Improved application of the HLLE Riemann solver for the shallow water equations with source terms

Abstract

The present work addresses the numerical prediction of shallow water flows with the application of the HLLE approximate Riemann solver. This Riemann solver has several desirable properties, such as, ease of implementation, satisfaction of entropy conditions, high shock resolution and positivity preservation. A corrected upwind discretization of the source terms is applied, in conjunction with the HLLE solver, following some resent developments presented in the literature. Numerical results are obtained for a series of one-dimensional test cases by means of the proposed model and compared with analytical solutions or solutions presented in the literature. Strong numerical evidence shows that the proposed model implementation is accurate, robust, conservative and highly stable in capturing strong gradients and discontinuities in transcritical flows, as well as calculating dry areas (vacuum), and is a reliable model for one-dimensional (steady and unsteady) practical applications in hydraulics engineering. © 2003 John Wiley & Sons, Ltd.