对特定条件下高阶WENO格式计算结果误差的讨论

doi:10.7527/S1000-6893.2020.24940

Abstract

Abstract: In this paper, numerical results which obtained by simulating moving shock discontinuity, contact discontinuity, uniform flow in curvilinear coordinate system and shock regular reflection are given, and the comparisons of the numerical results simulated by the first-order upwind scheme and the fifth-order WENO schemes are discussed. The shock and contact discontinuities simulated in the WENO schemes were found to exhibit more pronounced non-physical fluctuations and more complicated flow field structures during the change from the initial discontinuity to the numerical transition region than the results of the first-order upwind scheme. Also, the geometrically induced errors and boundary approximation model errors due to coordinate transformations are significantly larger than those of the first-order upwind scheme. Numerical and theoretical analysis of the phenomena above leads to the following conclusion in this paper: higher-order WENO schemes run the risk of magnifying errors in the results under certain computational conditions. Finally, inspired by recently published articles, this paper discusses the contradiction between the current spatial multi-point construction method in high-order schemes and the characteristic line theory of hyperbolic equations.

Key words: finite difference method, high-order WENO schemes, geometrically induced errors, boundary approxi-mation model errors, hyperbolic governing equations

CLC Number:

V211.3

Jun LIU HAN -Fang. Discussions on the errors of high-order WENO schemes under some specific conditions[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, doi: 10.7527/S1000-6893.2020.24940.

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Discussions on the errors of high-order WENO schemes under some specific conditions

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