A symmetrized and simplified Bernoulli trial collision scheme in direct simulation Monte Carlo

Abstract

Here, a symmetrized and simplified Bernoulli trials (SSBT) scheme based on the probabilistic approach is introduced to provide less-restricted conditions in choosing selected pairs. Unlike the simplified Bernoulli trials (SBT) method, the SSBT scheme picks the second particle of a selected pair from a whole list of particles with equal probability; it prevents repetitive collisions by introducing a procedure to avoid duplicate colliding pairs. The efficiency of this newly introduced algorithm is investigated in benchmark problems such as a collision frequency test case, Fourier heat transfer, dissociation of simple gas, and hypersonic cylinder flow. Compared with SBT, no time counter (NTC), and nearest neighbor (NN) collision algorithms, the results show that the SSBT method predicts the solutions quite accurately. In the collision frequency test case and Fourier test case, we show that the SSBT scheme could work with few particles per cell (one or even less) if an appropriate space and time discretization is employed. The symmetrized algorithm of the SSBT scheme improves the quality of the selection process, which leads to a smaller sample size in the highly non-equilibrium problem of hypersonic cylinder flow to achieve the same convergence limit at that of the SBT and NN schemes. In addition, the SSBT scheme has inherently a lower separation of free paths in the stagnation point of the cylinder test case compared to the SBT scheme for the same grid test case. These features make SSBT a new, robust model that could be presented as an alternative to state-of-the-art models.