Simulating the gravitational interaction between two material points

[Signifier]

Hello, I am trying to make a very rough computer model of the clumping of matter into galaxies in the large scale structure of the universe. As a starting point, I'm randomly distributing particles across a rectangle and then letting all the particles (about 22500 particles) interact via the inverse square law. The particles can be thought of as stardust clumps, "mass clouds," whatever you want to call them; the important thing is that they don't have an internal structure.

However, I'm curious as to how to exactly model the interaction between these particles. With Newton's law alone, the "particles" attract each other until they're a distance 0 apart; but of course with real matter the two particles cannot occupy the same space. How might one model this "same space" repulsion? What I have been doing is saying that once the particles get within a certain radius of each other, they stop attracting one another. It might be better to say that within some radius they begin repelling each other, but I'm not sure what this repulsion would look like. The way I'm doing gives me some interesting results but it seems arbitrary and unphysical (see attached gif).

This may not be the right place for this post, but I don't consider this purely or primarily a computer simulation question... Thank anyone for any suggestions or criticisms.

 

[tony873004]

Why would they repel? If 2 objects get too close to each other, presumably closer than the sum of their radii, just merge them into 1 particle with the combined mass and momentum of the original 2 objects.

 

[pervect]

Two objects will bump into each other if they approach closer than their radii. As far as whether or not they stick together after bumping, I would expect that it would depend on the velocity with which they collided - too fast, and they'd bounce off each other rather than stick. Without more information on the objects, I don't see how to make even a rough guess as to how to model whether the objects stick or bounce apart as a function of the impact velocity.

 

[neurocomp2003]

in HPC they use a smoothing coefficient which basically means its collisionless and you let them pass through or by each other.
...unfortunately my knowledge stops at that...