Simulating the Stabilization Process by Boundary Conditions of a Quasi-Two-Dimensional Flow with a Four-Vortex Structure

Abstract

A numerical stabilization problem by the boundary conditions of the given initial flow is considered for a two-dimensional system of Navier-Stokes equations that approximately describes the motion of a viscous incompressible fluid in a rectangular cell under an external electro-magnetic force and has an unstable quasi-stationary solution with a four-vortex structure for the selected values of the parameters. A mathematical statement of the problem, a method to solve it, and the results of the numerical computations are presented.