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ON CABARET SCHEME FOR INCOMPRESSIBLE FLUID FLOW PROBLEMS WITH FREE SURFACE
Abstract
The problem of a vortex pair motion under a free surface is considered. It is known (Barker S.J. & Crow S.?., 1977) that the vortices fly apart with respect to each other in the horizontal direction. The domain of computation will be on the half-plane with the symmetry condition on one of the vertical boundaries. Previously was received (Gushchin V.A. & Konshin V.N, 1992), that for the correct mathematical modeling of an unsteady thick layer of homogeneous incompressible liquid flow through an obstacle, it is necessary to solve a complete system of Navier-Stokes equations. The authors suggested a second-order CABARET scheme in a Lagrangian grid with nodes fixed in the horizontal direction. A transition is made to new curvilinear coordinates, such that the nodes are uniformly distributed in the vertical direction. According to the methodology ([15] Goloviznin V.M. et al., 2013) of the CABARET scheme for the new system of equations in the divergent form, a conservative difference scheme is proposed. Also, along with conservative variables, we derive the characteristic form of the equations for local Riemann invariants. Splitting by physical factors for the motion equations is used. The aim of the paper is to construct a new difference scheme for the problems of motion of an incompressible fluid. Nonlinear nonstationary phenomena are significant in a wide range of flow parameters in the presence of a free surface.
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References15
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