Summary
An error analysis is presented of the numerical calculation of the steady flow on an infinite domain around a given airfoil by a domain-splitting (=zonal) method. This method combines a fully-conservative finite-difference approximation on a finite domain around the airfoil with an approximate asymptotic solution outside this finite domain. The errors are analyzed as a function of the accuracy of the approximate asymptotic expansion, of the distance to the airfoil of the far-field boundary of the finite domain and of the mesh size. The numerical experiments show that, for a given desired accuracy level, large reduction in grid sizes are possible, if the usual far-field asymptotic approximation (uniform flow plus first-order perturbation by a circulation vortex at infinity) is augmented by only a few extra terms in the approximate asymptotic far-field solution. In this way, considerable numerical efficiency improvements can be realized. It is expected that this conclusion can be generalized to many other applications where computations on infinite domains are performed.
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References
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Exploratory research study of the National Aerospace Laboratory NLR, Amsterdam, The Netherlands, ordernumber 554.203, workplan 1982 3.5.C.6. The results of the study have been reported in a doctoral script of the first author, presented at the University of Technology, Twente, The Netherlands [1]. The authors are indebted to Prof. dr. ir. P.J. Zandbergen and prof. dr. ir. C.R. Traas for their contributions and stimulation.
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Wubs, F.W., Boerstoel, J.W. & Van Der Wees, A.J. Grid-size reduction in flow calculations on infinite domains by higher-order far-field asymptotics in numerical boundary conditions. J Eng Math 18, 157–177 (1984). https://doi.org/10.1007/BF00042733
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DOI: https://doi.org/10.1007/BF00042733