  A new approach for simulating flows over complex geometries is developed by
introducing an accurate virtual interpolation point scheme as well as a virtual
local stencil approach. The present method is based on the concept of point
collocation on a virtual staggered structure together with a fractional step
method. The use of a virtual staggered structure arrangement, which stores all
the variables at the same physical location and employs only one set of nodes
using virtual interpolation points, reduces the geometrical complexity. The
virtual staggered structure consists of the virtual interpolation points and
the virtual local stencil. Also, computational enhancement of the virtual
interpolation point method is considerable since the present method directly
discretizes the strong forms of the incompressible Navier-Stokes equations
without numerical integration. It makes a key difference from others. In the
virtual interpolation point method, the choice of an accurate interpolation
scheme satisfying the spatial approximation in the complex domain is important
because there is the virtual staggered structure for computation of the
velocities and pressure since there is no explicit staggered structure for
stability. In our proposed method, the high order derivative approximations for
constructing node-wise difference equations are easily obtained. Several
different flow problems (decaying vortices, lid-driven cavity, triangular
cavity, flow over a circular cylinder and a bumpy cylinder) are simulated using
the virtual interpolation point method and the results agree very well with
previous numerical and experimental results. They verify the accuracy of the
present method.
