Construction of exact numerical solutions of the stationary traveling wave type for viscous thin films

Autor: M. A. Kaplan, E. A. Demekhin
Rok vydání: 1990
Předmět:
Zdroj: Fluid Dynamics. 25:408-414
ISSN: 1573-8507
0015-4628
Popis: An effective numerical procedure, based on the Galerkin method, for finding solutions of the stationary traveling wave type in the complete formulation is proposed for the case of viscous liquid films. Examples of a viscous film flowing freely down a vertical surface have been calculated. The calculations have been made for various values of the dimensionless surface tension γ, including γ=0. The method makes it possible to predict a number of bifurcations that occur as γ decreases. The existence of numerous families of stationary traveling waves when γ ≫ 1 was demonstrated in [6]. The present study shows that as γ→1 all but one of these families of wave solutions disappear. The shape of the periodic and solitary waves and the pressure distribution in the film are found for various γ. When γ=0 and the wave number α is fairly small, the periodic solution has a singularity, as predicted in [14]: at the crest of the wave a corner point appears; the angle between the tangents at this point ϕ=140–150. The method proposed can be used to calculate other wavy film flows.
Databáze: OpenAIRE
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