Co-located diffuse approximation method for two dimensional incompressible channel flows

The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of a scalar field has the remarkable advantage to work on discretization points (thus avoiding mesh generation). It has been shown that the DAM is much better than the finite element method for the computation of gradients [1-2]. In a previous paper [3], we have shown that it can be used to solve laminar natural convection problems. In this work, we discuss the applicability of this method to channel flows with a particular emphasis on the form of the weighting function.