A conservative flux‐splitting method for steady shock capturing. (3rd December 2020)

• Record Type: Journal Article
• Authors: Zhu, Zhibin; Shang, Qing; Shen, Qing
• Is Part Of: International journal for numerical methods in fluids. Volume 93:Number 5(2021)
• Page Start: 1564
• Page End: 1577
• Publication Date: 2020-12-03
• Subjects: conservative flux‐splitting -- numerical oscillations -- shock capturing -- steady shock; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4942
• Languages: English
• ISSNs: 0271-2091

Abstract

Abstract: A novel flux‐splitting method that can preserve the flux conservation properties for the steady shock waves is proposed in present paper. The proposed method is based on the total variation diminishing (TVD) scheme, and the dissipative flux term is constructed by the flux directly instead of conservative variables. Similar transformations are imposed on the anti‐dissipation term, which is formulated by utilizing the limiter function. Numerical experiments were performed on the one, quasi one‐ and two‐dimensional shock wave problems. The computed results show that, the steady shock waves can be accurately captured within two grid points by the proposed conservative flux‐splitting (CFS) method, and numerical oscillations are successfully eliminated near the flow discontinuities. The conservation and accuracy of present method are demonstrated by comparisons with the TVD, flux vector splitting and flux difference splitting methods. Abstract : A novel flux‐splitting method that can preserve the flux conservation properties for the steady shock waves is proposed in present paper. Numerical experiments demonstrate the superb capability for shock capturing of the proposed method. The conservative flux‐splitting method is capable of locating the shock accurately within two grid points without numerical dissipation or oscillations near the shock waves.