name = "field" id = "pressureButton" onclick = "scene.showPressure = !scene.showPressure;"> Pressure
	<input type = "checkbox" name = "field" id = "smokeButton" onclick = "scene.showSmoke = !scene.showSmoke;" checked>Smoke
	<input type = "checkbox" id = "overrelaxButton" onclick = "scene.overRelaxation = scene.overRelaxation == 1.0 ? 1.9 : 1.0" checked>Overrelax
	<br>
	<canvas id="myCanvas" style="border:2px solid"></canvas>
	
<script>

	var canvas = document.getElementById("myCanvas");
	var c = canvas.getContext("2d");	
	canvas.width = window.innerWidth - 20;
	canvas.height = window.innerHeight - 100;

	canvas.focus();

	var simHeight = 1.1;	
	var cScale = canvas.height / simHeight;
	var simWidth = canvas.width / cScale;

	var U_FIELD = 0;
	var V_FIELD = 1;
	var S_FIELD = 2;

	var cnt = 0;

	function cX(x) {
		return x * cScale;
	}

	function cY(y) {
		return canvas.height - y * cScale;
	}

	// ----------------- start of simulator ------------------------------

	class Fluid {
		constructor(density, numX, numY, h) {
			this.density = density;
			this.numX = numX + 2; 
			this.numY = numY + 2;
			this.numCells = this.numX * this.numY;
			this.h = h;
			this.u = new Float32Array(this.numCells);
			this.v = new Float32Array(this.numCells);
			this.newU = new Float32Array(this.numCells);
			this.newV = new Float32Array(this.numCells);
			this.p = new Float32Array(this.numCells);
			this.s = new Float32Array(this.numCells);
			this.m = new Float32Array(this.numCells);
			this.newM = new Float32Array(this.numCells);
			this.m.fill(1.0)
			var num = numX * numY;
		}

		integrate(dt, gravity) {
			var n = this.numY;
			for (var i = 1; i < this.numX; i++) {
				for (var j = 1; j < this.numY-1; j++) {
					if (this.s[i*n + j] != 0.0 && this.s[i*n + j-1] != 0.0)
						this.v[i*n + j] += gravity * dt;
				}	 
			}
		}

		solveIncompressibility(numIters, dt) {

			var n = this.numY;
			var cp = this.density * this.h / dt;

			for (var iter = 0; iter < numIters; iter++) {

				for (var i = 1; i < this.numX-1; i++) {
					for (var j = 1; j < this.numY-1; j++) {

						if (this.s[i*n + j] == 0.0)
							continue;

						var s = this.s[i*n + j];
						var sx0 = this.s[(i-1)*n + j];
						var sx1 = this.s[(i+1)*n + j];
						var sy0 = this.s[i*n + j-1];
						var sy1 = this.s[i*n + j+1];
						var s = sx0 + sx1 + sy0 + sy1;
						if (s == 0.0)
							continue;

						var div = this.u[(i+1)*n + j] - this.u[i*n + j] + 
							this.v[i*n + j+1] - this.v[i*n + j];

						var p = -div / s;
						p *= scene.overRelaxation;
						this.p[i*n + j] += cp * p;

						this.u[i*n + j] -= sx0 * p;
						this.u[(i+1)*n + j] += sx1 * p;
						this.v[i*n + j] -= sy0 * p;
						this.v[i*n + j+1] += sy1 * p;
					}
				}
			}
		}

		extrapolate() {
			var n = this.numY;
			for (var i = 0; i < this.numX; i++) {
				this.u[i*n + 0] = this.u[i*n + 1];
				this.u[i*n + this.numY-1] = this.u[i*n + this.numY-2]; 
			}
			for (var j = 0; j < this.numY; j++) {
				this.v[0*n + j] = this.v[1*n + j];
				this.v[(this.numX-1)*n + j] = this.v[(this.numX-2)*n + j] 
			}
		}

		sampleField(x, y, field) {
			var n = this.numY;
			var h = this.h;
			var h1 = 1.0 / h;
			var h2 = 0.5 * h;

			x = Math.max(Math.min(x, this.numX * h), h);
			y = Math.max(Math.min(y, this.numY * h), h);

			var dx = 0.0;
			var dy = 0.0;

			var f;

			switch (field) {
				case U_FIELD: f = this.u; dy = h2; break;
				case V_FIELD: f = this.v; dx = h2; break;
				case S_FIELD: f = this.m; dx = h2; dy = h2; break

