A stochastic method for solving Smoluchowski's coagulation equation

Mathematics and Computers in Simulation

Volumn 49, Issue 1-2, 1999, Pages 57-79

  Kolodko, A ^a   Sabelfeld, K ^a,b   Wagner, W ^b  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND MATHEMATICAL GEOPHYSICS   (Russian Federation)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002760243     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(99)00008-7     Document Type: Article

References (25)

1. H. Babovsky, R. Illner, A convergence proof for Nanbu's simulation method for the full Boltzmann equation, SIAM J. Numer. Anal. 26(1) (1989) 41-55.
2. J.M. Ball, J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness and density conversation, J. Stat. Phys. 61 (1990) 203-234.
3. M.H. Bayewitz, J. Verushalmi, S. Katz, R. Shinnar, The extent of correlations in a stochastic coalescence process, J. Atmos. Sci. 31(6) (1974) 1604-1614.
4. U. Frisch, Turbulence. Cambridge University Press, 1996.
5. D.N. Gillespie, The stochastic coalescence model for cloud droplet growth, J. Atmos. Sci. 29 (1972) 1496-1510.
6. A.A. Kolodko, Direct statistical simulation of the coagulation process, Preprint No. 1072 of the Computing Center, Russ. Acad. Sei., Siberian Branch, Novosibirsk, 1996.
7. A.A. Kolodko, W. Wagner, Convergence of a Nanbu-type method for the Smoluchowski equation, Monte Carlo Methods Appl. 3(4) (1997) 255-273.
8. K.P. Kutzenogii, A.I. Levykin, K.K. Sabelfeld, Numerical simulation of the kinetics of aerosol formation in the free molecular collision regime, J. Aerosol Sci. 27(5) (1996) 665-679.
9. O. Kurbanmuradov, K. Sabelfeld, Coagulation of aerosol particles in turbulent flows, Preprint No. 421 of the Weierstrass Institute for Applied Analysis and Stochastics, Berlin, 1998.
10. O. Kurbanmuradov, K. Sabelfeld, D. Koluhin, Stochastic Lagrangian models for two-particle motion in turbulent flows. Numerical results, Monte Carlo Methods Appl. 3(3) (1997) 199-223.
11. J.D. Langrebe, S.E. Pratsinis, A discrete-sectional model for particulate production by gas-phase chemical reaction and aerosol coagulation in the free-molecular regime, J. Coll. Interface Sci. 139 (1990) 1.
12. K. Liffman, A direct simulation Monte Carlo method for cluster coagulation, J. Comp. Phys. 100 (1992) 116-127.
13. A.H. Marcus, Stochastic coalescence, Technometrics 10(1) (1968) 133-143.
14. A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics, vol. 2, M.I.T. Press, Cambridge, MA, 1975.
15. K. Nanbu, Direct simulation scheme derived from the Boltzmann equation. I. Monocomponent gases, J. Phys. Soc. Jpn 49(5) (1980) 2042-2049.
16. S.E. Pashenko, S.V. Rogasinsky, K.K. Sabelfeld, V.V. Karasev, Statistical simulations of the coagulation process of high dispersed systems, Preprint No. 574 (1985), Computing Centre, Russian Acad. Sci., Siberian Branch, Novosibirsk.
17. K.K. Sabelfeld, Monte Carlo Methods in Boundary Value Problems, Springer-Verlag, Heidelberg-New York-Berlin, 1991.
18. K.K. Sabelfeld, A.A. Kolodko, Monte Carlo simulation of the coagulation process governed by Smoluchowski equation with random coefficients, Monte Carlo Methods Appl. 3(4) (1997) 275-311.
19. K.K. Sabelfeld, S.V. Rogasinsky, A.A. Kolodko, A.I. Levykin, Stochastic algorithms for solving Smoluchowski coagulation equation and applications to aerosol growth simulation, Monte Carlo Methods Appl. 2(1) (1996) 41-87.
20. K.K. Sabelfeld, O.A. Kurbanmuradov, Stochastic Lagrangian models for two-particle motion in turbulent flows, Monte Carlo Methods Appl. 3 (1997) 53-72.
21. P. Saffman, J.S. Turner, On the collision of drops in turbulent clouds, J. Fluid Mech. 1 (1956) 16-30.
22. M. Smoluchowski, Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Z. Phys. Chem. 92 (1917) 129.
23. V.M. Voloshtchuk, Ju.S. Sedunov, The coagulation processes in dispersed systems. Gidromet, L., 1975.
24. W. Wagner, A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation, J. Stat. Phys. 66 (1992) 689-722.
25. M.M.R. Williams, S.K. Loyalka, Aerosol Science, Theory and Practice, Pergamon, New York, 1991.