|
Mechanics
At present different versions of the boundary elements method (BEM) are widely used to solve the fluid dynamics problems with free boundaries. The boundary-integral formulation of problem, which is used by the BEM, does not require construction of the calculation grid inside the region and is limited only by discretization of the boundary. In the case of allowing for nonlinear effects the discrete representation of the region is needed merely to calculate the additional integrals concerned with nonlinearity. The advantage of the BEM formulated led to publication of a large number of works considering mainly the potential flows of inviscid fluid. In this case the mathematical statement formulated by M.A. Lavrentiev is realized which applies the Laplas’s equation for the velocity potential with a boundary condition in the form of Cochi-Lagrang’s integral at the free surface. The main difficulty in numerical solution of this problem is to develop a stable computing algorithm for moving a free boundary which would be consistent with the employed version of the BEM.
In this paper several methods of free surface evolution calculation are considered in combination with an indirect version of the BEM both in plane and in axially symmetric cases. The algorithms suggested by the authors are tested on the problem of inviscid liquid drop oscillations under the influence of surface tension for case of arbitrary initial drop deformations. For small of initial deformations the results are in a good agreement with the linearized Rayleigh’s solution. In addition to the potential flow problem of inviscid fluid the application of the BEM to the investigations of viscid liquid flows is considered on the assumption of creep motion. The technics of allowing for nonlinear terms in the governing equations have been developed, which permit to simulate flows of rheologically complicated media. The problems of plane and spatial canal fillup and of the flow in a partially filled rotating cylinder have been analyzed. The computation accuracy has been verified by comparing the present numerical results with experimental data.
Note. Abstracts are published in author's edition
Last update: 06-Jul-2012 (11:52:45)