/* Simple forward Euler method for velocity integration in time */
void euler(double &x, double &y, double timestep, const FluidQuantity &u, const FluidQuantity &v) const {
double uVel = u.lerp(x, y)/_hx;
double vVel = v.lerp(x, y)/_hx;
x -= uVel*timestep;
y -= vVel*timestep;
}
/* Builds the pressure right hand side as the negative divergence */
void buildRhs() {
double scale = 1.0/_hx;
for (int y = 0, idx = 0; y < _h; y++) {
for (int x = 0; x < _w; x++, idx++) {
_r[idx] = -scale*(_u->at(x + 1, y) - _u->at(x, y) +
_v->at(x, y + 1) - _v->at(x, y));
}
}
}
double maxTimestep() {
double maxVelocity = 0.0;
for (int y = 0; y < _h; y++) {
for (int x = 0; x < _w; x++) {
double u = _u->lerp(x + 0.5, y + 0.5);
double v = _v->lerp(x + 0.5, y + 0.5);
double velocity = sqrt(u*u + v*v);
maxVelocity = max(maxVelocity, velocity);
}
}
double maxTimestep = 4.0*_hx/maxVelocity;
return min(maxTimestep, 1.0);
}
/* Returns the maximum allowed timestep. Note that the actual timestep
* taken should usually be much below this to ensure accurate
* simulation - just never above.
*/
double maxTimestep() {
double maxVelocity = 0.0;
for (int y = 0; y < _h; y++) {
for (int x = 0; x < _w; x++) {
/* Average velocity at grid cell center */
double u = _u->lerp(x + 0.5, y + 0.5);
double v = _v->lerp(x + 0.5, y + 0.5);
double velocity = sqrt(u*u + v*v);
maxVelocity = max(maxVelocity, velocity);
}
}
/* Fluid should not flow more than two grid cells per iteration */
double maxTimestep = 2.0*_hx/maxVelocity;
/* Clamp to sensible maximum value in case of very small velocities */
return min(maxTimestep, 1.0);
}
/* Convert fluid density to RGBA image */
void toImage(unsigned char *rgba) {
for (int i = 0; i < _w*_h; i++) {
int shade = (int)((1.0 - _d->src()[i])*255.0);
shade = max(min(shade, 255), 0);
rgba[i*4 + 0] = shade;
rgba[i*4 + 1] = shade;
rgba[i*4 + 2] = shade;
rgba[i*4 + 3] = 0xFF;
}
}
void update(double timestep) {
buildRhs();
project(600, timestep);
applyPressure(timestep);
_d->advect(timestep, *_u, *_v);
_u->advect(timestep, *_u, *_v);
_v->advect(timestep, *_u, *_v);
_d->flip();
_u->flip();
_v->flip();
}
void update(double timestep) {
buildRhs();
project(600, timestep);
applyPressure(timestep);
_d->advect(timestep, *_u, *_v);
_u->advect(timestep, *_u, *_v);
_v->advect(timestep, *_u, *_v);
/* Make effect of advection visible, since it's not an in-place operation */
_d->flip();
_u->flip();
_v->flip();
}
/* Applies the computed pressure to the velocity field */
void applyPressure(double timestep) {
double scale = timestep/(_density*_hx);
for (int y = 0, idx = 0; y < _h; y++) {
for (int x = 0; x < _w; x++, idx++) {
_u->at(x, y ) -= scale*_p[idx];
_u->at(x + 1, y ) += scale*_p[idx];
_v->at(x, y ) -= scale*_p[idx];
_v->at(x, y + 1) += scale*_p[idx];
}
}
for (int y = 0; y < _h; y++)
_u->at(0, y) = _u->at(_w, y) = 0.0;
for (int x = 0; x < _w; x++)
_v->at(x, 0) = _v->at(x, _h) = 0.0;
}
/* Third order Runge-Kutta for velocity integration in time */
void rungeKutta3(double &x, double &y, double timestep, const FluidQuantity &u, const FluidQuantity &v) const {
double firstU = u.lerp(x, y)/_hx;
double firstV = v.lerp(x, y)/_hx;
double midX = x - 0.5*timestep*firstU;
double midY = y - 0.5*timestep*firstV;
double midU = u.lerp(midX, midY)/_hx;
double midV = v.lerp(midX, midY)/_hx;
double lastX = x - 0.75*timestep*midU;
double lastY = y - 0.75*timestep*midV;
double lastU = u.lerp(lastX, lastY);
double lastV = v.lerp(lastX, lastY);
x -= timestep*((2.0/9.0)*firstU + (3.0/9.0)*midU + (4.0/9.0)*lastU);
y -= timestep*((2.0/9.0)*firstV + (3.0/9.0)*midV + (4.0/9.0)*lastV);
}
/* Set density and x/y velocity in given rectangle to d/u/v, respectively */
void addInflow(double x, double y, double w, double h, double d, double u, double v) {
_d->addInflow(x, y, x + w, y + h, d);
_u->addInflow(x, y, x + w, y + h, u);
_v->addInflow(x, y, x + w, y + h, v);
}