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

TL;DR

This paper extends a classical non-iterative transformation method to solve a modified Blasius problem with extended boundary conditions, enabling efficient numerical solutions for boundary layer flows involving moving walls and rarefied gases.

Contribution

It introduces an extension of the non-iterative transformation method to handle extended boundary conditions and develops an iterative approach for fixed physical parameters.

Findings

Successfully extended the transformation method to new boundary conditions

Developed an iterative scheme for specific physical parameters

Enhanced numerical solution techniques for moving-wall boundary layer flows

Abstract

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 a scaling group of point transformation, 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 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.