Abstract: In this paper, the local grid refinement is focused by
using a nested grid technique. The Cartesian grid numerical method is
developed for simulating unsteady, viscous, incompressible flows
with complex immersed boundaries. A finite volume method is used in
conjunction with a two-step fractional-step procedure. The key aspects
that need to be considered in developing such a nested grid solver are
imposition of interface conditions on the inter-block and accurate
discretization of the governing equation in cells that are with the
inter-block as a control surface. A new interpolation procedure is
presented which allows systematic development of a spatial
discretization scheme that preserves the spatial accuracy of the
underlying solver. The present nested grid method has been tested by
two numerical examples to examine its performance in the two
dimensional problems. The numerical examples include flow past a
circular cylinder symmetrically installed in a Channel and flow past
two circular cylinders with different diameters. From the numerical
experiments, the ability of the solver to simulate flows with
complicated immersed boundaries is demonstrated and the nested grid
approach can efficiently speed up the numerical solutions.