International Conference «Mathematical and Informational Technologies, MIT-2013»

(X Conference «Computational and Informational Technologies for Science,

Engineering and Education»)

## Arkhipov D.G. Khabakhpashev G.A.## Numerical modeling of the form channel influence on a transformation of weakly nonlinear perturbations of an interface of two shallow liquids## Reporter: Khabakhpashev G.A.
The combined approach for the dynamics description of spatial waves on an interface of a two-layered liquid in a channel with fixed rigid lid and bottom is proposed. It is presumed that characteristic horizontal dimensions of perturbations are moderately large, their amplitudes are small but finite, the lid and bottom may be weakly sloping, and capillary effects are not big. The deduced system of equations may be applied for a simulation of waves propagating simultaneously in arbitrary horizontal directions. This system is calculated similarly [1]. The solutions of several characteristic planar problems are found numerically, and the effect of lid and bottom shapes on the evolution of disturbances which are lengthy or solitary in space is shown.
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