We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the finite-volume-particle method is to use different schemes for the flow and pollution computations: the shallow water equations are numerically integrated using a finite-volume scheme, while the transport equation is solved by a particle method. This way the specific advantages of each scheme are utilized at the right place. A special attention is given to the recovery of the point values of the numerical solution from its particle distribution. The reconstruction is obtained using a dual equation for the pollutant concentration. This results in a significantly enhanced resolution of the computed solution and also makes it much easier to extend the finite-volume-particle method to the two-dimensional case.
Mots-clés : shallow water equations, transport of passive pollutant, finite-volume schemes, particle method
@article{M2AN_2004__38_6_1071_0,
author = {Chertock, Alina and Kurganov, Alexander},
title = {On a hybrid finite-volume-particle method},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1071--1091},
publisher = {EDP-Sciences},
volume = {38},
number = {6},
year = {2004},
doi = {10.1051/m2an:2004051},
mrnumber = {2108945},
zbl = {1077.65091},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004051/}
}
TY - JOUR AU - Chertock, Alina AU - Kurganov, Alexander TI - On a hybrid finite-volume-particle method JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 1071 EP - 1091 VL - 38 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004051/ DO - 10.1051/m2an:2004051 LA - en ID - M2AN_2004__38_6_1071_0 ER -
%0 Journal Article %A Chertock, Alina %A Kurganov, Alexander %T On a hybrid finite-volume-particle method %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 1071-1091 %V 38 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004051/ %R 10.1051/m2an:2004051 %G en %F M2AN_2004__38_6_1071_0
Chertock, Alina; Kurganov, Alexander. On a hybrid finite-volume-particle method. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 1071-1091. doi : 10.1051/m2an:2004051. http://www.numdam.org/articles/10.1051/m2an:2004051/
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