We present the design of software packages called Particle Movers that have been developed to simulate the motion of particles in two dimensional domains. These simulations require the solution of nonlinear Navier-Stokes equations for fluids coupled with Newton's equations for particle dynamics. Furthermore, realistic simulations are extremely computationally intensive, and are feasible only with algorithms that can exploit parallelism effectively. We describe the computational structure of the simulation, including a distributed multilevel preconditioner for the inner systems arising from the nonlinear iteration. A software framework, GVec, has also been developed to support this new algorithm set. It is highly extensible and portable, while maintaining excellent performance and scalability. Large scale simulations, with thousands of particles, demonstrate very good speedup on a large number of processors.