Roll waves simulation using shallow water equations and Weighted Average Flux method

Abstract

The weighted average flux method is used to represent trough 1-D shallow water equations the development of natural roll waves in rectangular channels. The method is reformulated in such a way that all source terms are incorporated into the local Riemann problem by means of a useful transformation of the equations, maintaining second-order accuracy of the solution.

A code based on this method has been developed and results of numerical applications to a Venturi channel and to the attenuation of waves are presented to check for well known situations how accurately the source terms are evaluated.

The code is applied to reproduce Brock's experiments on roll waves performed in a rectangular laboratory channel. The numerical solution accurately represents roll waves evolution due to uniform flow instability as well as wave intensity increase due to instability and wave coalescence. A sensitivity analysis of the numerical solution to changes of computational parameters is performed, in order to explain the discrepancies among computed and experimental values.