Extension of the SBT-TAS algorithm to curved boundary geometries

Extension of the SBT-TAS algorithm to curved boundary geometries Bijan Goshayeshi, Ehsan Roohi, Stefan Stefanov, and Javad Abolfazli Esfahani Citation: AIP Conference Proceedings 1628, 266 (2014); doi: 10.1063/1.4902602 View online: http://dx.doi.org/10.1063/1.4902602 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1628?ver=pdfcov Published by the AIP Publishing Articles you may be interested in DSMC simulation of micro/nano flows using SBT-TAS technique AIP Conf. Proc. 1628, 255 (2014); 10.1063/1.4902601 Generalizing the extensibility of a dynamic geometry software AIP Conf. Proc. 1479, 482 (2012); 10.1063/1.4756171 DSMC Moving‐Boundary Algorithms for Simulating MEMS Geometries with Opening and Closing Gaps AIP Conf. Proc. 1333, 760 (2011); 10.1063/1.3562738 ‘‘A’’ weighting curve algorithm J. Acoust. Soc. Am. 112, 2257 (2002); 10.1121/1.4778996 Quantum geometry of field extensions J. Math. Phys. 40, 2311 (1999); 10.1063/1.532866 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 138.38.44.95 On: Fri, 17 Jul 2015 03:03:39 Extension of the SBT-TAS Algorithm to Curved Boundary Geometries Bijan Goshayeshia, Ehsan Roohib, Stefan Stefanovc, Javad Abolfazli Esfahania a Department of Mechanical Engineering, Ferdowsi University of Mashhad, P.O. Box: 91775-1111, Mashhad, Iran b Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran c Institute of Mechanics, Bulgarian Academy of Science, Acad. G. Bontchev Str., 1113, Sofia, Bulgaria 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. Keywords: Simplified Bernoulli-trials (SBT) scheme, Transient Adaptive Subcell (TAS), collision frequency, mean collision separation divided by the mean free path (SOF), nearest neighbor (NN). PACS: 47.45.-n INTRODUCTION In contrast to the Molecular Dynamics, or MD, which deals with particle interactions in a deterministic manner, the Direct Simulation of Monte Carlo, or DSMC, considers these interactions on probabilistic physical simulations [1, 2, 3]. This means that, the DSMC creates particles, that each of them represents ୬ number of molecules, and then in two successive stages, within every single time step, it allows them to freely move in space and experience binary collisions, while their move and collision operations are decoupled. A standard mathematical equation for describing molecular regimes is the Boltzmann equation. Wanger [4] proved that, if the molecule number tends toward infinity while the time step and the grid size are also getting close enough to zero, the DSMC will faithfully solve this equation. For fulfilling the most important DSMC principle—the decoupling of move and collision stages—DSMC has imposed some restrictions on the assignation of the time step and cell size, in which the time step should be sufficiently smaller than mean collision time, and cell size must also be smaller than the mean free path of gas molecules. On the other hand, conventional collision routines such as no time counter (NTC) needs to have a large number of simulated particles for reducing statistical fluctuations, and also enabling them to prevent repeated collision occurrences within the cell space. This subject compelled these routines to provide large unnecessary amount of particles, say 20-30 particles per cell, so that their collision frequencies could approach to the real values and reduce the stochastic errors. In this sense, Belotserkovskii and Yanitiskiy [5] and Yanitiskiy [6] proposed a new collision algorithm based on Bernoulli-trials scheme, which avoids the collision pairing system from successive selections, and as a result it made it possible for the DSMC to eliminate those unnecessary particles. By considering this achievement, Stefanov used this innovation and proposed a modified version of Bernoulli trial scheme called “Simplified Bernoulli-trials,” or SBT [7,8], which fundamentally coincides with its original version Proceedings of the 29th International Symposium on Rarefied Gas Dynamics AIP Conf. Proc. 1628, 266-275 (2014); doi: 10.1063/1.4902602 © 2014 AIP Publishing LLC 978-0-7354-1265-1/$30.00 266 to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: This article is copyrighted as indicated in the article. Reuse of AIP content is subject 138.38.44.95 On: Fri, 17 Jul 2015 03:03:39