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Труды Института механики им. Р.Р. Мавлютова
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Proceedings of the Mavlyutov Institute of Mechanics

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Liapidevskii V.Yu. Nonlinear dispersion hyperbolic models of continuous media Proceedings of the Institute of Mechanics of Ufa Branch of RAS. 5 (2007). 273–278.
2007. Vol. 5. Issue 1, Pp. 273–278
DOI: 10.21662/uim2007.1.034
Nonlinear dispersion hyperbolic models of continuous media
Liapidevskii V.Yu
Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk


Nonequilibrium flows of an inhomogeneous liquid in channels and pipes are considered in the long-wave approximation. Nonlinear dispersion hyperbolic flow models are derived allowing taking into account the influence of internal inertia during the relative motion of phases upon the structure of nonlinear wave fronts. The asymptotic derivation of dispersion hyperbolic models is shown on the example of classical Boussinesq equations. It is shown that the hyperbolic approximation of the equations has the same order of accuracy as the primary model.


channel approximation,
shallow water equations,
nonlinear dispersion,
hyperbolic models