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

✍ Scribed by L.A. Monthe; F. Benkhaldoun; I. Elmahi

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 623 KB
• Volume: 178
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(99)00015-8

✦ Synopsis

The motion of ¯ood 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 diusion equation and solved on structured and non-structured grids. An entropy ®x for the numerical scheme enables to handle initial dry area ¯ows even in complicated geometry cases, without loss of mass positivity. To discretize the diusion term, a nine point spatial discretization is used on a structured grid and a four point ®nite volume scheme is used on unstructured meshes. In order to have ¯exibility upon the complex con®gurations 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.