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

• Published in: International journal for numerical methods in fluids Vol. 71; no. 7; pp. 805 - 829
• Main Authors: Stegeman, P. C., Young, M. E., Soria, J., Ooi, A.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 10.03.2013; Wiley Subscription Services, Inc
• Subjects: advection; anisotropic error; Anisotropy; compact difference; directional error; Error analysis; Errors; Euler equations; Eulers equations; finite difference; Group velocity; Mathematical analysis; Mathematical models; spectral analysis; Wavenumber
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.3683

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. This article provides an overview of the structure of anisotropy in group velocity error when solving the Euler equations using finite difference methods. Analysis of this structure provides understanding to the propagation of error in such solutions and the development of future multidimensionally optimized schemes .