A Fast Stokes Solver for Generalized Flow Problems

摘要

Computing drag forces on geometrically complicated 3-D micromachined structures, such as an entire comb resonator, is a challenging problem. The recently developed Fast Stokes solver, based on precorrected-FFT accelerated iterative methods, has made analyzing such problems much less expensive. For this reason, there have been several extensions to the program to analyze unsteady flow and to improve computational efficiency. In this paper we develop several additional extensions to FastStokes. In particular, the direct BEM formulation is used to allow mixed velocity-pressure boundary conditions. We demonstrate the accuracy of the numerical approach by comparing computed results to the results from the indirect BEM formulation and low frequency asymptotic expansions for an oscillating sphere with Dirichlet boundary conditions. We show the ability of this solver to handle problems with mixed boundary conditions. Finally, the drag force on a micro-resonator packaged in the air is presented.