			}

			var x0 = Math.min(Math.floor((x-dx)*h1), this.numX-1);
			var tx = ((x-dx) - x0*h) * h1;
			var x1 = Math.min(x0 + 1, this.numX-1);
			
			var y0 = Math.min(Math.floor((y-dy)*h1), this.numY-1);
			var ty = ((y-dy) - y0*h) * h1;
			var y1 = Math.min(y0 + 1, this.numY-1);

			var sx = 1.0 - tx;
			var sy = 1.0 - ty;

			var val = sx*sy * f[x0*n + y0] +
				tx*sy * f[x1*n + y0] +
				tx*ty * f[x1*n + y1] +
				sx*ty * f[x0*n + y1];
			
			return val;
		}

		avgU(i, j) {
			var n = this.numY;
			var u = (this.u[i*n + j-1] + this.u[i*n + j] +
				this.u[(i+1)*n + j-1] + this.u[(i+1)*n + j]) * 0.25;
			return u;
				
		}

		avgV(i, j) {
			var n = this.numY;
			var v = (this.v[(i-1)*n + j] + this.v[i*n + j] +
				this.v[(i-1)*n + j+1] + this.v[i*n + j+1]) * 0.25;
			return v;
		}

		advectVel(dt) {

			this.newU.set(this.u);
			this.newV.set(this.v);

			var n = this.numY;
			var h = this.h;
			var h2 = 0.5 * h;

			for (var i = 1; i < this.numX; i++) {
				for (var j = 1; j < this.numY; j++) {

					cnt++;

					// u component
					if (this.s[i*n + j] != 0.0 && this.s[(i-1)*n + j] != 0.0 && j < this.numY - 1) {
						var x = i*h;
						var y = j*h + h2;
						var u = this.u[i*n + j];
						var v = this.avgV(i, j);
//						var v = this.sampleField(x,y, V_FIELD);
						x = x - dt*u;
						y = y - dt*v;
						u = this.sampleField(x,y, U_FIELD);
						this.newU[i*n + j] = u;
					}
					// v component
					if (this.s[i*n + j] != 0.0 && this.s[i*n + j-1] != 0.0 && i < this.numX - 1) {
						var x = i*h + h2;
						var y = j*h;
						var u = this.avgU(i, j);
//						var u = this.sampleField(x,y, U_FIELD);
						var v = this.v[i*n + j];
						x = x - dt*u;
						y = y - dt*v;
						v = this.sampleField(x,y, V_FIELD);
						this.newV[i*n + j] = v;
					}
				}	 
			}

			this.u.set(this.newU);
			this.v.set(this.newV);
		}

		advectSmoke(dt) {

			this.newM.set(this.m);

			var n = this.numY;
			var h = this.h;
			var h2 = 0.5 * h;

			for (var i = 1; i < this.numX-1; i++) {
				for (var j = 1; j < this.numY-1; j++) {

					if (this.s[i*n + j] != 0.0) {
						var u = (this.u[i*n + j] + this.u[(i+1)*n + j]) * 0.5;
						var v = (this.v[i*n + j] + this.v[i*n + j+1]) * 0.5;
						var x = i*h + h2 - dt*u;
						var y = j*h + h2 - dt*v;

						this.newM[i*n + j] = this.sampleField(x,y, S_FIELD);
 					}
				}	 
			}
			this.m.set(this.newM);
		}

		// ----------------- end of simulator ------------------------------


		simulate(dt, gravity, numIters) {

			this.integrate(dt, gravity);

			this.p.fill(0.0);
			this.solveIncompressibility(numIters, dt);

			this.extrapolate();
			this.advectVel(dt);
			this.advectSmoke(dt);
		}
	}

	var scene = 
	{
		gravity : -9.81,
		dt : 1.0 / 120.0,
		numIters : 100,
		frameNr : 0,
		overRelaxation : 1.9,
		obstacleX : 0.0,
		obstacleY : 0.0,
		obstacleRadius: 0.15,
		paused: false,
		sceneNr: 0,
		showObstacle: false,
		showStreamlines: false,
		showVelocities: false,	
		showPressure: false,
		showSmoke: true,
		fluid: null
	};

