关键词: 对流扩散方程, 数值解法, 有限分析法, 涡区分离解法

Abstract: The convection-diffusion equation is a fundamental equation in many fluid flow problems. The numerical solution of this equation will lead to an algebraic equation set of high order, the solving of which by conventional methods needs large amount of computer space and computing time. This paper proposes an eddy separated method. Taking the advantage of the upwind nature of the convection-diffusion equation, this method separates the eddy regions from the convention-dominated region, then establishes and solves several smaller algebraic equation sets for the flow in the eddy regions. In the convection-dominated region, on the other hand, a series of explicit schemes can be simply used. This method keeps high accuracy.The results are as same as those obtained with previous methods. Because the order and bandwidth of these algebraic equation sets are much smaller than those formulated with previous methods, both computer space and computing time can be greatly reduced. This method is especially efficient for flows of higher Reynolds numbers with local eddy regions.

Key words: Convection-diffusion Equation, Numerical solution, Finite analytic method, Eddy separated method