Study on a Gridless Solver for Micro-Scale Flows based on the Boltzmann Equation

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In this study, a novel simulation method based on the Boltzmann equation has been developed for gas flows in micro scales. Numerical simulation for gas flows about micro devices is one of the recent new frontiers of computational fluid dynamics(CFD). It can be an essential tool for understanding the fluid behavior around Micro-Electro-Mechanical Systems(MEMS) and Nano Technology Base Systems(NTBS). Since the Knudsen numbers, the ratio of molecular mean free path to a characteristic flow length, of the flows around MENS and NTBS are typically between 0.01 and 10, simulation method based on the Boltzmann (kinetic) approach should be preferable. One of the numerical methods widely used for the Boltzmann equation is the direct simulation Monte Carlo(DSMC) method. The DSMC method is a powerful simulation tool for supersonic rarefied gas flows. The method, however, becomes a poor simulation tool for the flows in micro scales, because the micro-scale flows are low speed flows, for which huge sample size is required to reduce the inherent statistical scatter of the DSMC method. In contrast with it, the novel simulation method for the Boltzmann equation does not have any statistical scatter in the solution. The third order upwind gridless method is used for estimating the convective terms of the equation. The collision integral is approximated with a kinetic model collision term, which correctly resembles the lower 13 moments of the Boltzmann equation. The simulation method is as powerful as the DSMC method for supersonic flows and definitely superior to the DSMC method for subsonic flows. The simulation method can predict micro-scale low speed flows and is also superior to the IP(Information Preservation) method, which is a novel statistical method developed for low speed rarefied gas flows.