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MATHEMATICAL MODELING:
Direct Simulation
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
Nonequilibrium
processes in the planetary and cometary atmospheres.
A kinetic approach to modeling,
Space Science Reviews, 1996, 76, Nos. 1/2, 1-202.
Stochastic modeling of chemistry in
the planetary atmospheres.
In: Avduevsky
V.S and Kolesnichenko A.V. (Eds.) Modern
problems of space mechanics and physics,
Stochastic models of hot planetary
and satellite coronas.
Solar System
Research (English translation of "Astonomicheskij Vestnik"),
2004, 38, No.1, 28-38 (abstract).
·
Shematovich, V.I.
Hot Planetary Coronae.
In: Rarefied Gas Dynamics 25, Proceedings
of 25th
International Symposium on Rarefied Gas Dynamics
held in
Edited by Mikhail S. Ivanov and Alexey K. Rebrov. 2007, Publishing House of the Siberian Branch of the RAS,
Kinetics of suprathermal atoms and
molecules in the rarefied planetary atmospheres.
In:
RARIFIED
GAS DYNAMICS:
Proceedings of the 26th International Symposium on Rarefied Gas
Dynamics.
AIP Conference Proceedings, Volume 1084, pp.1047-1054, 2008.
and monograph
Nonequilibrium
processes in the planetary and cometary atmospheres:
Theory and Applications.
Kluwer
Academic Publishers, 1997,
This
approach can be considered as a strictly Markovian
modification of the
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.
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.
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,
Ukrainian SSR,
- 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.
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).
-
·
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,
·
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).