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Developing a hybrid flux function suitable for hypersonic flow simulation with high‐order methods
Author(s) -
Wang Dongfang,
Deng Xiaogang,
Wang Guangxue,
Dong Yidao
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.4186
Subject(s) - hypersonic speed , robustness (evolution) , nonlinear system , computational fluid dynamics , shock (circulatory) , euler equations , shock wave , mechanics , heat flux , control theory (sociology) , computer science , mathematics , physics , heat transfer , mathematical analysis , medicine , biochemistry , chemistry , control (management) , quantum mechanics , artificial intelligence , gene
Summary In this paper, we develop a new hybrid Euler flux function based on Roe's flux difference scheme, which is free from shock instability and still preserves the accuracy and efficiency of Roe's flux scheme. For computational cost, only 5 % extra CPU time is required compared with Roe's FDS. In hypersonic flow simulation with high‐order methods, the hybrid flux function would automatically switch to the Rusanov flux function near shock waves to improve the robustness, and in smooth regions, Roe's FDS would be recovered so that the advantages of high‐order methods can be maintained. Multidimensional dissipation is introduced to eliminate the adverse effects caused by flux function switching and further enhance the robustness of shock‐capturing, especially when the shock waves are not aligned with grids. A series of tests shows that this new hybrid flux function with a high‐order weighted compact nonlinear scheme is not only robust for shock‐capturing but also accurate for hypersonic heat transfer prediction. Copyright © 2015 John Wiley & Sons, Ltd.