On numerical treatment of the source terms in the shallow water equations

Abstract

Upwind schemes are very well adapted to advection dominated flows and have become popular for applications involving the Euler system of equations. Recently, Riemann solver-based techniques such as Roe’s scheme have become a successful tool for numerical simulation of other conservation laws like the shallow water equations. One of the disadvantages of this technique is related to the treatment of the source terms of the equations. The conservativity of the scheme can be seriously damaged if a careless treatment is applied. Previous papers studied the way to treat the terms arising from bed level changes. This paper deals with the analysis of the main reasons leading to a correct treatment of the geometrical source terms, that is, those representing the changes in cross-section which may be linked to the specific dependence of the flux function on the geometry.