Numerical analysis of ideal fluid flows through plane duct of finite length

Abstract

The results of numerical study of the non-stationary problem in which the governing equations are the 2D Euler equations are presented. On the boundary of the duct the normal velocity is prescribed everywhere and the vorticity is given on the inflow parts. The variant of vortex particles-in-cells method is proposed and is used for PDE approximation. Firstly we have studied dynamics of different types of initial vorticity patches for classical flows (uniform, Couette and Poiseuille flows). We have found that for sufficiently big perturbations of initial vorticity a new stable separated flows (which are consist of a trough flow zone and a recirculation zone) can be realized. We present a number of examples of separated flows with different structure. Investigation of vorticity behavior in time and structures of stable separated flows are also presented.