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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="boundaryShader" type="x-shader/x-fragment">
precision mediump float;
uniform sampler2D u_texture;
uniform float u_scale;
uniform vec2 u_textureSize;
void main() {
vec2 fragCoord = gl_FragCoord.xy;
if (fragCoord.x < 1.0){
gl_FragColor = u_scale*texture2D(u_texture, (fragCoord + vec2(1.0, 0.0))/u_textureSize);
return;
} else if (fragCoord.x >= u_textureSize.x-1.0){
gl_FragColor = u_scale*texture2D(u_texture, (fragCoord + vec2(-1.0, 0.0))/u_textureSize);
return;
} else if (fragCoord.y < 1.0){
gl_FragColor = u_scale*texture2D(u_texture, (fragCoord + vec2(0.0, 1.0))/u_textureSize);
return;
} else if (fragCoord.y >= u_textureSize.y-1.0){
gl_FragColor = u_scale*texture2D(u_texture, (fragCoord + vec2(0.0, -1.0))/u_textureSize);
return;
}
gl_FragColor = texture2D(u_texture, (fragCoord)/u_textureSize);
}
</script>
<script id="2d-render-shader" type="x-shader/x-fragment">
precision mediump float;
uniform sampler2D u_material;
uniform vec2 u_textureSize;
void main() {
vec2 fragCoord = gl_FragCoord.xy;
vec3 background = vec3(0.96, 0.87, 0.68);
vec3 material1 = vec3(0.925, 0, 0.55);
vec3 material2 = vec3(0.0, 0.70, 0.63);
vec3 material3 = vec3(0.52, 0.81, 0.70);
vec3 material4 = vec3(1.0, 0.7, 0.07);
float val = texture2D(u_material, fragCoord/u_textureSize).x/2.0;
if (val > 1.0) val = 1.0;
if (val < 0.0) val = 0.0;
vec3 color = vec3(0.0);
if (val < 0.25) {
val *= 4.0;
color = background*(1.0-val) + material1*val;
} else if (val < 0.5) {
val -= 0.25;
val *= 4.0;
color = material1*(1.0-val) + material2*val;
} else if (val < 0.75) {
val -= 0.50;
val *= 4.0;
color = material2*(1.0-val) + material3*val;
} else {
val -= 0.75;
val *= 4.0;
color = material3*(1.0-val) + material4*val;
}
gl_FragColor = vec4(color, 1);
}
</script>
<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;
uniform float u_const;
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, 0, 0, 0);
}
</script>
<script id="addMaterialShader" type="x-shader/x-fragment">
precision mediump float;
uniform sampler2D u_material;
uniform vec2 u_textureSize;
uniform vec2 u_mouseCoord;
uniform float u_mouseLength;
uniform float u_mouseEnable;
uniform float u_reciprocalRadius;
void main() {
vec2 fragCoord = gl_FragCoord.xy;
float currentMaterial = texture2D(u_material, fragCoord/u_textureSize).x;
if (u_mouseEnable == 1.0){
vec2 pxDist = fragCoord - u_mouseCoord;
currentMaterial += u_mouseLength*0.1*exp(-(pxDist.x*pxDist.x+pxDist.y*pxDist.y)*u_reciprocalRadius);
}
if (currentMaterial > 0.0) currentMaterial -= 0.002;//material disappears over time
gl_FragColor = vec4(currentMaterial, 0, 0, 0);
}
</script>
<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_reciprocalRadius;
uniform float u_dt;
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)*u_reciprocalRadius);
}
gl_FragColor = vec4(currentVelocity, 0, 0);
}
</script>
<script id="jacobiShader" type="x-shader/x-fragment">
precision mediump float;
uniform sampler2D u_b;
uniform sampler2D u_x;
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;
//implicitly solve diffusion via jacobi iteration
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);
}
</script>
<script id="advectShader" type="x-shader/x-fragment">
precision mediump float;
uniform sampler2D u_velocity;
uniform sampler2D u_material;
uniform vec2 u_textureSize;
uniform float u_scale;
uniform float u_dt;
vec2 bilinearInterp(vec2 pos, sampler2D texture, vec2 size){
//bilinear interp between nearest cells
vec2 pxCenter = vec2(0.5, 0.5);
vec2 ceiled = ceil(pos);
vec2 floored = floor(pos);
vec2 n = texture2D(texture, (ceiled+pxCenter)/size).xy;//actually ne
vec2 s = texture2D(texture, (floored+pxCenter)/size).xy;//actually sw
if (ceiled.x != floored.x){
vec2 se = texture2D(texture, (vec2(ceiled.x, floored.y)+pxCenter)/size).xy;
vec2 nw = texture2D(texture, (vec2(floored.x, ceiled.y)+pxCenter)/size).xy;
n = n*(pos.x-floored.x) + nw*(ceiled.x-pos.x);
s = se*(pos.x-floored.x) + s*(ceiled.x-pos.x);
}
vec2 materialVal = n;
if (ceiled.y != floored.y){
materialVal = n*(pos.y-floored.y) + s*(ceiled.y-pos.y);
}
return materialVal;
}
void main() {
vec2 fragCoord = gl_FragCoord.xy;
vec2 pxCenter = vec2(0.5, 0.5);
vec2 currentVelocity;
if (u_scale == 1.0) currentVelocity = 1.0/u_scale*texture2D(u_velocity, fragCoord/u_textureSize).xy;
else {
vec2 scaledCoord = (fragCoord-pxCenter)*u_scale;
vec2 scaledSize = u_textureSize*u_scale;
currentVelocity = 1.0/u_scale*bilinearInterp(vec2(1.0, 1.0) + scaledCoord/scaledSize*(scaledSize-vec2(3.0, 3.0)), u_velocity, scaledSize);
}
//implicitly solve advection
if (length(currentVelocity) == 0.0) {//no velocity
gl_FragColor = vec4(texture2D(u_material, fragCoord/u_textureSize).xy, 0, 0);
return;
}
vec2 pos = fragCoord - pxCenter - u_dt*currentVelocity;
vec2 materialVal;
//empty boundary
if (pos.x < 0.0 || pos.x >= u_textureSize.x-1.0 || pos.y < 0.0 || pos.y >= u_textureSize.y-1.0) materialVal = vec2(0.0);
else materialVal = bilinearInterp(pos, u_material, u_textureSize);
gl_FragColor = vec4(materialVal, 0, 0);
}
</script>
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<b>Fluid Simulation Shader</b><br/><br/>
I used the following sources to write this simulation:<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>.
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