An improved third-order weighted essentially non-oscillatory scheme achieving optimal order near critical points

作者：Xu, Weizheng^*; Wu, Weiguo

来源：Computers & Fluids, 2018, 162: 113-125.

DOI：10.1016/j.compfluid.2017.12.010

• WENO schemes
• Smoothness indicators
• Convergence accuracy
• High-resolution
• Hyperbolic conservation laws

In this paper, we present an improved third-order weighted essentially non-oscillatory scheme to recover its convergence order at critical points. This scheme is constructed with the way of Taylor expansion of the smoothness indicators for third-order convergence. The recovery of design-order is verified by several linear wave tests. The performance of the proposed scheme is demonstrated on a variety of one-dimensional problems like the Shu-Osher problem, Titarev-Toro problem and the Interacting blast wave problem, As well as two-dimensional problems such as Rayleigh-Taylor instability, Two-dimensional Riemann problem and Double Mach reflection of a strong shock problem. Numerical results indicate that the present scheme provides better results in comparison with the WENO-JS3, WENO-Z3 and WENO-N3 schemes.

• 出版日期2018-1-30
• 单位武汉理工大学