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Central-difference and upwind-biasedschemes for steady and unsteady Euler aerofoilcomputations

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 computationof steady and unsteady Euler flows. These areapplied to steady and unsteady flows about the NACA0012 aerofoil, using structured grids generated bythe transfinite interpolation technique. An explicitcentral-difference scheme is produced based on thecell-vertex method of Ni modified by Hall. Themethod is second-order accurate in time and space,and with flow quantities stored at boundaries theboundary conditions are simple to apply. This is adefinite advantage over the cell-centred approach ofJameson, where extrapolation of the flow quantitiesis required at the boundaries, making unsteadyboundary conditions difficult to apply. An explicitupwind-biased scheme is also produced, based on theflux-vector splitting of van Leer. The method adoptsa three stage Runge-Kutta time-stepping scheme and ahigh-order spatial discretisation which is formallythird-order accurate for one-dimensionalcalculations. The upwind scheme is shown to beslightly more accurate than the central-differencescheme for steady aerofoil flows, but it is notclear which is the more accurate for unsteadyaerofoil flows. However, the central-differencescheme requires less than half the CPU time of theupwind-difference scheme, and hence is attractive,especially when considering three-dimensional flows.The transfinite interpolation technique is ideal forgenerating moving structured grids due to itssimplicity, and grid speeds are availablealgebraically by the same interpolation as gridpoints. The method is also ideal for use in amulti-block approach.

Information

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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