Large scale simulation of particulate flows

Simulations of particles in fluid flows are of great interest to numerous industries using sedimentation, fluidization, lubricated transport, and hydraulic fracturing of hydrocarbon reservoirs. Simulating incompressible viscoelastic flows with millions of rigid particles is computationally a very challenging problem. In addition to using sophisticated modeling techniques and numerical algorithms, one must develop a scalable parallel formulation of the simulation. This task is further complicated by the dynamic nature of the system resulting from unrestricted motion of the particles. In this paper we present an efficient algorithm for simulating particulate flows and discuss its parallel implementation. At each time step, a number of linear systems are solved using preconditioned iterative methods in which the matrix-vector product does not require explicit computation and storage of the matrix. The preconditioners developed for these systems are optimal so that convergence is assured in a fixed number of iterations. Moreover these preconditioners do not require matrix inversion, and can be applied efficiently in parallel using their matrix-free forms. As a result the algorithm is highly parallel and scalable, and achieves good speed improvement on the SGI Origin 2000