Abstract
Plane stagnation point flow is one of a small class of problems for which a self-similar solution of the incompressible Navier-Stokes equations exists. The self-similar solution and its derivatives can be expressed in terms of the solution of a transformed problem comprising a partially coupled system of quasilinear ordinary differential equations defined on a semi-infinite interval. In this paper a novel iterative numerical method for the solution of the transformed problem is described and used to compute numerical approximations to the self-similar solution and derivatives. The numerical method is layer-resolving which means that for each of the components, error bounds of the form C p N -p can be calculated where C p and p are independent of the Reynolds number, showing that these numerical approximations are of controllable accuracy.
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© 2001 Springer-Verlag Berlin Heidelberg
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Miller, J.J.H., Musgrave, A.P., Shishkin, G.I. (2001). A Robust Layer-Resolving Numerical Method for Plane Stagnation Point Flow. 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_70
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DOI: https://doi.org/10.1007/3-540-45262-1_70
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