A high-resolution, hybrid compact-WENO scheme with minimized dispersion and controllable dissipation

• Published in: Science China. Physics, mechanics & astronomy Vol. 57; no. 5; pp. 971 - 982
• Main Authors: Sun, ZhenSheng, Hu, Yu, Luo, Lei, Zhang, ShiYing, Yang, ZhengWei
• Format: Journal Article
• Language: English
• Published: Heidelberg Science China Press 01.05.2014; Springer Nature B.V
• Subjects: Approximation; Astronomy; Classical and Continuum Physics; Controllability; Dispersions; Dissipation; Finite difference method; High resolution; Mathematical analysis; Observations and Techniques; Physics; Physics and Astronomy; Spectra; Stability; Wave propagation; WENO格式; 分散性; 可控; 最小化; 混合动力; 紧凑; 耗散; 高分辨率; nonlinear spectral analysis; spectral optimization; shock-capturing schemes; binaries: high-resolution schemes
• ISSN: 1674-7348; 1869-1927
• DOI: 10.1007/s11433-013-5305-0

In this paper, a high-resolution, hybrid compact-WENO scheme is developed based on the minimized dispersion and controllable dissipation reconstruction technique. Firstly, a sufficient condition for a family oftri-diagonal compact schemes to have independent dispersion and dissipation is derived. Then, a specific 4th order compact scheme with low dispersion and adjustable dissipation is constructed and analyzed. Finally, the optimized compact scheme is blended with the WENO scheme to form the hybrid scheme. Moreover, the approximation dispersion relation approach is employed to optimize the spectral properties of the nonlinear scheme to yield the true wave propagation behavior of the finite difference scheme. Several test cases are carried out to verify the high- resolution as well as the robust shock-capturing capabilities of the proposed scheme.