APPROXIMATE RIEMANN SOLVERS IN FVM FOR 2D HYDRAULIC SHOCK-WAVE MODELING

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 characteristi c theory are used in the finite volume method (FVM) for solving the tw o-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 analy sis on the computational stability of the methods. The effects of chan ges in bed elevations on the solutions are also investigated. Comparis on of numerical and analytical solutions indicates that very good agre ement can be obtained by all three approximate Riemann solvers. Differ ences in accuracy, computer time, and numerical stability among the th ree schemes are not significant. For practical purposes, all of them c an satisfactorily simulate the hydraulic phenomena in subcritical and supercritical hows as well as in smooth and discontinuous flows, espec ially shock wave modeling. These solvers are useful for studying levee failure or dam break due to extreme hood events, or the sudden openin g or closing of sluice gates in a channel.