Null-collision technique in the direct-simulation Monte Carlo method

Koura, Katsuhisa

doi:10.1063/1.865826

Cited by 188 publications

(70 citation statements)

References 5 publications

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“…Molecules were also introduced via the interfaces in the appropriate equilibrium conditions. The computations for the intermolecular collisions occurring in each collision cell during ∆t were carried out by the nullcollision method (19) . After a steady-state shock wave had formed, the temporal mean of the flow field was taken and the macroscopic physical quantities were calculated.…”

Section: Analysis Of Normal Shock Waves Structurementioning

confidence: 99%

Transport Coefficients of Inelastic Collision Model in the Direct Simulation Monte Carlo Method

Matsumoto

2006

JSME international journal. Ser. B, Fluids and thermal engineer

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The rotational energy gain function for Monte Carlo simulation of an inelastic molecular collision in rarefied gas flow is revised by analysis using a combination of Monte Carlo integration and classical trajectory calculation (CTC) for diatomic molecules. The rotational energy gain function presented here is combined with the statistical inelastic cross-section (SICS) model and applied to evaluation of the transport coefficients of nitrogen gas using the Wang-Chang-Uhlenbeck (WCU) theory. The normal shock wave structures for nitrogen determined by the proposed energy gain function, Parker's energy gain function, and from experimental data are compared, and it is shown that the transport coefficients and shock wave structures given by the proposed function are in better agreement with the experimental results than Parker's energy gain function.

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Section: Analysis Of Normal Shock Waves Structurementioning

confidence: 99%

Transport Coefficients of Inelastic Collision Model in the Direct Simulation Monte Carlo Method

Matsumoto

2006

JSME international journal. Ser. B, Fluids and thermal engineer

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“…Several related methods have been developed by other researchers, including Koura (1986), Nanbu (1986), and Goldstein, Sturtevant and Broadwell (1988). Additional modifications of Nanbu's method, including use of quasi-random sequences, have been developed by Babovsky, Gropengiesser, Neunzert, Struckmeier and Wiesen (1990).…”

Section: Particle Methodsmentioning

confidence: 99%

Monte Carlo and Quasi-Monte Carlo Methods

Jakob¹,

Marschner²

2016

Springer Proceedings in Mathematics &Amp; Statistics

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Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~1^2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence are correlated to provide greater uniformity. The resulting quadrature method, called quasi-Monte Carlo, has a convergence rate of approximately O ((log N^N' 1 ).For quasi-Monte Carlo, both theoretical error estimates and practical limitations are presented. Although the emphasis in this article is on integration, Monte Carlo simulation of rarefied gas dynamics is also discussed. In the limit of small mean free path (that is, the fluid dynamic limit), Monte Carlo loses its effectiveness because the collisional distance is much less than the fluid dynamic length scale. Computational examples are presented throughout the text to illustrate the theory. A number of open problems are described.

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“…(27) would require a computational effort proportional to N 2 p . This difficulty is circumvented by the adoption of a majorant collision frequency scheme (Koura 1986) in which N c is estimated by a stochastic algorithm whose computational effort grows linearly with N p . An upper bound ν ijm for each ν ijm is easily obtained as…”

Section: The Numerical Methodsmentioning

confidence: 99%