An improved third-order weighted essentially non-oscillatory scheme achieving optimal order near critical points. (30th January 2018)

• Record Type: Journal Article
• Authors: Xu, Weizheng; Wu, Weiguo
• Is Part Of: Computers & fluids. Volume 162(2018)
• Page Start: 113
• Page End: 125
• Publication Date: 2018-01-30
• Subjects: WENO schemes -- Smoothness indicators -- Convergence accuracy -- High-resolution -- Hyperbolic conservation laws; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2017.12.010
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: An improved third-order WENO-Z scheme for recovering its convergence order at critical points is proposed. The proposed scheme performs better than WENO-JS3, WENO-Z3 and WENON3 schemes. The flow characteristics of the physical problems should be considered for designing a scheme. Abstract: 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 WENON3 schemes.