An adaptive cartesian grid method for the incompressible navier-stokes equations

An adaptive unstructured grid generation algorithm, which adopts Cartesian grid to decompose a background domain and adopts a cut cell approach to express curvilinear boundaries, is presented for solving steady incompressible Navier-Stokes equations. By using quadtree data structure to store mesh data, simplifying cut types into six schemes, and employing the curl and divergence of velocity as criteria of grid refinement, this approach can implement mesh generation and adaptive refinement for arbitrary complex geometries automatically. A solution of N-S equations via finite volume method for this mesh is derived. The SIMPLE based smoothing pressure correction is chosen to suppress the checkerboard pressure oscillation due to collocated variables arrangement. The present method is applied to two benchmark problems and is verified to be accurate and efficient.