Numerical modelling of river flow (numerical schemes for one type of nonconservative systems)

Marek Brandner, Jiri Egermaier, Hana Kopincova

In this paper we propose a new numerical scheme to simulate the river
flow in the presence of a variable bottom surface. We use finite volume approach, our method is based on
the technique described by D. L. George for shallow water equations. The main goal is to construct
the scheme, which is well balanced, ie maintains not only some special steady states but
all steady states which can occur. Furthermore this should preserve nonnegativity of
some quantities, which are essentially nonnegative from their physical fundamental, for example the cross section or depth. Our scheme can be
extended to the second order accuracy. We also present numerical experiments.