8.2.10 Summary

In section 8.2, we investigated the flow over an impulsively translated cylinder for a wide range of Reynolds numbers $Re=550$ to $40,000$. We compared our computed streamlines, velocity field, vorticity field, and drag coefficients with those obtained from experiments and many recent high resolution computations.

For small times, our computed velocity fields and drag values are in excellent agreement with the boundary layer computations of Van Dommelen & Shankar (unpublished), and small time expansions of Collins & Dennis [60].

For longer times, there is an excellent agreement between our computed velocity fields and those of the high resolution simulations of Anderson & Reider [3], Fischer & Kruse [120], and Wu, Wu, Ma, & Wu [249]. Our computed vorticity fields is in excellent agreement with the instantaneous vorticity fields obtained from the experiments of Shih, Lourenco & Ding [212]. Our computed vorticity fields also agree excellently with high resolution simulations of Fischer & Kruse [120], Anderson & Reider [3], and Koumoutsakos & Leonard [117]. In fact, based on evidence detailed in subsection 8.2.9, we believe that our results may well be the most accurate ones presently available. Yet, we use much less computational points than any of the other computations.

In the next section, we compute another flow as a simple illustration of the flexibility of our method.