	function setupScene(sceneNr = 0) 
	{
		scene.sceneNr = sceneNr;
		scene.obstacleRadius = 0.15;
		scene.overRelaxation = 1.9;

		scene.dt = 1.0 / 60.0;
		scene.numIters = 40;

		var res = 100;
		
		if (sceneNr == 0)
			res = 50;
		else if (sceneNr == 3)
			res = 200;

		var domainHeight = 1.0;
		var domainWidth = domainHeight / simHeight * simWidth;
		var h = domainHeight / res;

		var numX = Math.floor(domainWidth / h);
		var numY = Math.floor(domainHeight / h);

		var density = 1000.0;

		f = scene.fluid = new Fluid(density, numX, numY, h);

		var n = f.numY;

		if (sceneNr == 0) {   		// tank

			for (var i = 0; i < f.numX; i++) {
				for (var j = 0; j < f.numY; j++) {
					var s = 1.0;	// fluid
					if (i == 0 || i == f.numX-1 || j == 0)
						s = 0.0;	// solid
					f.s[i*n + j] = s
				}
			}
			scene.gravity = -9.81;
			scene.showPressure = true;
			scene.showSmoke = false;
			scene.showStreamlines = false;
			scene.showVelocities = false;
		}
		else if (sceneNr == 1 || sceneNr == 3) { // vortex shedding

			var inVel = 2.0;
			for (var i = 0; i < f.numX; i++) {
				for (var j = 0; j < f.numY; j++) {
					var s = 1.0;	// fluid
					if (i == 0 || j == 0 || j == f.numY-1)
						s = 0.0;	// solid
					f.s[i*n + j] = s

					if (i == 1) {
						f.u[i*n + j] = inVel;
					}
				}
			}

			var pipeH = 0.1 * f.numY;
			var minJ = Math.floor(0.5 * f.numY - 0.5*pipeH);
			var maxJ = Math.floor(0.5 * f.numY + 0.5*pipeH);

			for (var j = minJ; j < maxJ; j++)
				f.m[j] = 0.0;

			setObstacle(0.4, 0.5, true)

			scene.gravity = 0.0;
			scene.showPressure = false;
			scene.showSmoke = true;
			scene.showStreamlines = false;
			scene.showVelocities = false;

			if (sceneNr == 3) {
				scene.dt = 1.0 / 120.0;
				scene.numIters = 100;
				scene.showPressure = true;
			}

		}
		else if (sceneNr == 2) { // paint

			scene.gravity = 0.0;
			scene.overRelaxation = 1.0;
			scene.showPressure = false;
			scene.showSmoke = true;
			scene.showStreamlines = false;
			scene.showVelocities = false;
			scene.obstacleRadius = 0.1;
		}

		document.getElementById("streamButton").checked = scene.showStreamlines;
		document.getElementById("velocityButton").checked = scene.showVelocities;
		document.getElementById("pressureButton").checked = scene.showPressure;
		document.getElementById("smokeButton").checked = scene.showSmoke;
		document.getElementById("overrelaxButton").checked = scene.overRelaxation > 1.0;
		
	}


	// draw -------------------------------------------------------

	function setColor(r,g,b) {
		c.fillStyle = `rgb(
			${Math.floor(255*r)},
			${Math.floor(255*g)},
			${Math.floor(255*b)})`
		c.strokeStyle = `rgb(
			${Math.floor(255*r)},
			${Math.floor(255*g)},
			${Math.floor(255*b)})`
	}

	function getSciColor(val, minVal, maxVal) {
		val = Math.min(Math.max(val, minVal), maxVal- 0.0001);
		var d = maxVal - minVal;
		val = d == 0.0 ? 0.5 : (val - minVal) / d;
		var m = 0.25;
		var num = Math.floor(val / m);
		var s = (val - num * m) / m;
		var r, g, b;

		switch (num) {
			case 0 : r = 0.0; g = s; b = 1.0; break;
			case 1 : r = 0.0; g = 1.0; b = 1.0-s; break;
			case 2 : r = s; g = 1.0; b = 0.0; break;
			case 3 : r = 1.0; g = 1.0 - s; b = 0.0; break;
		}

