MATHEMATICAL MODELING:

Direct Simulation Monte Carlo method (DSMC) for chemically reacting gases

Physical and chemical kinetics of nonthermal particles in the planetary atmospheres can be rigorously described by a set of nonlinear Boltzmann type equations with the source terms. For the numerical analysis of nonthermal particle kinetics and dynamics the discrete mathematical model is used. This model is developed on the base of the probabilistic description of the collisional aeronomical processes and is realized on a computer as the numerical system (stochastic model).

Generally, the stochastic simulation may be presented as a numerical realization of one of the physical-probabilistic analogues of the considered physical process. The essence of this approach consists in constructing a stochastic process, the probabilistic description of which is connected to the kinetic description of considered physical process. Then, instead of a direct solution of these stochastic equations, the constructed stochastic process is manifold times simulated in a computer realization using the Monte-Carlo algorithms. All necessary physical characteristics may be estimated from the computer realizations of this stochastic process.

This kinetic approach applied to planetary atmospheres is described in detail in the following review papers

  • Marov, M.Ya., Shematovich, V.I., Bisikalo, D.V.

            Nonequilibrium processes in the planetary and cometary atmospheres. A kinetic approach to modeling,

           Space Science Reviews, 1996, 76, Nos. 1/2, 1-202.

  • Shematovich, V.I.

            Stochastic modeling of chemistry in the planetary atmospheres.

            In: Avduevsky V.S and Kolesnichenko A.V. (Eds.) Modern problems of space mechanics and physics,

           Moscow, Fizmatlit, 186-198, (in Russian).

  • Shematovich V.I.

            Stochastic models of hot planetary and satellite coronas.

             Solar System Research (English translation of "Astonomicheskij Vestnik"), 2004, 38, No.1, 28-38 (abstract).

 

and monograph

  • Marov, M.Ya., Shematovich, V.I., Bisikalo, D.V. and Gerard J.-C.

            Nonequilibrium processes in the planetary and cometary atmospheres: Theory and Applications.

            Kluwer Academic Publishers, 1997, Dordrecht, 293 pp.

This approach can be considered as a strictly Markovian modification of the Monte Carlo Direct Simulation (MCDS) method.

Development, modification and applications of the MCDS method:

- Stochastic modeling of the chemically reacting gas:

·       Zmievskaia, G. I.; Piarnpuu, A. A.; Shematovich, V. I.

      Modeling of physical and chemical processes in a gas mixture (abstract).

      Doklady Akademii Nauk SSSR, 1979, 248, no. 3, 1979, p. 561-564. (In Russian)

·       Zmievskaia, G. I.; Piarnpuu, A. A.; Shematovich, V. I.

      Statistical modeling of gas mixture states with allowance for energy exchange between the translational

     and internal degrees of freedom (abstract).

    PMTF - Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, 1980, p. 19-29.( In Russian).

·       Piarnpuu, A. A.; Shematovich, V. I.; Zmievskaia, G. I.

     Development of a constructive physical-probabilistic analog of collisional processes in a rarefied gas (abstract).

     Doklady Akademii Nauk SSSR, 1981, 258, no. 4, p. 815-818.( In Russian).

·       Zmievskaia, G. I.; Piarnpuu, A. A.; Shematovich, V. I.

      A statistical model of nonstationary nonequilibrium processes in rarefied multicomponent chemically reacting gases (abstract).

      In: Molecular gas dynamics. Moscow, Izdatel'stvo Nauka, 1982, p. 184-193.( In Russian ).

·       Shematovich, V. I.; Zmievskaia, G. I.; Piarnpuu, A. A.

      Stochastic modeling of uniformly expanding rarefied gases (abstract).

      Doklady Akademii Nauk SSSR, 1982, 266, no. 3, p. 573-576.( In Russian).

·       Zmievskaia, G. I.; Marov, M. Ya.; Maurakh, M. M.; Shematovich, V. I.

      Stochastic simulation of nonequilibrium physicochemical processes in rarefied media (abstract).

      In: Nonlinear and turbulent processes in physics; Proceedings of the Second International Workshop, Kiev,

      Ukrainian SSR, October 10-25, 1983. Volume 2. Switzerland and New York, Harwood Academic Publishers, 1984, p. 1117-1123.

- Structural stochastic modeling:

·       Piarnpuu, A. A.; and Shematovich, V. I.

      Construction of structural stochastic models of collision processes in rarefied gas media (abstract).

      Russian Journal of Theoretical and Applied Mechanics, 1991, 1, p. 229-234.

·       Piarnpuu, A. A.; Tsvetkov, G.A.; Shematovich, V. I.

      Numerical study of relaxation processes in rarefied gas mixtures (abstract).

      In: Molecular gas dynamics and the mechanics of inhomogeneous media. Moscow,

      Izdatel'stvo Nauka, 1990, p. 99-109. (In Russian).

·       Shematovich V.I., Pyarnpuu A.A., Cheredov V.V., and Tsvetkov, G.A.

      Hybrid stochastic modeling of kinetic systems.

      Mathematical Modeling, 2002, 14, No.8, 96-101 (in Russian).

 

- Monte Carlo modeling of the chemical reactions near the solid surfaces:

·       Piarnpuu, A. A.; Tsvetkov, G.A.; Shematovich, V. I.

     Kinetic simulation of chemical reactions in rarefied multicomponent gases near solid surfaces (abstract).

      In: Rarefied gas dynamics; Proceedings of the 17th International Symposium, Aachen, Germany, July 8-14, 1990.

      Weinheim, Germany and New York, VCH Verlagsgesellschaft mbH, 1991, p. 1385-1390.

·       Pyarnpuu A.A., Rymarchuk A.V., and Shematovich V.I.

      Nonthermal chemical reactions in the spacecraft plume.

      Mathematical Modeling, 1999, 11, No.2, 33-44 (in Russian).

·       Pyarnpuu A.A., and Shematovich V.I.

      Kinetic modeling of of chemical reactions near the satellite surface.

      Mathematical Modeling, 2000, 12, No. 5, 22-26 (in Russian).

·       Pyarnpuu A.A., Cheredov V.V., and Shematovich V.I

      Kinetic modeling of 'hot' hydrogen molecules ejected from interstellar grains.

      Mathematical Modeling, 2001, 13, No.7, 88-93 (in Russian).