Finite Element Method For Solving 3-D Convection-Diffusion Problems

Numerical solution of convection-diffusion problem is an important subject in heat and mass transfer. To this problem, it provides important theoretic and practical significance to seek a fast, stable and practical numerical method. At present, there are many methods to solve this class of problems, with its different points. Among these methods, design and implementation of programs were developed by structure languages mostly, and less by object-oriented program comparatively. The subject of this paper is to develop an object-oriented finite element analysis program of three-dimensional convection-diffusion equation. We mainly study the finite element method for three-dimensional steady-state convection-diffusion equation in the case of the value of Peclet is small, and then develop a general program with object-oriented C++ language and give the numerical simulation to the corresponding convection-diffusion problems.The main of this paper is outlined as follows:1.The background of this paper is described, and the basic theory of object-oriented program is summarized.2.The finite element analysis of three-dimensional steady-state convection-diffusion equation is given by using 4-node tetrahedral elements and 8-node hexahedral elements.3.The finite element program of three-dimensional steady-state convection-diffusion problems is developed by using the object-oriented C++ language, which can be applied to a large general finite element science and engineering computation software.4.The primary discussion and the remarks about the results of four numerical examples are made, and then the validity and utility of the method proposed in this paper is verified.