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要旨:
In this paper we deal with Prandtl‘s boundary layer
problem for incompressible laminar flow past a
wedge. 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 fitted mesh technique appropriate to the parabolic boundary layer.
We use the numerical method to approximate the self--similar solution of
Prandtl‘s problem in a finite rectangle excluding the leading
edge of the wedge, which is the source of an additional singularity
caused by incompatibility of the problem data. We verify that the
constructed numerical method is robust in the sense that the computed
errors for the velocity components and their derivatives in the discrete
maximum norm are Reynolds uniform. We construct and apply a special
numerical method related to the Falkner--Skan
technique to compute a reference solution for the error
analysis of the velocity components and their derivatives.
By means of extensive numerical experiments we show
that the constructed direct numerical method is
Reynolds--uniform.
