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A Reynolds‐uniform numerical method for the Prandtl solution and its derivatives for stagnation line flow
Author(s) -
Miller John J. H.,
Musgrave Alison P.,
Shishkin Grigorii I.
Publication year - 2003
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.589
Subject(s) - prandtl number , reynolds number , mathematics , flow (mathematics) , turbulent prandtl number , stagnation point , convergence (economics) , stagnation temperature , mathematical analysis , mechanics , physics , geometry , heat transfer , nusselt number , turbulence , economics , economic growth
Abstract Farrell et al . ( Robust Computational Techniques for Boundary Layers . Chapman & Hall/CRC: Boca Raton, 2000) develop a Reynolds‐uniform numerical method for the solution of the Prandtl equations in the case of flow past a flat plate. In this paper, we examine the applicability of this Prandtl method to the stagnation line flow problem in a domain that includes the stagnation line. Stagnation line flow has been chosen because of its self‐similar nature; reference solutions that approximate the exact solution of the problem to high levels of accuracy can be numerically obtained, allowing the error in the numerical approximations generated by the Prandtl method to be calculated. We present detailed results which verify that the method is Reynolds uniform. Global Reynolds‐uniform error bounds are constructed for the numerical approximations to the velocity components and their scaled first derivatives, and the practical uses of these bounds are discussed. We show that the number of iterations required for convergence of this iterative method is Reynolds uniform. In addition, we test an experimental technique for computing global Reynolds‐uniform error bounds, which can be used when solving flow problems for which no exact or reference solution is available. Experimental error bounds are constructed using this technique and are shown to be realistic upper bounds for the error values obtained with the use of the reference solutions. Copyright © 2003 John Wiley & Sons, Ltd.