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The purpose of this paper is to present a new method for the detection and resolution of the contact point between two ellipsoids. Numerical simulations of ellipsoidal particles in a rotary cylinder are also presented.

An algebraic condition is developed for the internal contact between two ellipsoids and an efficient contact detection algorithm for overlapping ellipsoids is implemented.

This method was found to have the advantages of effectiveness and speed in the detection and resolution of the contact point.

The dynamics of granular materials are of great importance in many industries dealing with powders and grains, such as pharmaceutical, chemical, and food industries. The main difficulty of such simulations is the excessive CPU time required for a large number of particles. In the discrete element method, contact detection between grains is the most expensive step in solving a nonlinear system for determination of the contact point, the normal vector and the overlap distance between ellipsoids. The numerical behavior and the optimization of the new algorithm presented in this paper are important also.