A Parallel Coupled Ordinates Method for Rarefied Gas Dynamics Simulations

Deterministic solution techniques for non-equilibrium rarefied flows in RF MEMS switches are frequently based on the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) form of the Boltzmann kinetic equation. These numerical schemes involve the sequential solution of the distribution function in velocity space. However, these schemes have poor convergence rates, especially at low Knudsen numbers, because of the explicit coupling of the distribution functions in velocity space. Furthermore, parallel implementation of these schemes is inefficient, making simulation of real-life devices practically impossible. In this paper we describe the parallel performance of a recently-developed numerical procedure called the coupled ordinates method (COMET) to solve ESBGK equations. In this method, the distribution functions for all velocity ordinates are strongly coupled at each physical point, resulting in an implicit solution procedure in velocity space. The coupled procedure is used as a relaxation sweep in a geometric multigrid scheme to promote spatial coupling. Results show that COMET gives excellent CPU scaling on multiple processors even for very small workload per processor. The solver is also shown to have very good strong and weak scaling characteristics. The parallel COMET solver also gives significantly faster solutions than the parallel implementation of the conventional sequential solution procedure. It is believed that the parallel COMET solver can become an efficient tool to model real-life RF MEMS switches.