# Reynolds--uniform numerical method for  Prandtl's problem with
suction--blowing based on  Blasius' approach

**Source**: https://www.maths.tcd.ie/report_series/abstracts/tcdm0007.html
**Parent**: https://www.maths.tcd.ie/research/papers/

**Reynolds--uniform numerical method for Prandtl's problem with
suction--blowing based on Blasius' approach**

We construct a new numerical method for computing {\it reference}
numerical solutions to the self--similar
solution to the problem of incompressible laminar flow past
a thin flat plate with suction--blowing. The method generates global
numerical approximations to the
velocity components and their scaled derivatives for arbitrary values of the
Reynolds number in the range $[1,
\infty)$ on a domain including the boundary layer but excluding a
neighbourhood of the leading edge. The method is
based on Blasius' approach. Using an experimental error estimate technique
it is shown that
these numerical approximations are pointwise accurate and that they satisfy
pointwise error estimates which
are independent of the Reynolds number for the flow. The Reynolds--uniform
orders of convergence of the
reference numerical solutions, with respect to the number of mesh
subintervals used in the solution of
Blasius'problem, is at least 0.86 and the error constant is not more than
80. The number of iterations required to solve
the nonlinear Blasius problem is independent of the Reynolds number.
Therefore the method generates reference
numerical solutions with $\varepsilon$--uniform errors of any prescribed
accuracy.