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High‐order k ‐exact WENO finite volume schemes for solving gas dynamic Euler equations on unstructured grids
Author(s) -
Li Wanai,
Ren Yu-Xin
Publication year - 2011
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.2710
Subject(s) - finite volume method , classification of discontinuities , euler equations , robustness (evolution) , unstructured grid , algorithm , mathematics , euler's formula , computer science , shock (circulatory) , mathematical optimization , mathematical analysis , grid , geometry , mechanics , medicine , biochemistry , chemistry , physics , gene
SUMMARY This paper presents a family of High‐order finite volume schemes applicable on unstructured grids. The k ‐exact reconstruction is performed on every control volume as the primary reconstruction. On a cell of interest, besides the primary reconstruction, additional candidate reconstruction polynomials are provided by means of very simple and efficient ‘secondary’ reconstructions. The weighted average procedure of the WENO scheme is then applied to the primary and secondary reconstructions to ensure the shock‐capturing capability of the scheme. This procedure combines the simplicity of the k ‐exact reconstruction with the robustness of the WENO schemes and represents a systematic and unified way to construct High‐order accurate shock capturing schemes. To further improve the efficiency, an efficient problem‐independent shock detector is introduced. Several test cases are presented to demonstrate the accuracy and non‐oscillation property of the proposed schemes. The results show that the proposed schemes can predict the smooth solutions with uniformly High‐order accuracy and can capture the shock waves and contact discontinuities in high resolution. Copyright © 2011 John Wiley & Sons, Ltd.