# Cartesian Grid Approach with Virtual Boundary Method and Its Applications

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## Summary

The DNSs of the incompressible flows 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. In order to validate the present method, the DNSs of flow around a circular cylinder are considered. The flow characteristics are in very good agreement with the other DNS results. Next, the present method is applied to the DNSs of flows around a sphere and two spheres. In the flow around a sphere, the flow characteristics are in excellent agreement with other numerical and experimental results, and it is clearly observed that the hairpin vortex ring is released and the flow transits from laminar to turbulence in *Re* = 1000. It is shown in the flow around two spheres that the released vortex rings interfere each other. Consequently, the present method is very promising for the DNSs of the incompressible complicated flow.

## Keywords

Circular Cylinder Vortex Ring Incompressible Flow Cartesian Grid Spatial Accuracy## Preview

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