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Preventing numerical oscillations in the flux‐split based finite difference method for compressible flows with discontinuities, II
Author(s) -
He Zhiwei,
Zhang Yousheng,
Li Xinliang,
Tian Baolin
Publication year - 2015
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.4080
Subject(s) - classification of discontinuities , discretization , finite difference , nonlinear system , mathematical analysis , mathematics , compressibility , finite difference method , compressible flow , flux (metallurgy) , flow (mathematics) , finite volume method , mechanics , physics , geometry , materials science , quantum mechanics , metallurgy
Summary Problems in the characteristic‐wise flux‐split based finite difference method when compressible flows with contact discontinuities or material interfaces are computed were presented and analyzed. The current analysis showed the following: (i) Even with the local characteristic decomposition technique, numerical errors could be caused by point‐wise flux vector splitting (FVS) methods, such as the Steger–Warming FVS or the van Leer FVS. Therefore, the Lax–Friedrichs type FVS method is required. (ii) If the isobars of a material are vertical lines, the combination of using the local characteristic decomposition and the global Lax–Friedrichs FVS can avoid velocity and pressure oscillations of contact discontinuities in this material for weighted essentially non‐oscillatory (WENO) schemes. (iii) For problems with material interfaces, the quasi‐conservative approach can be realized using characteristic‐wise flux‐split based finite difference WENO schemes if nonlinear WENO schemes in genuinely nonlinear characteristic fields can be guaranteed to be the same and the decomposition equation representing material interfaces is discretized properly. Copyright © 2015 John Wiley & Sons, Ltd.