Explicit Finite Difference Schemes for Particulate Flows

Mr. Andy Perrin
Ph.D. Candidate
Advisor: Professor Howard H. Hu
Mechanical Engineering and Applied Mechanics
University of Pennsylvania

Abstract
Many schemes have been proposed for direct numerical simulation of particles in fluids, but they can be quite complicated and require a lot of memory when the fraction of particles is high. Explicit finite difference schemes on a Cartesian grid are one way around these issues. The fluid velocity and density can be marched in time without inverting any matrices, and the particles can be moved according to Newton's laws. Enforcing the no-slip condition on the spherical particle's surfaces as they move on a Cartesian grid is not so easy, however, so we have proposed a spectral expansion method that exactly satisfies no-slip to deal with the problem. This method allows a grid as coarse as ten grid spacings per particle diameter to give smooth forces and accurately resolved pressure distributions on the particle surface. Up to 1035 particles have been simulated on a (fast) PC.

Friday, March 28th
337 Towne Bldg.
2:00 – 3:00 p.m.