MULTILEVEL METHODS FOR TEMPORAL AND SPATIAL FLOW TRANSITION SIMULATION IN A ROUGH CHANNEL

We investigate the instability of 2D incompressible flows in a rough p lanar channel by tracking the growth of the unstable mode in its early stage. We develop both second- and fourth-order finite difference met hods on a staggered grid, together with a fully implicit time-marching scheme, using grid generation to accommodate fairly general geometrie s. A multigrid full approximation scheme based on the line-distributiv e relaxation method is used for fast convergence. For a 2D smooth chan nel, numerical results show good agreement with the analytic solution obtained from linear theory for small disturbances. Numerical results for a 2D channel with one and two roughness elements are analysed by F ourier analysis. They show how the roughness elements affect the growt h of the perturbation.