Approximate Riemann Solvers in FVM for 2D Hydraulic Shock Wave Modeling

Abstract

This paper presents three approximate Riemann solver schemes, namely: the flux vector splitting (FVS), the flux difference splitting (FDS), and the Osher scheme. Originally used to solve the Euler equations in aerodynamic problems, these Riemann solvers based on the characteristic theory are used in the finite volume method (FVM) for solving the two-dimensional shallow water equations. The three solvers are compared in this paper according to theoretical development, difference schemes, practical applications to shock wave problems, and sensitivity analysis on the computational stability of the methods. The effects of changes in bed elevations on the solutions are also investigated. Comparison of numerical and analytical solutions indicates that very good agreement can be obtained by all three approximate Riemann solvers. Differences in accuracy, computer time, and numerical stability among the three schemes are not significant. For practical purposes, all of them can satisfactorily simulate the hydraulic phenomena in subcritical and supercritical flows as well as in smooth and discontinuous flows, especially shock wave modeling. These solvers are useful for studying levee failure or dam break due to extreme flood events, or the sudden opening or closing of sluice gates in a channel.