Open Access

ARTICLE

A New Shooting Method for Solving Boundary Layer Equations in Fluid Mechanics

by Chein-Shan Liu¹, Chih-Wen Chang², Jiang-Ren Chang²

1 Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
2 Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan
3 Corresponding author, Tel.:+886-2-24622192-x6031. E-mail: cjr@mail.ntou.edu.tw

Computer Modeling in Engineering & Sciences 2008, 32(1), 1-16. https://doi.org/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 this novel approach has good efficiency and accuracy with a fast convergence speed by searching$r$ with the minimum norm to fit two targets.

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Keywords

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