I have a large system of solid particles moving in the liquid. I use traditional Newtonian equations of motion for the particles. There are many different interaction forces between particles and the most severe are "lubrication forces". These are forces which dependent on the distance between the two particles and their velocities and the force goes to infinity when the particles get into touch.
Which integration technique should I use to have as few time steps while stable?
I have implemented Runge-Kutta-Fehlberg method with adaptive time step following this article: http://www.trentfguidry.net/post/2009/10/09/Runge-Kutta-Fehlberg.aspx but it produces a large number of steps even if I allow for large errors.
I compare it with and Eulerian method where I estimate the future step length based on the allowed force changes. Such a dummy method produces less steps than the Runge-Kutta-Fehlberg and is stable but still is slow...
Any suggestions are appreciated!
PS: For those who are familiar with it. I use Lattice Boltzmann as fluid dynamics solver and Immersed Boundary Method for particles representation.