Weighted Least-Squares Collocation Method (WLSCM) for 2-D and 3-D Heat Conduction Problems in Irregular Domains

Abstract

In this article, the weighted least-squares collocation method (WLSCM) is adopted to deal with two- and three-dimensional heat conduction problems in irregular domains. A radial basis function (RBF) is selected to construct the approximation function. To improve the accuracy and stability, some auxiliary points are increased within the domain of interest. Only inner nodes are used to construct the approximation function, and the equilibrium equations are satisfied not only at collocation points but also at auxiliary points, so the equations should be solved in a least-square sense. A 2-D case that has an analytical solution is simulated by the proposed method and the outcome verifies that the present method can obtain desired accuracy and efficiency. Then the current method is adopted to compute one 2-D and two 3-D cases of engineering heat conduction problems in irregular complex domains. The results show that the present method can deal effectively with the heat conduction problems of both 2-D and 3-D irregular domains.