Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method. (English) Zbl 1115.76065

Summary: We consider the self-similar wall jet over an impermeable resting plane surface (Glauert jet). Through an analytic technique to solve nonlinear problems, namely the homotopy analysis method, we obtain an explicit series solution for the Glauert-jet problem. This series solution converges efficiently to the closed-form solution found by Glauert in the whole region \(0 \leqslant \xi < + \infty\) . In the frame of the homotopy analysis method, it is shown that the convergence region of the explicit series solution may be adjusted to obtain more accurate results.


76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76D25 Wakes and jets
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
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