A diffusive information preservation method for small Knudsen number flows

Keywords: DSMC IP Molecular diffusion Time step Cell size a b s t r a c t 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. Similar to the DSMC method, the downside of that approach suffers from computationally statistical noise. To solve the problem, a diffusion-based information preservation (DIP) 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 À3 –10 À4 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. Numerical schemes can be categorized into two kinds: continuum and particle. For real gas flows, a powerful molecular approach is the direct simulation Monte Carlo (DSMC) method [1] that has been successfully applied to various rarefied gas flows [2], especially hypersonic situations, e.g. the structures of strong shock waves [3], aerodynamic features of reentry vehicles [4]. There is a great interest to extend the DSMC method to other situations not only for understanding the mechanisms and patterns of gas flows at molecular level, but also for sometimes more conveniently and physically modeling the microscopic transport process behind macroscopic flow phenomena. To achieve the goal, an issue that has to be addressed firstly is the limitations of the cell size and time step for the DSMC method [5,6]. They become stringent when the temporal and spatial scales of a gas flow are much larger than those of molecular motion. The time step limitation of DSMC results from a core assumption that decouples molecular motion and collisions in a time step Dt [1]. It is physically reasonable only when Dt < s c , where s c is the mean collision time of …