Positivity preserving finite volume Roe: schemes for transport-diffusion equations Original Research Article

The motion of flood waves resulting from dam break are investigated numerically. The Roe approximate Riemann solver is applied to the system of shallow water equations. This system is combined with pollutant transport diffusion equation and solved on structured and non-structured grids. An entropy fix for the numerical scheme enables to handle initial dry area flows even in complicated geometry cases, without loss of mass positivity. To discretize the diffusion term, a nine point spatial discretization is used on a structured grid and a four point finite volume scheme is used on unstructured meshes. 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 possible to succesfully investigate problems with friction and non-horizontal ground.