A new approach on simulating two-dimensional shallow-water flow with uneven bottom

Abstract

Numerical simulation of 2D shallow-water flow over uneven bottom performed under a new form of shallow-water equations is reported in this paper. The original shallow water equations are rewritten so that it ensures the water units at the same water depth with the same potential energy. The balance between the flux gradient and the slope term is always matched so that the initial still water can keep static. The reformed equation set is also suitable for simulating the shallow water flow over sharply changed, uneven bottom. The numerical solution is based on the cell-centred finite-volume method and the advection terms in the shallow-water equations are treated by Harten, Lax and Van Leer's approximating Riemann solver. Several test cases are performed to verify the accuracy, stability and reliability of the program.