On a hybrid finite-volume-particle method
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) no. 6, pp. 1071-1091.

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.

DOI : https://doi.org/10.1051/m2an:2004051
Classification : 34A36,  35L67,  35Q35,  65M99
Mots clés : shallow water equations, transport of passive pollutant, finite-volume schemes, particle method
     author = {Chertock, Alina and Kurganov, Alexander},
     title = {On a hybrid finite-volume-particle method},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - 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},
     zbl = {1077.65091},
     mrnumber = {2108945},
     language = {en},
     url = {www.numdam.org/item/M2AN_2004__38_6_1071_0/}
Chertock, Alina; Kurganov, Alexander. On a hybrid finite-volume-particle method. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) no. 6, pp. 1071-1091. doi : 10.1051/m2an:2004051. http://www.numdam.org/item/M2AN_2004__38_6_1071_0/

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