A two-dimensional numerical method for incompressible flow problem based on SIMPLER algorithm and quadtree grid with collocated arrangement

A numerical method for Navier-Stokes equations based on SIMPLER algorithm and the adaptively-refined quadtree grid with collocated arrangement is presented. The modified momentum interpolation method is applied for reasonable solution independent of the underrelaxation factor and the time step. Furthermore, the interface variables are interpolated in the way similar to that in structured grid instead of reconstruction method in unstructured grid. It is shown that the proposed numerical method is valid for incompressible flow problems and the adaptive refinement is successfully implemented to get more accurate solution.