The localized method of approximated particular solutions for solving two-dimensional incompressible viscous flow field

The purpose of this paper is to demonstrate that the localized method of approximated particular solutions (LMAPS) is a stable, accurate tool for simulating two-dimensional incompressible viscous flow fields with Chorin׳s projection method. Totally there are two numerical experiments conducted: the two-dimensional lid-driven cavity flow problem, and the two-dimensional backward facing step problem. Throughout this study, the LMAPS has been tested by non-uniform point distribution, extremely narrow rectangular domain, internal flow, velocity or pressure driven flow and high velocity or pressure gradient, etc. All results are similar to results of finite element method (FEM) or other literature, and it is concluded that the LMAPS has high potential to be applied to more complicated engineering applications.