Numerical Solution of the Navier-Stokes Equations for the Flow in a Two-Dimensional Cavity

Abstract

The flow of viscous fluid in a two-dimensional rectangular cavity has been studied. It is assumed that the cavity is bounded by three rigid plane walls, on which the fluid velocity is zero, and by a flat plate moving in its own plane. For the ratio of the lengths of sides of rectangular cross section, three cases have been chosen: 2:1, 1:1, 1:2. The Reynolds number of the flow is varied as 0, 1, 2, 4, 8, 16, 32, 64, 128. For these cases, the Navier-Stokes equations have been numerically integrated with the aid of high-speed electronic digital computers. Stream-lines, equi-vorticity lines, and isobaric lines for some typical cases are shown in figures. Velocity distributions along the centre line and pressure distributions over the both side walls are also shown.