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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.