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A Reynolds--uniform numerical method for Prandtl‘s boundary layer problem for flow past a plate with mass transfer

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83842

Butler,  JS
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Butler, J., Miller, J., & Shishkin, G. (2004). A Reynolds--uniform numerical method for Prandtl‘s boundary layer problem for flow past a plate with mass transfer. International of Computational Engineering Science, 5(2), 387-402.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D93F-1
Abstract
In this paper we consider Prandtl‘s boundary layer problem for incompressible laminar flow past a plate with transfer of fluid through the surface of the plate. When the Reynolds number is large the solution of this problem has a parabolic boundary layer. We construct a direct numerical method for computing approximations to the solution of this problem using a piecewise uniform mesh appropriately fitted to the parabolic boundary layer. Using this numerical method we approximate the self--similar solution of Prandtl‘s problem in a finite rectangle excluding the leading edge of the plate, which is the source of an additional singularity caused by incompatibility of the problem data, for various rates of mass transfer. By means of extensive numerical experiments for values of Reynolds, mesh points and Mass--transfer, we verify that the constructed numerical method is Reynolds -- uniform in the sense that the computed errors for the velocity components and their derivatives in the discrete maximum norm are Reynolds uniform. We use a special numerical method related to the Blasius technique to compute a semi--analytic reference solution with required accuracy with respect to Reynolds and mass--transfer for use in the error analysis.