A spectral Legendre collocation method using pseudo time stepping that solves the steady Navier-Stokes equations for the lid driven cavity flow problem (sub-critical Reynolds numbers).
For marginally resolved flows error from aliasing becomes a problem. The code use de-aliasing of the convective terms through a projection approach, which is helpful for making an otherwise diverging solution, converge.
Solution on 48x48 grid: Contours of stream function (left) and contours of vorticity
with indication of magnitude; negative to positive colored blue to red (right).
Comparison of extreme velocities at centerlines
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W. Zhang, C.H. Xi, An explicit Chebyshev pseudospectral multigrid method for incompressibe Navier-Stokes equations, Computers & Fluids, 2010.