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Numerical Modeling of Pollutant Dispersion and Oil Spreading by the Stochastic Discrete Particles Method
Author(s) -
Arkhipov Boris,
Koterov Vladimir,
Solbakov Viacheslav,
Shapochkin Dmitry,
Yurezanskaya Yulia
Publication year - 2008
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2007.00394.x
Subject(s) - dispersion (optics) , diffusion , random walk , mathematics , molecular diffusion , particle (ecology) , function (biology) , discrete modelling , statistical physics , heuristic , mathematical analysis , mathematical optimization , physics , discrete system , statistics , thermodynamics , algorithm , geology , biology , metric (unit) , operations management , oceanography , evolutionary biology , optics , economics
We consider two applications of the stochastic discrete particles method. The first one is concerned with the dispersion of a passive pollutant by a turbulent stream with a scale dependent diffusion coefficient. The second application deals with the problem of an oil spill spreading on the water surface described by transport–diffusion equation with a nonlinear diffusion coefficient. For the first problem we develop a discrete particles algorithm provided the diffusion coefficient obeys Richardson's “4/3” law and show good correspondence with the numerical and analytical results. The second problem is more involved and we develop a heuristic procedure based on the standard discrete particles random walk algorithm updating the dependence of each particle step variance on the dependent function. The obtained solution coincides well with analytical and direct one‐dimensional finite‐difference solutions both for instantaneous and continuous oil release.