On One Method for Solving of a Non-stationary Fluid Flows with Free Surface

Abstract

The flow of an incompressible Newtonian fluid with a free boundary in contact with air is considered. In this paper, there will be problems with a flat bottom for different initial and boundary conditions. The choice of these tasks is based on the principle of “from simple to complex”. This stage is considered as the initial and “debugging” in the development of the CABARET technique in application to the problems of incompressible fluid flows with a free surface. The system of equations describing such a model of the medium is a transformed Navier-Stokes system in a curvilinear coordinate system, such that at any instant the curvilinear transformation conforms the computational domain into a rectangle of unit height. The free surface is described by the kinematic boundary condition, which is obtained from the assumption that the liquid particles located on the interface between the two media remain on this boundary all the time. The comparison of numerical results with some theoretical data is discussed.