High-accuracy WENO scheme for shallow water equations and its applications

In this paper, we propose a novel low-dissipation fifth-order WENO (Weighted Essentially Non-Oscillatory) scheme by decomposing the three small modal smoothness indicators in the classical WENO-JS scheme and recombining the resulting second-order derivative terms to construct a more accurate global smoothness indicator. First, we demonstrate through Taylor series expansion that the proposed scheme preserves fifth-order accuracy at both first-order and second-order critical points. Next, we verify its high-accuracy properties using continuous initial conditions for one-dimensional convection equations, and assess its high-resolution capability under discontinuous initial conditions for the same equations. The numerical stability of the scheme for nonlinear systems is further validated through the one-dimensional Euler equations shock-tube problem. Finally, we establish one- and two-dimensional dam-break flood models based on the shallow water equations and simulate the classical dam-break flow using the proposed scheme. Comparative results with other schemes show that our method significantly outperforms existing approaches in capturing strong intermittent phenomena. Therefore, the high-accuracy WENO scheme presented in this study is a high-performance tool for surge modeling and can be effectively applied to the numerical simulation of other intermittent flow problems.