<p>The right softening length for a problem depends upon lots of things -- timestep, configuration, scale of the problems of interest, choice of integrator, etc.  Generally speaking, if you want to suppress two-body relaxation you want some function of the Hill radius [as opposed to the physical radius, as it looks like you want to suppress the effects of close encounters, not mock up a collision.]</p>

<p>See <a href="http://arxiv.org/pdf/astro-ph/0011568v1.pdf" rel="nofollow">Walter Dehnen's paper</a> on the subject of choosing an optimal softening (although I'm dating myself a little by citing that; probably there are more up-to-date references).</p>
N-Body Simulation - How to choose the softening factor?
<p>I am in the process of writing a simplified version of All Pairs N-Body simulation. I am using CUDA/OpenGL to implement the algorithm and visualize the simulation. I am assuming that all bodies are spheres of uniform radius such that the mass of each sphere is the only difference(Assume that all spheres have radius == 1). Now, I would like to know how to choose the softening factor in the equation of Acceleration?
<img src="https://i.stack.imgur.com/Ebvec.jpg" alt="http://http.developer.nvidia.com/GPUGems3/elementLinks/680equ02.jpg"></p>

<p>What I am thinking of is that <code>epsilon == 2</code> is a good choice because it is the moment when two spheres collide in my case. Is that a reasonable choice? Is there a simple explanation of how to choose the softening factor?</p>

<p>I have looked at Chapter 31 of GPU Gems 3 but it doesn't say what the chosen value is and how you would choose a suitable value. I have looked at some research papers but I am unable to penetrate those academic papers on my own.</p>