		return[255*r,255*g,255*b, 255]
	}

	function draw() 
	{
		c.clearRect(0, 0, canvas.width, canvas.height);

		c.fillStyle = "#FF0000";
		f = scene.fluid;
		n = f.numY;

		var cellScale = 1.1;

		var h = f.h;

		minP = f.p[0];
		maxP = f.p[0];

		for (var i = 0; i < f.numCells; i++) {
			minP = Math.min(minP, f.p[i]);
			maxP = Math.max(maxP, f.p[i]);
		}

		id = c.getImageData(0,0, canvas.width, canvas.height)

		var color = [255, 255, 255, 255]

		for (var i = 0; i < f.numX; i++) {
			for (var j = 0; j < f.numY; j++) {

				if (scene.showPressure) {
					var p = f.p[i*n + j];
					var s = f.m[i*n + j];
					color = getSciColor(p, minP, maxP);
					if (scene.showSmoke) {
						color[0] = Math.max(0.0, color[0] - 255*s);
						color[1] = Math.max(0.0, color[1] - 255*s);
						color[2] = Math.max(0.0, color[2] - 255*s);
					}
				}
				else if (scene.showSmoke) {
					var s = f.m[i*n + j];
					color[0] = 255*s;
					color[1] = 255*s;
					color[2] = 255*s;
					if (scene.sceneNr == 2)
						color = getSciColor(s, 0.0, 1.0);
				}
				else if (f.s[i*n + j] == 0.0) {
					color[0] = 0;
					color[1] = 0;
					color[2] = 0;
				}

				var x = Math.floor(cX(i * h));
				var y = Math.floor(cY((j+1) * h));
				var cx = Math.floor(cScale * cellScale * h) + 1;
				var cy = Math.floor(cScale * cellScale * h) + 1;

				r = color[0];
				g = color[1];
				b = color[2];

				for (var yi = y; yi < y + cy; yi++) {
					var p = 4 * (yi * canvas.width + x)

					for (var xi = 0; xi < cx; xi++) {
						id.data[p++] = r;
						id.data[p++] = g;
						id.data[p++] = b;
						id.data[p++] = 255;
					}
				}
			}
		}

		c.putImageData(id, 0, 0);

		if (scene.showVelocities) {

			c.strokeStyle = "#000000";	
			scale = 0.02;	

			for (var i = 0; i < f.numX; i++) {
				for (var j = 0; j < f.numY; j++) {

					var u = f.u[i*n + j];
					var v = f.v[i*n + j];

					c.beginPath();

					x0 = cX(i * h);
					x1 = cX(i * h + u * scale);
					y = cY((j + 0.5) * h );

					c.moveTo(x0, y);
					c.lineTo(x1, y);
					c.stroke();

					x = cX((i + 0.5) * h);
					y0 = cY(j * h );
					y1 = cY(j * h + v * scale)

					c.beginPath();
					c.moveTo(x, y0);
					c.lineTo(x, y1);
					c.stroke();

				}
			}
		}

		if (scene.showStreamlines) {

			var segLen = f.h * 0.2;
			var numSegs = 15;

			c.strokeStyle = "#000000";

			for (var i = 1; i < f.numX - 1; i += 5) {
				for (var j = 1; j < f.numY - 1; j += 5) {

					var x = (i + 0.5) * f.h;
					var y = (j + 0.5) * f.h;

					c.beginPath();
					c.moveTo(cX(x), cY(y));

					for (var n = 0; n < numSegs; n++) {
						var u = f.sampleField(x, y, U_FIELD);
						var v = f.sampleField(x, y, V_FIELD);
						l = Math.sqrt(u*u + v*v);
						// x += u/l * segLen;
						// y += v/l * segLen;
						x += u * 0.01;
						y += v * 0.01;
						if (x > f.numX * f.h)
							break;

						c.lineTo(cX(x), cY(y));
					}
					c.stroke();
				}
			}
		}

		if (scene.showObstacle) {

			c.strokeW
			r = scene.obstacleRadius + f.h;
			if (scene.showPressure)
				c.fillStyle = "#000000";
			else
				c.fillStyle = "#DDDDDD";
			c.beginPath();	
			c.arc(
				cX(scene.obstacleX), cY(scene.obstacleY), cScale * r, 0.0, 2.0 * Math.PI); 
			c.closePath();
			c.fill();

