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

Chein-Shan Liu1, Chih-Wen Chang2, Jiang-Ren Chang2,3
Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan
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.

### Keywords

One-step group preserving scheme, Falkner-Skan equation, Blasius equation, Boundary value problem, Lie-group shooting method, Estimation of missing initial condition.

Liu, C., Chang, C., Chang, J. (2008). A New Shooting Method for Solving Boundary Layer Equations in Fluid Mechanics. CMES-Computer Modeling in Engineering & Sciences, 32(1), 1–16.

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