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The present study performs a block refinement technique for the simulation and computation of flows inside domains of arbitrary shaped bounds. The discretisation of the physical domains is achieved by the use of Cartesian grids only. The curvilinear geometries are approached in Cartesian co-ordinates by Cartesian grid lines. In order to achieve the best approach of the original contour, we choose the saw tooth method to determine the appropriate approximated Cartesian points. The refinement method is based on the use of a sequence of nested rectangular meshes in which numerical simulation is taking place. The method is applied for the solution of the incompressible Navier–Stokes equations, for steady and laminar flows, based on a cell centre approximation projection. We present the numerical simulation of internal and external flows for different values of a Reynolds number. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single grid and BFC grid algorithms.

Mesh block refinement technique for incompressible flows in complex geometries using Cartesian grids