Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

NIS participants

Numerical modelling of 2-D open flow with moving boundaries – watershed run-off and tsunamy run-up simulations

Kivva S.L., Zheleznyak M.J.

Institute of Mathematical Maschines and System Problems (Kiev)

Numerical method is proposed to simulate one- and two-dimensional open flows are described by the shallow water equations. The method was developed for modeling flows that can generate areas, in which the water depth could be equal to zero in some parts of a simulated area. . The shallow water equations are approximated by implicit nonlinear finite-difference scheme of the first order of approximation. A distinctive feature of the developed difference scheme is that it strictly ensures a non-negative water depth. The Newton-Raphson method was used for solution of the system of nonlinear difference equations. The developed algorithm was applied to simulated runoff generated by rain on a small catchment. The algorithm does not require explicit setup of the catchment boundaries, so it is enough to input a topography of a territory that includes considered catchment. The surface runoff begins in those areas of a catchment, where the intensity of precipitation exceeds intensity of losses which include infiltration into soil, evapotranspiration, interception by surface vegetation, and depression storage. The numerical modelling of the surface runoff is carried out by the calculations through all nodes of the simulation area including the dry regions. There presented results of the same methods implementation for simulation of tsumani run-up on a shore.

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Note. Abstracts are published in author's edition

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