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Central-difference and upwind-biased schemes for steady and unsteady Euler aerofoil computations

Published online by Cambridge University Press:  04 July 2016

C. B. Allen
C. B. Allen*
Affiliation:
Department of Aerospace Engineering, University of Bristol
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Abstract

Two numerical methods are presented for the computation of steady and unsteady Euler flows. These are applied to steady and unsteady flows about the NACA 0012 aerofoil, using structured grids generated by the transfinite interpolation technique. An explicit central-difference scheme is produced based on the cell-vertex method of Ni modified by Hall. The method is second-order accurate in time and space, and with flow quantities stored at boundaries the boundary conditions are simple to apply. This is a definite advantage over the cell-centred approach of Jameson, where extrapolation of the flow quantities is required at the boundaries, making unsteady boundary conditions difficult to apply. An explicit upwind-biased scheme is also produced, based on the flux-vector splitting of van Leer. The method adopts a three stage Runge-Kutta time-stepping scheme and a high-order spatial discretisation which is formally third-order accurate for one-dimensional calculations. The upwind scheme is shown to be slightly more accurate than the central-difference scheme for steady aerofoil flows, but it is not clear which is the more accurate for unsteady aerofoil flows. However, the central-difference scheme requires less than half the CPU time of the upwind-difference scheme, and hence is attractive, especially when considering three-dimensional flows. The transfinite interpolation technique is ideal for generating moving structured grids due to its simplicity, and grid speeds are available algebraically by the same interpolation as grid points. The method is also ideal for use in a multi-block approach.

Type
Research Article
Information
The Aeronautical Journal , Volume 99 , Issue 982 , February 1995 , pp. 52 - 62
Copyright
Copyright © Royal Aeronautical Society 1995 

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