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<title>Fluid Simulation</title>
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<script id="2d-vertex-shader" type="x-shader/x-vertex">
attribute vec2 a_position;
void main() {
gl_Position = vec4(a_position, 0, 1);
}
</script>
<script id="2d-render-shader" type="x-shader/x-fragment">
precision mediump float;
gl_FragColor = vec4(texture2D(u_material, fragCoord/u_textureSize).x, 0, 1, 1);
<script id="gradientSubtractionShader" type="x-shader/x-fragment">
precision mediump float;
uniform sampler2D u_velocity;
uniform sampler2D u_pressure;
uniform vec2 u_textureSize;
uniform float u_const;
void main() {
vec2 fragCoord = gl_FragCoord.xy;
vec2 currentVelocity = texture2D(u_velocity, fragCoord/u_textureSize).xy;
float n = texture2D(u_pressure, (fragCoord+vec2(0.0, 1.0))/u_textureSize).x;
float s = texture2D(u_pressure, (fragCoord+vec2(0.0, -1.0))/u_textureSize).x;
float e = texture2D(u_pressure, (fragCoord+vec2(1.0, 0.0))/u_textureSize).x;
float w = texture2D(u_pressure, (fragCoord+vec2(-1.0, 0.0))/u_textureSize).x;
gl_FragColor = vec4(currentVelocity-u_const*vec2(e-w, n-s), 0, 0);
}
</script>
<script id="divergenceShader" type="x-shader/x-fragment">
precision mediump float;
uniform sampler2D u_velocity;
uniform vec2 u_textureSize;
void main() {
vec2 fragCoord = gl_FragCoord.xy;
//finite difference formulation of divergence
float n = texture2D(u_velocity, (fragCoord+vec2(0.0, 1.0))/u_textureSize).y;
float s = texture2D(u_velocity, (fragCoord+vec2(0.0, -1.0))/u_textureSize).y;
float e = texture2D(u_velocity, (fragCoord+vec2(1.0, 0.0))/u_textureSize).x;
float w = texture2D(u_velocity, (fragCoord+vec2(-1.0, 0.0))/u_textureSize).x;
float div = u_const*(e-w + n-s);
gl_FragColor = vec4(div, div, 0, 0);
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<script id="forceShader" type="x-shader/x-fragment">
precision mediump float;
uniform sampler2D u_velocity;
uniform vec2 u_textureSize;
uniform vec2 u_mouseCoord;
uniform vec2 u_mouseDir;
uniform float u_mouseEnable;
uniform float u_dt;
const float reciprocalRadius = 0.01;
void main() {
vec2 fragCoord = gl_FragCoord.xy;
vec2 currentVelocity = texture2D(u_velocity, fragCoord/u_textureSize).xy;
if (u_mouseEnable == 1.0){
vec2 pxDist = fragCoord - u_mouseCoord;
currentVelocity += u_mouseDir*u_dt*exp(-(pxDist.x*pxDist.x+pxDist.y*pxDist.y)*reciprocalRadius);
}
gl_FragColor = vec4(currentVelocity, 0, 0);
}
</script>
uniform vec2 u_textureSize;
uniform float u_alpha;
uniform float u_reciprocalBeta;
void main() {
vec2 fragCoord = gl_FragCoord.xy;
vec2 currentState = texture2D(u_b, fragCoord/u_textureSize).xy;
vec2 n = texture2D(u_x, (fragCoord+vec2(0.0, 1.0))/u_textureSize).xy;
vec2 s = texture2D(u_x, (fragCoord+vec2(0.0, -1.0))/u_textureSize).xy;
vec2 e = texture2D(u_x, (fragCoord+vec2(1.0, 0.0))/u_textureSize).xy;
vec2 w = texture2D(u_x, (fragCoord+vec2(-1.0, 0.0))/u_textureSize).xy;
vec2 nextState = (n + s + e + w + u_alpha * currentState) * u_reciprocalBeta;
gl_FragColor = vec4(nextState, 0, 0);
}
uniform sampler2D u_velocity;
uniform sampler2D u_material;
vec2 currentVelocity = texture2D(u_velocity, fragCoord/u_textureSize).xy;
gl_FragColor = vec4(texture2D(u_material, fragCoord/u_textureSize).xy, 0, 0);
return;
}
vec2 pxCenter = vec2(0.5, 0.5);
//if (pos.x < 0.0 || pos.x >= u_textureSize.x-1.0 || pos.y < 0.0 || pos.y >= u_textureSize.y-1.0){
// //boundary
// gl_FragColor = vec4(0);
// return;
//}
//periodic boundary
if (pos.x < 0.0) pos.x += u_textureSize.x-1.0;
if (pos.x >= u_textureSize.x-1.0) pos.x -= u_textureSize.x-1.0;
if (pos.y < 0.0) pos.y += u_textureSize.y-1.0;
if (pos.y >= u_textureSize.y-1.0) pos.y -= u_textureSize.y-1.0;
//bilinear interp between nearest cells
vec2 ceiled = ceil(pos);
vec2 floored = floor(pos);
vec2 n = texture2D(u_material, (ceiled+pxCenter)/u_textureSize).xy;//actually ne
vec2 s = texture2D(u_material, (floored+pxCenter)/u_textureSize).xy;//actually sw
vec2 se = texture2D(u_material, (vec2(ceiled.x, floored.y)+pxCenter)/u_textureSize).xy;
vec2 nw = texture2D(u_material, (vec2(floored.x, ceiled.y)+pxCenter)/u_textureSize).xy;
n = n*(pos.x-floored.x) + nw*(ceiled.x-pos.x);
s = se*(pos.x-floored.x) + s*(ceiled.x-pos.x);
}
if (ceiled.y != floored.y){
materialVal = n*(pos.y-floored.y) + s*(ceiled.y-pos.y);
}
}
</script>
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<b>Fluid Simulation Shader</b><br/><br/>
<a href="https://pdfs.semanticscholar.org/84b8/c7b7eecf90ebd9d54a51544ca0f8ff93c137.pdf" target="_blank">Real-time ink simulation using a grid-particle method</a> - a method for real-time simulation of ink
in water using a coarse-grained fluid simulation with a particle simulation on top.<br/>
<a href="http://http.developer.nvidia.com/GPUGems/gpugems_ch38.html" target="_blank">Fast Fluid Dynamics Simulation on the GPU</a> - a very well written tutorial about programming the Navier-Stokes equations on a GPU.<br/>
<a href="http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/ns.pdf" target="_blank">Stable Fluids</a> - a paper about stable numerical methods for evaluating Navier-Stokes on a discrete grid.<br/>
<br/>
By <a href="http://www.amandaghassaei.com/" target="_blank">Amanda Ghassaei</a>, code on <a href="https://github.com/amandaghassaei/FluidSimulation" target="_blank">Github</a>.