应用维数分裂方法推广MUSCL和WENO格式的若干问题

doi:10.7527/S1000-6893.2021.25009

Abstract

Abstract: This paper first discuss the difference between finite difference method and finite volume method, subsequently supplementing new arguments for the existence of differences in the boundary condition treatment and grid requirements between these two methods based on the existing literature.The calculation process of the interface flux of the control volume by dimension-by-dimension derived MUSCL and WENO schemes is further introduced.Since the direct application of these schemes to the Gaussian integral finite volume method is considered not rigorous enough, it is concluded that the MUSCL scheme and WENO scheme constructed by the dimension splitting method do not belong to the Gaussian integral finite volume method, while the definition of "integral scheme" can more accurately reflect the characteristics of these schemes.In addition, the reasons for the inability of the MUSCL and WENO schemes to guarantee conservation in the curvilinear coordinate system are discussed, and the elimination methods briefly introduced.Finally, research results obtained according to the viewpoint of this paper are briefly presented.

Key words: dimension-by-dimension, finite volume method, MUSCL scheme, WENO scheme, geometric conservation law

CLC Number:

V211.3

LIU Jun, HAN Fang, WEI Yanxin. MUSCL and WENO schemes problems generated by dimension splitting approach[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(3): 125009.

References

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MUSCL and WENO schemes problems generated by dimension splitting approach

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