  We have proposed a method for the dynamic simulation of a collection of
self-propelled particles in a viscous Newtonian fluid. We restrict attention to
particles whose size and velocity are small enough that the fluid motion is in
the creeping flow regime. We have proposed a simple model for a self-propelled
particle, and extended the Stokesian Dynamics method to conduct dynamic
simulations of a collection of such particles. In our description, each
particle is treated as a sphere with an orientation vector $\te{p}$, whose
locomotion is driven by the action of a force dipole at a point slightly
displaced from its centre. In isolation, a self-propelled particle moves at a
constant speed in the direction of $\te{p}$. When it coexists with many such
particles, its hydrodynamic interaction with the other particles alters its
velocity and, more importantly, its orientation. As a result, the motion of the
particle is chaotic. Our simulations are not restricted to low particle
concentration, as we implement the full hydrodynamic interactions between the
particles, but we restrict the motion of particles to two dimensions to reduce
computation. We report the statistical properties of a suspension of
self-propelled particles, such as the distribution of particle velocity, the
pair correlation function and the orientation correlation function, for a range
of the particle concentration.
