International Conference «Mathematical and Informational Technologies, MIT-2013»
(X Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, September, 5–8, 2013

Budva, Montenegro, September, 9-14, 2013

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.
In the case of plane waves running only along one coordinate in the channel with the lid and bottom which depend on only this coordinate too, the obtained system is reduced to one equation for special function. The analogous equation for perturbations of a free surface of the shallow water is presented in [2]. The problem of the head-on collision of two solitary waves in the horizontal channel  is solved analytically. Results of computing experiments on the form channel influence on a transformation of perturbations  are shown.
1. Arkhipov D.G., Safarova N.S., Khabakhpashev G.A. Comput. Technol. 2011. V. 16, no. 1. P. 3–17.
2. Arkhipov D.G., Khabakhpashev G.A. JETP Letters. 2011. Vol. 93, no. 8. P. 423–426.

Abstracts file: MIT-2013-Khabakhpashev.doc
Full text file: Arkhipov-Khabakhpashev.pdf

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