Toward the improved simulation of microscale gas flow

Recent interest in fluidic micro-electro-mechanical systems (MEMS) in gaseous environments has increased the need for accurate simulation techniques to aid in their design process. Many fluidic MEMS operate in a low-speed non-equilibrium gas flow regime that is challenging to simulate both accurately and efficiently. Classic computational fluid dynamics techniques (e.g. Navier-Stokes simulation) are based on the assumption that the fluid behaves as a continuum. This assumption, however, becomes increasingly less accurate as the local flow conditions deviate further from local thermodynamic equilibrium. Alternatively, it is possible to achieve an accurate approximation of non-equilibrium gas flows using particle-based methods (e.g. DSMC), but the resulting simulations are much more computationally expensive than the continuum-based method. In fact, for the very low speeds commonly found in fluidic MEMS, the slow convergence of the DSMC solution can lead to intractably long computation times on all but the largest supercomputers.; Two different approaches are pursued in this investigation, in an effort to design a physically accurate and computationally efficient simulation of low-speed, non-equilibrium flows. The first approach constructs new empirical models to correct the error in the Navier-Stokes simulation in the transition regime due to the appreciable deviation from local thermodynamic equilibrium. The empirically corrected Navier-Stokes simulation is not actually predicting strongly non-equilibrium gas flows; however, it is shown to be a useful analysis tool in certain design situations. The second more novel approach develops an original quasi-Monte Carlo (QMC) particle simulation that retains the physical accuracy of the DSMC method while at the same time achieving a faster (near-linear) convergence rate. The design of a QMC method is far more complex in general than a Monte Carlo method for the same problem. Further, no known QMC particle simulation has been successfully implemented for general non-equilibrium gas flows. The technique in this investigation is therefore developed for low density gas flows in simple duct geometries dominated by particle-surface collisions. The new QMC particle simulation demonstrates an error convergence rate superior to traditional DSMC methods, yielding a computational speedup factor of 1.3 to 1,800 for the duct geometries tested.