# Dealing with simultaneous collisions in N-body sim

I have written an 2d N-body simulation in Python which allows collisions between the bodies.

A body is modeled as a circle whose area is proportional to its mass. Each time the sim advances by one time-step, I identify which bodies have overlapping radii and I replace them by one particle (respecting conservation of momentum and treating the collision as inelastic).

This worked well for N<100 but for higher N I encountered (not systematically, but depending on the initial conditions of the sim) a weird error: the number of particles N actually increased (and quickly exceeded the maximum integer value Python can handle).

I believe what is occuring is, after the new positions of the bodies have been calculated, it happens that (at least) 4 bodies mutually overlap. Each of the 6 pairs creates a new body and but we also delete the 4 bodies,so N increased by os we have 6-4=2. But the 6 new bodies are spawned in roughly the same positions as the original 4 bodies so now we have even more overlap (N can now increase by potentially (6 choose 2)-6=9 bodies). Hence why N can grow very fast.

How can I avoid this error?

The only thing I can think of is to reduce the radii of the bodies to reduce the change of 4 particles mutually overlapping. But this does not definitively fix the problem.

• You should not compute all collisions at once. When you have computed one collision, join the particles and then compute the remaining collisions with respect to the new particle situation that you have. – H. Rittich Sep 25 '17 at 16:27