Conservative Species Weighting Scheme for the Direct Simulation Monte Carlo Method

The direct simulation Monte Carlo method (DSMC) finds application to nonequilibriu m gas flows including hypersonic aerodynamics, spacecraft propulsion, materials synthesis, and flows in microma- chines. In many of these problems, the species of most interest are present in very small quantities. This presents a resolution problem for the DSMC technique in which a finite number of particles is employed. This study proposes a new numerical scheme for the simulation of trace species. Unlike an existing scheme, the new method explicitly conserves both linear momentum and energy during collisions. The scheme is applied to a number of problems to demonstrate its accuracy and utility. Reduced execution times and improved resolution of trace species properties may be obtained simultaneously with the new method. HE direct simulation Monte Carlo method (DSMC) is a physically accurate method for the computation of non- equilibrium gas flows. The technique is most useful in circum- stances where there are insufficient numbers of collisions in the flow to maintain the equilibrium forms of the distribution functions describing the various energy modes of the gas. Gen- erally, such conditions prevail when the average distance be- tween successive collisions of each particle, the mean free path, is comparable to the characteristic length scale of the flow. This type of nonequilibrium condition occurs in a variety of problems of current interest. These include hypersonic flows around vehicles flying at high altitude in planetary atmo- spheres, flows from small rockets used on satellites for control, flows involved in the synthesis of thin films, and flows in mi- cron-scale mechanical structures. The DSMC method employs particles simulated in the com- puter to represent the motions and collisions of real molecules and atoms. A typical simulation employs a few million parti- cles to represent the much larger number of real molecules. The particle weight W is the number of real molecules that each simulated particle represents. The basic assumption of the technique is that particle motion may be performed separately from particle collisions over a time step that is small compared to the average time between successive collisions of the same particle. In the DSMC method, particle motions and collisions are performed in the physical domain. Particles are moved through the length specified by the product of the time step and the velocity vector of each particle. The particles are then collected into cells, and only those particles that occupy a par- ticular cell are considered possible collision candidates. Col- lision selection is performed using statistical probability mod- els that are derived from basic kinetic theory. Macroscopic flow properties are obtained by time averaging particle prop- erties in the computational cells over several thousand itera- tions of the basic algorithm. In many of the applications of interest, the chemical species of most importance occur in very small quantities. To illustrate this point, one particular example is considered. The Bow Shock Ultra Violet (BSUV) flight experiments1'2 were designed