caa a22 4500 378936727 CHVBK 20180305123642.0 cr unu---uuuuu 161128s2004 xx s 000 0 eng 10.2478/cmam-2004-0023 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0023 A Generalized Relaxation Method for Transport and Diffusion of Pollutant Models in Shallow Water [Elektronische Daten] We present a numerical method based on finite difference relaxation approximations for computing the transport and diffusion of a passive pollutant by a water flow. The flow is modeled by the well-known shallow water equations and the pollutant propagation is described by a transport equation. The previously developed nonoscillatory relaxation scheme is generalized to cover problems with pollutant trans- port, in one and two dimensions and source terms, resulting in a class of methods of the first and the second order of accuracy in space and time. The methods are based on the classical relaxation models combined with a Runge-Kutta time splitting scheme, where neither Riemann solvers nor characteristic decompositions are needed. Numerical results are presented for several benchmark test problems. The schemes presented are verified by comparing the results with documented ones, proving that no special treatment is needed for the transport equation in order to obtain accurate results. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Shallow Water Equations nationallicence Relaxation Schemes nationallicence Finite Differences nationallicence TVD nationallicence Transport and Diffusion of Pollutant nationallicence Source Terms nationallicence Delis A.I. Department of Sciences, Division of Mathematics, Technical University of Crete, University Campus, Chania 73100, Crete, Greece. Katsaounis Th Institute of Mathematics, National Academy of Sciences, 3 Tereschenkivska Str., 01601 Kyiv, Ukraine. Institute of Applied and Computational Mathematics, FORTH, Heraklion 71110, Crete, Greece. Computational Methods in Applied Mathematics De Gruyter 4/4(2004), 410-430 1609-4840 4:4<410 2004 4 cmam https://doi.org/10.2478/cmam-2004-0023 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2004-0023 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Delis A.I. Department of Sciences, Division of Mathematics, Technical University of Crete, University Campus, Chania 73100, Crete, Greece NATIONALLICENCE 700 1- Katsaounis Th Institute of Mathematics, National Academy of Sciences, 3 Tereschenkivska Str., 01601 Kyiv, Ukraine. Institute of Applied and Computational Mathematics, FORTH, Heraklion 71110, Crete, Greece NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 4/4(2004), 410-430 1609-4840 4:4<410 2004 4 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter