Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 288-301
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The features of the stochastic discrete particle method are discussed as applied to the simulation of pollutant advection and diffusion in a turbulent flow and to the spread of a thin film of a viscous substance (oil) on the surface of water. The diffusion tensor in the former problem depends on the scale of the pollution cloud, and the diffusivity in the latter problem depends nonlinearly on the desired function. For pollution dispersion by a turbulent flow, a stochastic discrete particle algorithm is constructed in the case when the diffusion tensor corresponds to the Richardson 4/3 law. The numerical and analytical results are shown to agree well. The problem of oil film spreading is described by a quasilinear advection-diffusion equation. For this problem, a random walking algorithm is constructed in which the variance of the walking particle step depends on the desired function. For both instantaneous and time-continuous sources of pollutants, the solution produced by the stochastic discrete particle method agrees well with the analytical and/or numerical solutions to the test problems under consideration.
@article{ZVMMF_2007_47_2_a10,
author = {B. V. Arkhipov and V. N. Koterov and V. V. Solbakov and D. A. Shapochkin and Yu. S. Yurezanskaya},
title = {Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {288--301},
publisher = {mathdoc},
volume = {47},
number = {2},
year = {2007},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a10/}
}
TY - JOUR AU - B. V. Arkhipov AU - V. N. Koterov AU - V. V. Solbakov AU - D. A. Shapochkin AU - Yu. S. Yurezanskaya TI - Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2007 SP - 288 EP - 301 VL - 47 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a10/ LA - ru ID - ZVMMF_2007_47_2_a10 ER -
%0 Journal Article %A B. V. Arkhipov %A V. N. Koterov %A V. V. Solbakov %A D. A. Shapochkin %A Yu. S. Yurezanskaya %T Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2007 %P 288-301 %V 47 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a10/ %G ru %F ZVMMF_2007_47_2_a10
B. V. Arkhipov; V. N. Koterov; V. V. Solbakov; D. A. Shapochkin; Yu. S. Yurezanskaya. Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 288-301. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a10/