Conservative upwind difference schemes for open channel flows—theory and applications

Abstract

Conservative upwind finite-difference schemes are presented for the solution of the one-dimensional shallow water equations in open channels. Numerical results are presented and compared for different versions of the schemes when applied to a test problem comprising a channel with varying breadth and depth and friction terms. This includes consideration of the effect of treating part of the flux balance as a source, and a comparison of square-root and arithmetic averaging.