This paper investigates the Poiseuille flows for rectangular, regular hexagonal, and semicircular cross sections in transition regime using particle approaches, namely the direct simulation Monte Carlo (DSMC) method and the information preservation (IP) method. The DSMC and IP results compare well with each other, while the IP method is much more computationally efficient than the DSMC method. The mass flow rates given by IP and DSMC are in agreement with the BGK solutions of Hasegawa and Sone. For rectangular cross sections in the wide range of the width-to-height ratio, the simulation results of the mass flow rates and the velocity profiles along the midperpendicular line have been given for both methods to estimate the lateral wall influence. For the physical quantities, such as the mass flow rate, which are influenced by the whole field, the lateral wall influence must be considered even for width-to-height ratio as large as 10. And for the physical parameters, such as the maximum velocity and the velocity profile along the midperpendicular line, the lateral wall influence can be negligible if the width-to-height ratio is bigger than 5.

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