Solution of N-S equations based on the quadtree cut cell method

With the characteristic of the quadtree data structure, a new mesh generation method, which adopts square meshes to decompose a background domain and a cut cell approach to express arbitrary boundaries, is proposed to keep the grids generated with a good orthogonality easily. The solution of N-S equations via finite volume method for this kind of unstructured meshes is derived. The mesh generator and N-S solver are implemented to study two benchmark cases, i.e. a lid driven flow within an inclined square and a natural convection heat transfer flow in a square duct with an inner hot circular face. The simulation results are in agreement with the benchmark values, verifying that the present methodology is valid and will be a strong tool for two-dimensional flow and heat transfer simulations, especially in the case of complex boundaries.