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A Robust Layer-Resolving Numerical Method for Plane Stagnation Point Flow

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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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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References

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  2. Rogers, D. F.: Laminar Flow Analysis. Cambridge University Press (1992)

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  3. Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O’Riordan, E., Shishkin, G. I.: Robust Computational Techniques for Boundary Layers. CRC Press (2000)

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  4. Schlichting, H.: Boundary-Layer Theory. McGraw-Hill (1979)

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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