Analysis of numerical techniques of the direct simulation Monte Carlo method in the rarefied gas dynamics

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 3, Issue 6, 1988, Pages 453-466

  Ivanov, M S ^a   Rogasinsky, S V ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84961488486     PISSN: 09276467     EISSN: 15693988     Source Type: Journal    
DOI: 10.1515/rnam.1988.3.6.453     Document Type: Article

References (23)

1. V. V. Aristov and F. G. Cheremisin, Conservative splitting method for solving the Boltzmann equation. Zh. Vychisl. Mat. Mat. Fiz. (1980) 20, 191–207 (in Russian).
2. O. M. Belotserkovsky and V. E. Yanitsky, Statistical method of particles in cells for solving problems in rarefied gas dynamics. Zh. Vychisl. Mat. Mat. Fiz. (1975) 15(5), 1195–1208, 15(6), 1553–1567 (in Russian).
3. O. M. Belotserkovsky, A. I. Erofeev and V. E. Yanitsky, On a non-stationary method of direct statistical simulation of rarefied gas flows. Zh. Vychisl. Mat. Mat. Fiz. (1980) 20, 1174–1204 (in Russian).
4. G. A. Bird, Molecular Gas Dynamics. Clarendon Press, Oxford, 1976.
5. G. A. Bird, Direct simulation and the Boltzmann equation. Phys. Fluids (1970) 13, 2677–2681.
6. K. M. Case and P. F. Zweifel, Linear Transport Theory. Addison-Wesley Publishing Company, University of Michigan, 1967.
7. S. A. Denisik, J. G. Malama, S. N. Lebedev and L. S. Polak, Solution of problems in physical and chemical kinetics by Monte Carlo methods. In: Primenenie Vychisl. Matem. v Khim. i Fiz. Kinetike, Nauka, Moscow, 1969, pp. 179–231 (in Russian).
8. S. A. Denisik, S. N. Lebedev, J. G. Malama and A. N. Osipov, Application of the Monte Carlo method to solve gas kinetics problems. Fizika Goreniya i Vzryva (1972) 8, 331–349 (in Russian).
9. S. M. Ermakov, V. V. Nekrutkin, A. Ya. Proshkin and A. F. Sizova, On Monte Carlo solution of nonlinear kinetic equations. Dokl. Akad. Nauk SSSR 230 (2), 1976, 261–263 (in Russian).
10. S. M. Ermakov and G. A. Mikhailov, Statistical Modelling. Nauka, Moscow, 1982 (in Russian).
11. M. S. Ivanov and S. V. Rogasinsky, On an interrelation between the direct simulation technique and the Boltzmann equation. In: Statistical mechanics. Numerical methods in kinetic theory of gases. Inst. Prikl. Mat. Sibr. Otd. Akad. Nauk SSSR, Novosibirsk, 1986, 17–27 (in Russian).
12. M. Kac, Probability and Related Topics in Physical Sciences. Interscience. London, 1959.
13. Yu. L. Klimontovich, Statistical Physics. Nauka, Moscow, 1982 (in Russian).
14. Yu. N. Kondyurin, On a statistical approach to solving the Boltzman equation. Zh. Vychisl. Mat. Mat. Fiz. (1986) 26, 1527–1534 (in Russian).
15. K. Koura, Transient Couette flow of rarefied binary gas mixture. Phys. Fluids (1970) 13, 1457–1466.
16. K. Koura, Null-collision technique in the direct simulation Monte Carlo method. Phys. Fluids (1986) 29.
17. G. A. Mikhailov, Optimization of Weight Monte Carlo Methods. Nauka, Moscow, 1987 (in Russian).
18. K. Nanbu, Direct simulation scheme derived from the Boltzmann equation. J. Phys. Soc. Japan (1980) 49, 2042–2049.
19. K. Nanbu, Interrelations between various direct simulation methods for solving the Boltzmann equation. J. Phys. Soc. Japan (1983) 52, 3382–3388.
20. K. Nanbu, Theoretical basis of the direct simulation Monte Carlo method. In: Rarefied Gas Dynamics. 1, Italy, 1986, pp. 363–382.
21. I. Prigogin, Non-Equilibrium Statistical Mechanics. Interscience, London, 1966.
22. S. V. Rogasinsky, Theory of direct simulation technique for solving the Boltzmann equation (Bird's method). Preprint No. 706, Vychisl. Tsentr Sibir. Otd. Akad. Nauk SSSR. Novosibirsk, 1986 (in Russian).
23. J. Spaniez and E. Gelbard, Monte Carlo Principles and Neutron Transport Problems. Addison-Wesley Publishing Company, 1961.