The Lie-group shooting method for solving classical Blasius flat-plate problem. (English) Zbl 1231.76082

Summary: We propose a Lie-group shooting method to deal with the classical Blasius flat-plate problem and to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element \(\mathbf G(T)\) and the formation of a generalized mid-point Lie group element \(\mathbf G(r)\). Then, by imposing \(\mathbf G(T)=\mathbf G(r)\) we can derive some algebraic equations to recover the missing initial conditions. This is the first time that the Lie-group shooting method has been applied to solve the classical Blasius flat-plate problem. Numerical examples are worked out to show that this novel approach has better efficiency and accuracy, with a fast convergence speed obtained by searching for a suitable \(r\in(0,1)\) with the minimum norm to fit the targets


76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M50 Homogenization applied to problems in fluid mechanics
Full Text: DOI