(204q) On the Kac-Based Collision Models from Simplified Bernoulli till Its Intelligent Variants | AIChE

(204q) On the Kac-Based Collision Models from Simplified Bernoulli till Its Intelligent Variants

On the Kac-based collision models from Simplified Bernoulli till its Intelligent variants

Bijan Goshayeshi

High Performance Computing (HPC) Laboratory, Department of Mechanical Engineering, Ferdowsi University of Mashhad, P.O. Box: 91775-1111, Mashhad, Iran

 

Key words

Direct Simulation Monte Carlo method (DSMC), kinetic theory, rarefied gas flows, Simplified Bernoulli-trials (SBT) scheme, Intelligent Simplified Bernoulli-trials (ISBT) scheme, Transient Adaptive Subcell (TAS), Nearest Neighbor (NN).

Abstract

Graeme Bird [1] developed the Direct Simulation of Monte Carlo (DSMC) in the 1960s, and nowadays this method has gained popularity in simulation of rarefied gas dynamics and micro gas flow problems. In addition to the requirement of employing multidimensional computational mesh, the DSMC method uses a finite set of particles or simulators, denoted by their positions and velocities, to model the advection and collision terms of the Boltzmann equation. The requirement of these large computational resources have been a prohibitive barrier in the DSMC analysis of massive computational two- and three-dimensional problems in rarefied gas dynamics. This work is dedicated to review some recent advancements in reducing the DSMC computational requirements by using Kac model -based collision schemes [2-4] in the Direct Simulation of Monte Carlo. In general, two major concepts exist for obtaining collision schemes, and here we focus our attention to the one based on the Kac stochastic model. The common advantage of these schemes is that their algorithms avoid the repeat collisions, and can be used to reduce the number of particles as a portion of computational resources. The paper reviews this conception since Yanitiskiy first introduced the Bernoulli Trials collision scheme (BT), to the introduction of Simplified Bernoulli Trials (SBT), proposed by Stefanov. We also present a new intelligent variant of the SBT collision scheme, entitled ISBT, which enters some semi-deterministic elements in the SBT scheme, that ensure selection of closer placed collision pairs.

References

[1] Bird, G. A. (1994) Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford :Clarendon Press.

[2] Stefanov, S. K. (2011). Particle Monte Carlo algorithms with small number of particles in grid cells. In Numerical Methods and Applications, 110-117P. Tata, C. Toto, A theory of many things, Fluid Dyn. Res. 44, 031202 (2012)

[3] Goshayeshi, B., Roohi, E., & Stefanov, S. (2015). DSMC Simulation of hypersonic flows using an improved SBT-TAS technique. Journal of Computational Physics.

[4] Goshayeshi, B., Roohi, E., Stefanov, S. (2015). A novel Simplified Bernoulli Trials collision scheme in the DSMC with intelligence over particle distances, Physics of Fluids, To appear in Vol. 27(10).