Positivity preserving finite volume Roe schemes for transport-diffusion equations

The motion of flood waves resulting from dam break are investigated numeric ally. The Roe approximate Riemann solver is applied to the system of shallo w water equations. This system is combined with pollutant transport diffusi on equation and solved on structured and non-structured grids. An entropy f ix for the numerical scheme enables to handle initial dry area flows even i n complicated geometry cases, without loss of mass positivity. To discretiz e the diffusion term, a nine point spatial discretization is used on a stru ctured grid and a four point finite volume scheme is used on unstructured m eshes. In order to have flexibility upon the complex configurations domain, non-structured grid meshing is utilized. A semi-implicit discretization of the source terms, as well as the use of second order schemes, makes it pos sible to successfully investigate problems with friction and non-horizontal ground. (C) 1999 Elsevier Science S.A. All rights reserved.