On a hybrid finite-volume-particle method
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA.
2 Department of Mathematics, Tulane University, New Orleans, LA 70118, USA. email@example.com.
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.
Mathematics Subject Classification: 34A36 / 35L67 / 35Q35 / 65M99
Key words: Shallow water equations / transport of passive pollutant / finite-volume schemes / particle method.
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