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In this technical note, we demonstrate the robustness of our numerical schemeof vorticity iteration in dealing with the dipole-wall interaction at smallviscosity, with emphasis on mesh convergence, boundary vorticity as well aswall viscous dissipation. In particular, it is found that, among the fourdifferent dipole configurations, the processes of vortex-wall collision atno-slip surfaces are exceedingly complex and are functions of the initialconditions. The critical issue direct numerical simulations is to establishmesh convergence which appears to be case-dependent. Roughly speaking,converged $2D$ meshes are found to be inversely proportional to viscosity atuniform spacings. Essentially, we have ruled out the possibility of anomalousenergy dissipation in the limit of small viscosity. Our computational resultsshow that the rate of the energy degradation follows the predictive trend ofthe well-known Prandtl scaling.

Viscous flow regimes in a square. Part 2. Impact and rebound process of vortex dipole-wall interaction