DNS of the incompressible flows around a sphere using Cartesian grid approach with virtual boundary method

The DNSs of the incompressible flows around a sphere are performed by using the Cartesian grid approach with virtual boundary method. In the virtual boundary method, the body surface is expressed by a set of plural points, and the velocity components on virtual boundary are feedbacked to the momentum equations as the additional forcing terms. The DNSs are carried out in the range from Re = 10 to Re = 1000. In the steady flows up to Re = 240 in order to validate the present method, the flow characteristics are in good agreement with the other results. In the unsteady flows, it is clearly observed that the hairpin vortex ring is released and the flow transits from laminar to turbulence. Consequently, the present method is very promising for the DNSs of the incompressible complicated flow.