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static const std::string COLLIDE_SHADER_CODE = R"(
#version 430
layout (local_size_x = 1, local_size_y = 1) in;
layout (std430, binding=1) buffer bufferCollide { float collideCells[]; };
layout (std430, binding=2) buffer bufferStream { float streamCells[]; };
layout (std430, binding=3) buffer bufferFluid { float fluidCells[]; };
/// LBM constants
uniform uint nX;
uniform uint nY;
const uint q = 9;
const float weight[q] = float[](
1./36., 1./9., 1./36.,
1./9. , 4./9., 1./9. ,
1./36 , 1./9., 1./36.
);
const float tau = 0.8;
const float omega = 1/tau;
/// Vector utilities
float comp(int i, int j, vec2 v) {
return i*v.x + j*v.y;
}
float sq(float x) {
return x*x;
}
float norm(vec2 v) {
return sqrt(dot(v,v));
}
/// Array indexing
uint indexOfDirection(int i, int j) {
return 3*(i+1) + (j+1);
}
uint indexOfLatticeCell(uint x, uint y) {
return q*nX*y + q*x;
}
uint indexOfFluidVertex(uint x, uint y) {
return 3*nX*y + 3*x;
}
/// Data access
float w(int i, int j) {
return weight[indexOfDirection(i,j)];
}
float get(uint x, uint y, int i, int j) {
return collideCells[indexOfLatticeCell(x,y) + indexOfDirection(i,j)];
}
void set(uint x, uint y, int i, int j, float v) {
streamCells[indexOfLatticeCell(x,y) + indexOfDirection(i,j)] = v;
}
void setFluid(uint x, uint y, vec2 v) {
const uint idx = indexOfFluidVertex(x, y);
fluidCells[idx + 0] = v.x;
fluidCells[idx + 1] = v.y;
}
int getMaterial(uint x, uint y) {
const uint idx = indexOfFluidVertex(x, y);
return int(fluidCells[idx + 2]);
}
/// Moments
float density(uint x, uint y) {
const uint idx = indexOfLatticeCell(x, y);
float d = 0.;
for ( int i = 0; i < q; ++i ) {
d += collideCells[idx + i];
}
return d;
}
vec2 velocity(uint x, uint y, float d) {
return 1./d * vec2(
get(x,y, 1, 0) - get(x,y,-1, 0) + get(x,y, 1, 1) - get(x,y,-1,-1) + get(x,y, 1,-1) - get(x,y,-1,1),
get(x,y, 0, 1) - get(x,y, 0,-1) + get(x,y, 1, 1) - get(x,y,-1,-1) - get(x,y, 1,-1) + get(x,y,-1,1)
);
}
/// Equilibrium distribution
float equilibrium(float d, vec2 v, int i, int j) {
return w(i,j) * d * (1 + 3*comp(i,j,v) + 4.5*sq(comp(i,j,v)) - 1.5*sq(norm(v)));
}
/// Material number meaning (geometry is only changed by the interaction shader)
bool isBulkFluidCell(int material) {
return material == 1 || material == 4 || material == 5 || material == 6;
}
bool isBounceBackCell(int material) {
return material == 2 || material == 3;
}
bool isInflowCell(int material) {
return material == 5;
}
bool isOutflowCell(int material) {
return material == 6;
}
float getExternalMassInflux(int material) {
if ( material == 4 ) {
return 1.5;
} else {
return 0.0;
}
};
/// Actual collide&stream kernel
void main() {
const uint x = gl_GlobalInvocationID.x;
const uint y = gl_GlobalInvocationID.y;
if ( !(x < nX && y < nY) ) {
return;
}
const int material = getMaterial(x,y);
float d = max(density(x,y), getExternalMassInflux(material));
vec2 v = velocity(x,y,d);
if ( isBulkFluidCell(material) ) {
if ( isInflowCell(material) ) {
v = vec2(0.1,0.0);
}
if ( isOutflowCell(material) ) {
d = 1.0;
}
setFluid(x,y,v);
for ( int i = -1; i <= 1; ++i ) {
for ( int j = -1; j <= 1; ++j ) {
set(x+i,y+j,i,j, get(x,y,i,j) + omega * (equilibrium(d,v,i,j) - get(x,y,i,j)));
}
}
}
if ( isBounceBackCell(material) ) {
for ( int i = -1; i <= 1; ++i ) {
for ( int j = -1; j <= 1; ++j ) {
set(x+(-1)*i,y+(-1)*j,(-1)*i,(-1)*j, get(x,y,i,j) + omega * (equilibrium(d,v,i,j) - get(x,y,i,j)));
}
}
}
}
)";
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