#### Submitted to IPPS/SPDP 1999 on September 26, 1998

# Large Scale Simulation of Particulate Flows

**Ahmed H. Sameh and Vivek Sarin**

**Department of Computer Science**

**Purdue University**

**West Lafayette, IN 47907-1398**

**{sameh,sarin}@cs.purdue.edu**

**Tel: (765)494-7801**

**Fax: (765)494-0739**
### Abstract:

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.

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