Extension of the SBT-TAS algorithm to curved boundary geometries

Abstract

The current paper suggests an alternative to the Nearest-neighbor (NN) algorithm, which requires comparable or less computational time and memory in many applications of the Direct Simulation Monte Carlo (DSMC) method. The new approach uses the Simplified Bernoulli Trials (SBT) collision algorithm in combination with the transient adaptive subcell (TAS) technique. The Direct Simulation Monte Carlo (DSMC) is a particle-based method used to solve the Boltzmann equation through statistical schemes. The major role of any DSMC method is played by its collision algorithm, which tries to solve the most sophisticated term of the Boltzmann equation, and at the same time preserving its statistical restrictions by using specified number of particles per cell. The Simplified Bernoulli-trials (SBT) collision algorithm has already been introduced as a scheme that provides accurate results with a smaller number of particles and its combination with transient adaptive subcell (TAS) technique will enable SBT to have smaller grid sizes. In this paper, in order to have a closer look up on SBT, the Nearest neighbor (NN) algorithm in Bird DS2V code is replaced by SBT-TAS and comparisons between it and NN are made over an appropriate test case that is designed to have a wide spectrum of collision frequency. Hypersonic gas flow passing a cylinder, suggested by G. Bird, is a well-known benchmark problem that provides a wide collision frequency range from the downstream back-cylinder till the upstream stagnation point. Unlike NN, SBT does not need to calculate the required selection number of collision pairs and instead of that it lets its probability function to do this job. Since the probability function and subcell volumes are dependent, the necessity of having a logical volume approximation is very important. This volume calculation scheme, on the one hand needs to preserve the SBT logic well enough that it doesn’t change the collision frequency, and on the other hand it must be easy and simple without adding any further burden on calculation costs. It’ll be shown that SBT-TAS combination will reduce the desired number of cells and particle per cells while it still preserves the accuracy of NN.