Journal
JOURNAL OF HYDRODYNAMICS
Volume 18, Issue 3, Pages 103-108Publisher
SPRINGER
DOI: 10.1016/S1001-6058(06)60038-3
Keywords
One-step group preserving scheme; Falkner-Skan equation; Blasius equation; boundary value problem; Lie-group shooting method; estimation of missing initial condition
Categories
Funding
- National Science Council [NSC 94-2212-E-019-005]
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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 is an element of (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.
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