The Lie-group shooting method for boundary layer equations in fluid mechanics

Abstract

In this paper, we propose a Lie-group shooting method to tackle two famous boundary layer equations in fluid mechanics, namely, the Falkner-Skan and the Blasius equations. We can employ this method to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element G(T) and the formation of a generalized mid-point Lie group element G(r). Then, by imposing G(T) = G(r) we can seek the missing initial conditions through a minimum discrepancy of the target in terms of the weighting factor r ɛ (0,1). It is the first time that we can apply the Lie-group shooting method to solve the boundary layer equations. Numerical examples are worked out to persuade that this novel approach has good efficiency and accuracy with a fast convergence speed by searching r with the minimum norm to fit two targets.