Numerical Transformation Methods for a Moving-Wall Boundary Layer Flow
of a Rarefied Gas Free Stream over a Moving Flat Plate
The first contribution of this paper is the extension of the
non-iterative transformation method, proposed by T\”opfer
more than a century ago and defined for the numerical solution of the
Blasius problem, to a Blasius problem with extended boundary conditions.
This method, which makes use of the invariance of two physical
parameters with respect to an extended scaling group of point
transformations, allows us to solve numerically the Blasius problem with
extended boundary conditions by solving a related initial value problem
and then rescaling the obtained numerical solution. Therefore, our
method is an initial value method. However, in this way, we cannot fix
in advance the values of the physical parameters, and if we need just to
compute the numerical solution for given values of the two parameters we
have to define an iterative extension of the transformation method,
which is the second contribution of this work.