Chein-Shan Liu1, Chih-Wen Chang2, Jiang-Ren Chang2,3
CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 1-16, 2008, DOI:10.3970/cmes.2008.032.001
Abstract In this paper, we propose a new method to tackle of 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$\mathbf {G}(T)$ 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 seek the missing initial conditions through a minimum discrepancy from the target in terms of a weighting factor$r \in (0, 1)$. Numerical examples are worked out to persuade that… More >
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