A diffusive information preservation method for small Knudsen number flows

Abstract

The direct simulation Monte Carlo (DSMC) method is a powerful particle-based method for modeling gas flows. It works well for relatively large Knudsen (Kn) numbers, typically larger than 0.01, but quickly becomes computationally intensive as Kn decreases due to its time step and cell size limitations. An alternative approach was proposed to relax or remove these limitations, based on replacing pairwise collisions with a stochastic model corresponding to the Fokker–Planck equation [J. Comput. Phys., 229, 1077 (2010); J. Fluid Mech., 680, 574 (2011)]. Similar to the DSMC method, the downside of that approach suffers from computationally statistical noise. To solve the problem, a diffusion-based information preservation (D-IP) method has been developed. The main idea is to track the motion of a simulated molecule from the diffusive standpoint, and obtain the flow velocity and temperature through sampling and averaging the IP quantities. To validate the idea and the corresponding model, several benchmark problems with Kn∼10−3–10−4 have been investigated. It is shown that the IP calculations are not only accurate, but also efficient because they make possible using a time step and cell size over an order of magnitude larger than the mean collision time and mean free path, respectively.