Kinetic description of flow past a micro-plate

• Authors: Andrew J. Christlieb;W. Nicholas G. Hitchon;Iain D. Boyd;Quanhua Sun
• Venue: Journal of Computational Physics
• Year: 2004

In this work we discuss a novel numerical scheme and present numerical results for the problem of 'high' (of order unity) Knudsen number, Kn = λ/L, low velocity gas flow past a micro-plate. The scheme used here is similar to one employed in the past to examine heat flow, but in order to deal with momentum transport in the vicinity of a plate, new techniques had to be developed. These include a new scheme for finding 'transition probabilities', which eliminates some forms of numerical diffusion, and a method for handling reflections off surfaces which preserves the essential properties of the flow. The purpose of the paper is to present these methods and examine their performance. The method is found to function well, but the results indicate that the collision operator which is employed here must be improved in order to obtain accurate results for the drag. Low speed neutral particle transport, in long mean free path (LMFP) environments, presents challenges for well-established techniques, such as the direct simulation Monte Carlo (DSMC) method. In particular, at low flow velocities, statistical methods suffer from noise that may render them impractical in LMFP environments. Solution of the Boltzmann equation is the alternative to these statistical methods. As computing power increases, Boltzmann-based approaches become more accessible. We discuss here a novel non-statistical (no random numbers are used) kinetic model for particle transport and explore its accuracy and sensitivity to resolution and other details of its implementation. The model is an enhanced version of the transition probability matrix (TPM) method. The results generated by the TPM are compared with the information preservation (IP) method, the Navier-Stokes (NS) slip model and when applicable to DSMC. We provide a qualitative comparison of the models and then we compare the results of the different models for various Kn for flow past a plate. For Kn in the slip flow regime, the TPM, IP and NS models exhibit similar flow features. As the Kn passes through the transitional regime, the TPM and IP results are quantitatively similar, while the NS model fails to adequately describe the flows. For Kn in the free molecular regime, we compare the TPM to an analytic approximation to flow past a flat plate; the TPM and analytic solution exhibit similar characteristics. The drag coefficient is in agreement in the two cases, although it is sensitive to the angular distribution employed in the collision operator, when particles are relaunched after collisions.