Premium
A conservative flux‐splitting method for steady shock capturing
Author(s) -
Zhu Zhibin,
Shang Qing,
Shen Qing
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4942
Subject(s) - flux limiter , total variation diminishing , classification of discontinuities , dissipative system , mechanics , shock (circulatory) , shock wave , dissipation , flux (metallurgy) , conservation law , mathematics , physics , numerical analysis , mathematical analysis , classical mechanics , thermodynamics , materials science , medicine , metallurgy
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.