shallow water equations, finite volume evolution Galerkin method, river simulations, well-balanced scheme, hyperbolic balance laws
510: Mathematik
Finite-Volumen-Methode
Galerkin-Methode
Erhaltungssatz
510
65L05:Initial value problems
65M06:Finite difference methods
65L05
65M06
Beschreibung:
The aim of the paper is numerical modeling of the shallow water equation with source terms by genuinely multdimensional finite volume evolution Galerkin schemes. The shallow water system, or its one-dimensional analogy the Saint-Venant equation, is used extensively for numerical simulation of natural rivers. Mathematically the shallow water system belongs to the class of balance laws. A special treatment of the source terms describing the bottom topography as well as frictions effects is necessary in order to reflect their balance with the gradients of fluxes. We present behaviour of our new well-balance FVEG scheme for several benchmark test problems and compare our results with those obtained by the finite element scheme of Teschke et al. used for practical river simulations.