Parallel Computational Strategies for Viscous Hydrodynamics with Applications to Microfluidics

Abstract

Determination of the motion of particles in a viscous fluid is a problem found in disciplines including colloid science, suspension rheology and protein science. These low-Reynolds-number flows also from the basis of the new technologies that exploit microfluidics.

Three-dimensional flows involving such complex fluid-solid boundaries gain a reduction in dimensionality by the use of integral representations that convert the governing PDEs to a two-dimensional integral equation.

We describe a boundary integral formulation that yields a Fredholm integral equation of the second kind; these are amenable to iterative solution, an ideal strategy for parallel computing. For very large problems (systems on the order of 1, 000, 000 boundary elements) communication bottlenecks dictate a switch to asynchronous “Block Gauss-Siedel” iterations. The challenge is to design algorithms that scale up efficiently to large problems on large numbers of processors. Some ideas for tailoring scalable algorithms for scalable architectures will be presented.

Research conducted while the author was on the faculty of the Dept. of Chemical Engineering, Univ. of Wisconsin.