A generalized form of the Bernoulli Trial collision scheme in DSMC: Derivation and evaluation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:354

Article

Roohi, Ehsan¹  Stefanov, Stefan²  Shoja-Sani, Ahmad¹  Ejraei, Hossein¹ 

[1] Ferdowsi Univ Mashhad, Dept Mech Engn, High Performance Comp HPC Lab, Mashhad 917751111, Iran

[2] Bulgarian Acad Sci, Inst Mech, Acad G Bontchev Str, Sofia 1113, Bulgaria

关键词: Direct Simulation Monte Carlo method;    Kac stochastic equation;    Probability analysis;    Collision model;    Bernoulli Trial;   

DOI  :  10.1016/j.jcp.2017.10.033

来源: Elsevier

【 摘 要 】

The impetus of this research is to present a generalized Bernoulli Trial collision scheme in the context of the direct simulation Monte Carlo (DSMC) method. Previously, a subsequent of several collision schemes have been put forward, which were mathematically based on the Kac stochastic model. These include Bernoulli Trial (BT), Ballot Box (BB), Simplified Bernoulli Trial (SBT) and Intelligent Simplified Bernoulli Trial (ISBT) schemes. The number of considered pairs for a possible collision in the above-mentioned schemes varies between N-(l)(N-(l) - 1)/2in BT, 1 in BB, and (N-(l) - 1) in SBT or ISBT, where N-(l) is the instantaneous number of particles in the lthcell. Here, we derive a generalized form of the Bernoulli Trial collision scheme (GBT) where the number of selected pairs is any desired value smaller than (N-(l) - 1), i.e., N-sel < (N-(l) - 1), keeping the same the collision frequency and accuracy of the solution as the original SBT and BT models. We derive two distinct formulas for the GBT scheme, where both formula recover BB and SBT limits if N-sel is set as 1 and N-(l) - 1, respectively, and provide accurate solutions for a wide set of test cases. The present generalization further improves the computational efficiency of the BT-based collision models compared to the standard no time counter (NTC) and nearest neighbor (NN) collision models. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free