Abstract:
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 achieve a more accurate global smoothness indicator. Firstly, we demonstrate through Taylor series expansion that the new scheme maintains fifth-order accuracy at both first-order and second-order critical points. Secondly, we validate the high-precision characteristics of the new scheme using continuous initial conditions for one-dimensional convective equations, and its high-resolution characteristics using discontinuous initial conditions for the same equations. Lastly, we establish one- and two-dimensional dam-break flood models based on the shallow water equations and simulate the classical dam-break flow using our new scheme. We compare these results with those obtained using other schemes, showing that our scheme performs significantly better in capturing strong intermittent phenomena. Therefore, the high-precision WENO scheme proposed in this paper is a high-performance format for capturing surges and can be effectively used for the numerical simulation of other intermittent problems.