Application of the Transition Probability Matrix Method to High Knudsen Number Flow Past a Micro‐Plate

摘要

In this work we present numerical results for the problem of ‘high’ (of order unity) Knudsen number gas flow past a micro‐airfoil, for low flow velocity. The results are generated using an enhanced version of the transition probability matrix (TPM) method. The TPM is a non‐statistical kinetic method [1] for computing neutral particle transport in high Knudsen number flows. The problem of high Knudsen number, low Mach number gas flow has been studied in the past using several computational approaches, such as the Information Preservation (IP) method [2] and the direct simulation Monte Carlo (DSMC) method [2]. For low Mach numbers, the DSMC approach suffers from statistical noise [3]. The IP method extends the range of the particle method by reducing the statistical noise of the approach. The need for a method which is capable of describing the particle distribution function for high Knudsen number flows at low flow velocities has led to an investigation of alternative kinetic approaches, such as the IP[4]. In this paper we present an altogether different approach to the problem of statistical noise, the transition probability matrix (TPM) method [1, 5, 6, 7]. We give a brief overview of the TPM method, and compare its strengths and weaknesses to those of the IP and DSMC methods. Finally, we present results for the micro‐plate and compare them to the results generated by both the IP and DSMC methods. © 2003 American Institute of Physics