On the collision detection for ellipsoidal particles in turbulence

Collisions of small and heavy non-spherical particles settling in a turbulent environment are very important to various fields of physics and engineering. However, in contrast to spherical particles the collision probabilities are virtually unknown. In this study we focus on a very important condition for the numerical determination of collision probabilities: The collision detection. We discuss the need for efficient strategies to narrow down the number of possible collision pairs and compare three collision detection methods for ellipsoidal particles. We derive an analytical formula for the collision probability in the case of gravitational settling and validate the collision detection methods with this. Finally, we present statistics of the accuracy and efficiency of the methods. For the case of ellipsoidal particles in turbulence we find that the continuous collision detection with neglected rotation within a time step is the optimal trade-off between accuracy and efficiency.