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On TVD difference schemes for the three‐dimensional Euler equations in general co‐ordinates
Author(s) -
Takakura Yoko,
Ishiguro Tomiko,
Ogawa Satoru
Publication year - 1989
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.1650090808
Subject(s) - euler equations , total variation diminishing , numerical analysis , euler's formula , robustness (evolution) , mathematics , wing , computational fluid dynamics , computer simulation , leading edge , finite difference , numerical stability , mathematical analysis , mechanics , physics , biochemistry , chemistry , gene , thermodynamics
An improved treatment for the Harten–Yee and Chakravarthy–Osher TVD numerical flux functions in general co‐ordinates is presented. The proposed formulation is demonstrated by a series of numerical experiments for three‐dimensional flows around the ONERA‐M6 wing. The numerical results indicate that it is important to use a suitable artificial compression parameter in order to obtain more accurate solutions around the leading edge of the wing. The two TVD numerical fluxes give excellent results: they capture the shock wave without numerical oscillations, they capture the rapid expansion around the leading edge sharply, they have self‐adjusting mechanisms regarding numerical viscosity and they also have robustness.