Abstract
We construct a new numerical method for computing reference numerical solutions to the self-similar solution to the problem of incompressible laminar flow past a thin flat plate with suction-blowing. The method generates global numerical approximations to the velocity components and their scaled derivatives for arbitrary values of the Reynolds number in the range [1,∞) on a domain including the boundary layer but excluding a neighbourhood of the leading edge. The method is based on Blasius’ approach. Using an experimental error estimate technique it is shown that these numerical approximations are pointwise accurate and that they satisfy pointwise error estimates which are independent of the Reynolds number for the flow. The Reynolds-uniform orders of convergence of the reference numerical solutions, with respect to the number of mesh subintervals used in the solution of Blasius’ problem, is at least 0.86 and the error constant is not more than 80. The number of iterations required to solve the nonlinear Blasius problem is independent of the Reynolds number. Therefore the method generates reference numerical solutions with ∈ -uniform errors of any prescribed accuracy.
This research was supported in part by the National Science Foundation grant DMS-9627244, by the Enterprise Ireland grant SC-98-612 and by the Russian Foundation for Basic Research grant No. 98-01-00362.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
H. Schlichting, Boundary Layer Theory, 7th Edition, McGraw Hill, 1951.
P. Farrell, A. Hegarty, J. J. H. Miller, E. O’Riordan, G. I. Shishkin, Robust Com-putational Techniques for Boundary Layers, Series in Applied Mathematics and Mathematical Computation (Eds. R J Knops and K W Morton), Chapman and Hall/CRC Press, 2000.
D. F. Rogers, Laminar Flow Analysis, Cambridge University Press, 1992.
B. Gahan, J. J. H. Miller, G. I. Shishkin: Accurate numerical method for Blasius’ problem for flow past a flat plate with mass transfer. TCD Maths Department Preprint no. 00-xx.
D. J. Acheson, Elementary Fluid Dynamics, Oxford: Clarendon, 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gahan, B., Miller, J.J.H., Shishkin, G.I. (2001). Reynolds-Uniform Numerical Method for Prandtl’s Problem with Suction-Blowing Based on Blasius’ Approach. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_36
Download citation
DOI: https://doi.org/10.1007/3-540-45262-1_36
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41814-6
Online ISBN: 978-3-540-45262-1
eBook Packages: Springer Book Archive