Accurate three-dimensional lid-driven cavity flow

A Chebyshev-collocation method in space is introduced, which allows an accurate calculation of three-dimensional lid-driven cavity flows. The time integration is carried out by an Adams–Bashforth backward–Euler scheme. The accuracy of the method relies on the representation of the solution as a superposition of stationary local asymptotic solutions and a residual flow field. This way the most severe discontinuities in the boundary conditions, which arise along the lines where moving and stationary walls meet, are taken care of analytically and thus do not spoil the numerical part of the solution. Calculations are carried out for no-slip boundary conditions at the cavity end-walls as well as for periodic end-wall conditions. In general, the spatial accuracy is better than fifth order. For rigid end-wall conditions, the accuracy is reduced near the end-walls to O ( N 3 / 2 ) , but recovers in the bulk. Tabulated data are provided for the most interesting flow properties.