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

Upwind schemes are very well adapted to advection dominated flows and have become popular for applications involving the Euler system of equations. Re cently, Riemann solver-based techniques such as Roe's scheme have become a successful tool for numerical simulation of other conservation laws like th e shallow water equations. One of the disadvantages of this technique is re lated to the treatment of the source terms of the equations. The conservati vity of the scheme can be seriously damaged if a careless treatment is appl ied. Previous papers studied the way to treat the terms arising from bed le vel changes. This gaper deals with the analysis of the main reasons leading to a correct treatment of the geometrical source terms, that is, those rep resenting the changes in cross-section which may be linked to the specific dependence of the flux function on the geometry. (C) 2000 Elsevier Science Ltd. All rights reserved.