Numerical Transformation Methods for a Moving-Wall Boundary Layer Flow of a Rarefied Gas Free Stream over a Moving Flat Plate

In this paper, we present an original numerical method for the solution of a Blasius problem with extended boundary conditions. To this end, we extend to the proposed problem the non-iterative transformation method, proposed by Töpfer more than a century ago and defined for the numerical solution of the Blasius problem. The proposed 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 the Blasius problem numerically 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 the values of the physical parameters in advance, and if we just need to compute the numerical solution for given values of the two parameters, we have to define an iterative extension of the transformation method. Thus, in this paper, for the problem under study, we define a non-ITM and an ITM based on Lie groups scaling invariance theory.