Modeling and simulation of active suspensions containing large numbers of interacting micro-swimmers

•Fast numerical method to compute the colonial dynamics of micro-swimmers.•Includes long-range interactions and short-range steric effects between swimmers.•The methodology uses the immersed boundary framework.•Can efficiently simulate many thousands of interacting motile particles in 3D.•Can use the method to study many biological and physical phenomena. We present a mathematical model and simulation method to compute the colonial dynamics of micro-swimmers that interact directly and through the fluid they are suspended in. The model uses the stress generated by each self-motile particle for long-range interactions and includes short-range steric effects between particles. The time-step computational cost is O(NlogN+M), with N the total number of mesh points, and M the number of swimmers. This fast method enables us to efficiently simulate many thousands of interacting self-propelling particles in three dimensions and with background flows. We show examples of collective behavior in suspensions of “pusher” and “puller” micro-swimmers.