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Analysis of the anisotropy of group velocity error due to spatial finite difference schemes from the solution of the 2D linear Euler equations

Authors

  • P. C. Stegeman,

    Corresponding author
    • Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, Australia
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  • M. E. Young,

    1. Air Vehicles Division, Defence Science and Technology Organisation, Fishermans Bend, Victoria, Australia
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  • J. Soria,

    1. Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, Australia
    2. Department of Aeronautical Engineering, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia
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  • A. Ooi

    1. Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria, Australia
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Correspondence to: P. C. Stegeman, Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3168, Australia.

E-mail: Paul.Stegeman@Monash.Edu

SUMMARY

Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension, are functions of a wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of the wave. For the Euler equations, the direction of flow and flow velocity are also important. Spectral analysis was used to predict the error in magnitude and direction of the group velocity of vorticity–entropy and acoustic waves in the solution of the linearised Euler equations in a two-dimensional Cartesian space. The anisotropy in these errors, for three schemes, were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. Numerical experiments were run to provide confirmation of the developed theory. Copyright © 2012 John Wiley & Sons, Ltd.

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