INCOMPRESSIBLE NAVIER STOKES EQUATIONS SOLUTION USING BLOCK NESTED CARTESIAN GRID

摘要

A method for the solution of the incompressible 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. 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 laminar flows and based on a cell-centre approximation projection. We present the numerical simulation of both an internal and an external flow, about the fluid flow inside a stenosed tube and around a symmetric airfoil respectively. 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.