A new direct simulation Monte Carlo implementation for more efficient simulation of hypersonic flow over arbitrarily shaped bodies using dynamic cells

Abstract

Methods are reported for less computationally expensive and more accurate implementations of the direct simulation Monte Carlo (DSMC) method for the simulation of high speed gas flows over arbitrarily shaped bodies. A new particle-tracking algorithm with a saving of computational time of up to 10% is reported in which tracking of particles is done with the help of big triangles having vertices lying on the boundary curves. An algorithm has been developed to generate DSMC cells for collision and sampling that contain a prescribed number of molecules. This algorithm is able to generate over 90% cells having the optimum number of seven or eight molecules for simulating collisions. Sampling for macroscopic properties is done on dynamic cells that contain a number of particles varying spatially as a function of the local number density. A criterion for finding the number of particles in sampling cells is presented. This criterion has been found to result in accurate and fast simulation of two-dimensional hypersonic flows of argon over a wedge, and argon and nitrogen over a circular cylinder.

Fast algorithms for particle searching and positioning by cell registration and area comparison

“…CD is one of the edges of the cell containing the particle at time t. The exit edge is found only when the fi rst condition is false and the second is true. Reji, et al [17], used the following two conditions:…”

“…P2L was fi rst introduced by Zhou, et al [14], following which this method was improved and applied to various geometries by many researchers [13,15,16]. Instead of T2L, Reji, et al [17] presented a method based on geometric calculation. However, it must be pointed out that, in P2L and T2L, the vertices of each cell must be ordered anticlockwise, which makes them somewhat complicated to apply to three dimensions.…”