RUSS. J. Numer. Anal. Math. Modelling, Vol.13, No.4, pp. 271-278 (1998) © VSP 1998 Numerical modelling of fluid oscillations caused by an instantaneous slope of the reservoir base V.B. BARAKHNIN- and G.S. KHAKIMZYANOV" Abstract — We consider the numerical solution of a problem of fluid oscillations caused by an instantaneous slope of the reservoir base. The calculations are carried out in the framework of a potential flow model, nonlinear and nonlinear dispersive shallow-water models. Using the computational experiments, we specify the limits of applicability of the used models and algorithms, give the quantitative calculation results. The dynamics of vessels with fluid that has a free surface have intensively been in- vestigated over nearly fifty years. Of considerable importance in this field are the monographs [4,6-8]. The analytic and numerical methods of solving the problems of free fluid oscillations in vessels of different forms are described in these monographs. The problems are often considered in a linear approximation, i.e. under the assumption that the oscillations are small. The nonlinear statements of problems of this class are investigated rather seldom. The study of the fluid oscillations caused by an instantaneous slope of the reservoir base is of great importance for designing toxic and radioactive substances storage. The study of this phenomenon requires direct numerical modelling because of the substantial nonlinearity of the process. If a vessel has large sizes and the fluid layer is not thin, the effect of viscosity can be disregarded and mathematical modelling can be based on models of an ideal fluid. It is difficult to specify what model is most suitable for the numerical study of the process considered. In this work we are guided by the concept of a computational experiment. According to this concept different models and computational algorithms are used to describe the same phenomenon, which leads to more reliable results. We use the models: two- and three-dimensional models of potential fluid flows (PF) as well as one- and two-dimensional (areal) approximate long-wave models. The potential flow model describes more adequately the phenomenon studied but involves larger computational costs. Therefore in order to reduce computer time it is advisable in some cases to use a nonlinear shallow water model in a first approximation (NL model) or some nonlinear dispersive model (NLD model), for example, the Zheleznyak- Pelinovskii model [10]. The latter model is interest because the assumption that the wave amplitude is small is not used to obtain it. The one-dimensional analogue of this model is also obtained in [9]. The aim of this work is to compare the results of the numerical modelling of the phenomenon studied, which are obtained in the framework of the potential flow model, the Zheleznyak-Pelinovskii nonlinear dispersive model, and the shallow water model in "Institute of Computational Technologies, Siberian Branch of the Russian Academy of Sciences, Novosi- birsk 630090, Russia The work was supported by the Program of Integration Fundamental Research, Siberian Branch of the Russian Academy of Sciences (43) and the Russian Foundation for the Basic Research (97-01-00819). Brought to you by | University of Arizona Authenticated Download Date | 6/5/15 11:01 PM