			c.lineWidth = 3.0;
			c.strokeStyle = "#000000";
			c.beginPath();	
			c.arc(
				cX(scene.obstacleX), cY(scene.obstacleY), cScale * r, 0.0, 2.0 * Math.PI); 
			c.closePath();
			c.stroke();
			c.lineWidth = 1.0;
		}

		if (scene.showPressure) {
			var s = "pressure: " + minP.toFixed(0) + " - " + maxP.toFixed(0) + " N/m";
			c.fillStyle ="#000000";
			c.font = "16px Arial";
			c.fillText(s, 10, 35);
		}
	}

	function setObstacle(x, y, reset) {

		var vx = 0.0;
		var vy = 0.0;

		if (!reset) {
			vx = (x - scene.obstacleX) / scene.dt;
			vy = (y - scene.obstacleY) / scene.dt;
		}

		scene.obstacleX = x;
		scene.obstacleY = y;
		var r = scene.obstacleRadius;
		var f = scene.fluid;
		var n = f.numY;
		var cd = Math.sqrt(2) * f.h;

		for (var i = 1; i < f.numX-2; i++) {
			for (var j = 1; j < f.numY-2; j++) {

				f.s[i*n + j] = 1.0;

				dx = (i + 0.5) * f.h - x;
				dy = (j + 0.5) * f.h - y;

				if (dx * dx + dy * dy < r * r) {
					f.s[i*n + j] = 0.0;
					if (scene.sceneNr == 2) 
						f.m[i*n + j] = 0.5 + 0.5 * Math.sin(0.1 * scene.frameNr)
					else 
						f.m[i*n + j] = 1.0;
					f.u[i*n + j] = vx;
					f.u[(i+1)*n + j] = vx;
					f.v[i*n + j] = vy;
					f.v[i*n + j+1] = vy;
				}
			}
		}
		
		scene.showObstacle = true;
	}

	// interaction -------------------------------------------------------

	var mouseDown = false;

	function startDrag(x, y) {
		let bounds = canvas.getBoundingClientRect();

		let mx = x - bounds.left - canvas.clientLeft;
		let my = y - bounds.top - canvas.clientTop;
		mouseDown = true;

		x = mx / cScale;
		y = (canvas.height - my) / cScale;

		setObstacle(x,y, true);
	}

	function drag(x, y) {
		if (mouseDown) {
			let bounds = canvas.getBoundingClientRect();
			let mx = x - bounds.left - canvas.clientLeft;
			let my = y - bounds.top - canvas.clientTop;
			x = mx / cScale;
			y = (canvas.height - my) / cScale;
			setObstacle(x,y, false);
		}
	}

	function endDrag() {
		mouseDown = false;
	}

	canvas.addEventListener('mousedown', event => {
		startDrag(event.x, event.y);
	});

	canvas.addEventListener('mouseup', event => {
		endDrag();
	});

	canvas.addEventListener('mousemove', event => {
		drag(event.x, event.y);
	});

	canvas.addEventListener('touchstart', event => {
		startDrag(event.touches[0].clientX, event.touches[0].clientY)
	});

	canvas.addEventListener('touchend', event => {
		endDrag()
	});

	canvas.addEventListener('touchmove', event => {
		event.preventDefault();
		event.stopImmediatePropagation();
		drag(event.touches[0].clientX, event.touches[0].clientY)
	}, { passive: false});


	document.addEventListener('keydown', event => {
		switch(event.key) {
			case 'p': scene.paused = !scene.paused; break;
			case 'm': scene.paused = false; simulate(); scene.paused = true; break;
		}
	});

	function toggleStart()
	{
		var button = document.getElementById('startButton');
		if (scene.paused)
			button.innerHTML = "Stop";
		else
			button.innerHTML = "Start";
		scene.paused = !scene.paused;
	}

	// main -------------------------------------------------------

	function simulate() 
	{
		if (!scene.paused)
			scene.fluid.simulate(scene.dt, scene.gravity, scene.numIters)
			scene.frameNr++;
	}

	function update() {
		simulate();
		draw();
		requestAnimationFrame(update);
	}
	
	setupScene(1);
	update();
	
</script> 
</body>
</html>

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