

SYMMETRY IN THE PROBLEM OF WAVE FLOW REGIMES OF A THIN LAYER OF VISCOUS LIQUID
Arkhipov D.G., Vozhakov I.S., Markovich D.M., Tsvelodub O.Yu.
Institute of Thermophysics SB RAS, Novosibirsk, Russia
Citation:
Arkhipov, D.G., Vozhakov, I.S., Markovich, D.M. and Tsvelodub, O.Yu., (2014) Symmetry in the problem of wave flow regimes of a thin layer of viscous liquid, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(14), PP. 109  114.

Keywords: flowing down film; model system; stability; evolution of perturbations; symmetry 
Abstracts:
A divergent system of equations for the simulation of nonlinear waves on a liquid film flowing down over a vertical plane was studied. It was found that in the computational domain _{} (the area of a real flow _{}) extended along the transverse coordinate, the divergent system of equations together with boundary conditions is invariant with respect to some transformation of parity. The effectiveness of this symmetry for the numerical solution of the problem with Galerkin methods was demonstrated. Several families of stationarytravelling system solutions were calculated. The complex topological structure of the such solutions branching was determined. For the case of moderate Reynolds numbers it was numerically shown that the stationarytravelling solutions of the systems have the detected symmetry 
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