An upstream flux-splitting finite-volume scheme for 2D shallow water equations

Abstract

An upstream flux-splitting finite-volume (UFF) scheme is proposed for the solutions of the 2D shallow water equations. In the framework of the finite-volume method, the artificially upstream flux vector splitting method is employed to establish the numerical flux function for the local Riemann problem. Based on this algorithm, an UFF scheme without Jacobian matrix operation is developed. The proposed scheme satisfying entropy condition is extended to be second-order-accurate using the MUSCL approach. The proposed UFF scheme and its second-order extension are verified through the simulations of four shallow water problems, including the 1D idealized dam breaking, the oblique hydraulic jump, the circular dam breaking, and the dam-break experiment with 45° bend channel. Meanwhile, the numerical performance of the UFF scheme is compared with those of three well-known upwind schemes, namely the Osher, Roe, and HLL schemes. It is demonstrated that the proposed scheme performs remarkably well for shallow water flows. The simulated results also show that the UFF scheme has superior overall numerical performances among the schemes tested. Copyright © 2005 John Wiley & Sons, Ltd.