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ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 2022, Vol. 43 ›› Issue (2): 124940-124940.doi: 10.7527/S1000-6893.2021.24940

• Fluid Mechanics and Flight Mechanics • Previous Articles     Next Articles

Numerical errors of high-order WENO schemes under specific conditions

LIU Jun, HAN Fang, WEI Yanxin   

  1. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
  • Received:2020-11-03 Revised:2020-11-26 Published:2022-03-04
  • Supported by:
    National Key R&D Program of China (2018YFB0204404); National Natural Science Foundation of China (11872144)

Abstract: This paper compares the numerical results obtained from simulation of moving shock discontinuity, contact discontinuity, uniform flow in the curvilinear coordinate system and shock regular reflection in the first-order upwind scheme and the fifth-order WENO schemes. The shock and contact discontinuities simulated in the WENO schemes exhibit more pronounced non-physical fluctuations and more complicated flow field structures while changing from the initial discontinuity to the numerical transition region than the results in the first-order upwind scheme. Furthermore, the geometrically induced errors and boundary approximation model errors caused by coordinate transformations are significantly larger than those in the first-order upwind scheme. Numerical and theoretical analyses of the phenomena above conclude that 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 methods, high-order WENO schemes, geometrically induced errors, boundary approximation model errors, hyperbolic governing equations

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