I am running a particle simulation of a rarefied gas where collisions occur very infrequently, my team is attempting to use particle simulations to make an estimate of where collisions occur within a simulated volume. We would like to make direct direction of collisions using distance checks, rather than DSMC or another probabilistic method.
The challenge is the particles travel ~100 particle diameters per time step and thus checking for collisions at the beginning and end of time steps may miss collisions that occur in the middle. Are there any known algorithms to detect collisions under such collisions or is the only option to reduce the time step?
We have used spatial binning to reduce the order of distance checks to ~O(N) but this doesn't solve the large time step problem. It may be possible to use large radii to check for collision candidates and then use more expensive math to check for collisions but it seems there should be a more elegant solution.