A method for the solution of the Navier-Stokes equation for the prediction of flows inside domains of arbitrary shaped bounds by the use of Cartesian grids with block-refinement in space is presented. In order to avoid the complexity of the body fitted numerical grid generation procedure, we use a saw tooth method for the curvilinear geometry approximation. By using block-nested refinement, we achieved the desired geometry Cartesian approximation in order to find an accurate solution of the N-S equations. The method is applied to incompressible laminar flows and is based on a cell-centred approximation. We present the numerical simulation of the flow field for two geometries, driven cavity and stenosed tubes. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single grid algorithm. The Cartesian block refinement algorithm can be used in any complex curvilinear geometry simulation, to accomplish a reduction in memory requirements and the computational time effort.

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.