Development of least-square-based two-dimensional finite-difference schemes and their application to simulate natural convection in a cavity

In this paper, two-dimensional mesh-free finite-difference schemes for solving incompressible viscous flows are presented. The method is based on the use of a weighted least-square approximation procedure together with a Taylor series expansion of the unknown function. Discretization error for derivatives is investigated analytically on the uniform mesh and the convergence property of the method is numerically tested. The role of the weighting function playing in the method is studied. Neumann-type boundary condition is treated by applying locally orthogonal boundary grids. Application to a problem of natural convection in a cavity is demonstrated on three different types of point distribution. (C) 2003 Elsevier Ltd. All rights reserved.