The statistical error associated with the direct simulation Monte Carlo technique is studied when it is applied to nonequilibrium cle method and a continuum approach. It is well known hypersonic and nozzle flows. A root mean square (rms) error is that the Monte Carlo method is physically accurate but employed as an indicator of the level of the statistical fluctuations. relatively expensive to use, while traditional CFD methods
The effects of number of particles per cell and sample size are become invalid for rarefied and strongly nonequilibrium analyzed and quantified. It is found that in order to adequately flows. The hybrid numerical method may employ either model the physics of interest, the number of particles in the simulation must be greater than a certain minimum. An equation is devel-the CFD or DSMC technique in various regions of the oped to model and analyze the rms errors. A range is provided of the flow field based on local flow conditions. In the first step appropriate number of particles to be employed in the simulation in of this development, a continuum breakdown parameter order to achieve the smallest statistical error at a fixed computawas derived for predicting failure of the CFD approach tional cost. Values are also recommended for the maximum number [2]. This parameter indicates where in a flow field the switch of sampling time steps to be used for efficient computation on memory limited computers. The effects of collision model and of should be made from the CFD to the DSMC technique. cloning particles on the statistical scatter are analyzed. แฎ 1996 Aca-Another key issue in the hybrid scheme is the passing demic Press, Inc.
of information between these two methods. The DSMC technique is a statistical method and, hence, always has fluctuations associated with its solutions. If the level of 434