【摘要】 本文采用剖开算子法将二维对流扩散方程分裂为对流过程、扩散过程以及源汇项三部分,然后用各自相应的、便利的解析方法求其解析解,从而找出问题的准解析解,并且在三角形网格上求解二维问题,得到了较为满意的结果。文中还分析了准分析解与解析解在对流扩散问题上的一致性;并将该法用于电厂周围温水排放计算,通过与其它方法计算结果比较表明,该法不仅能较好地模拟电厂周围的温度分布情况,而且具有物理概念明确、计算速度快、稳定性好以及与计算区域吻合好的优点。更多还原

【Abstract】 For the purpose of avoiding disadvantages of FDM and FEM in calculating multi-dimension problems, the authors presented a new numerical approach-QAM (Quasi-Analytical Method) of solving engineering and mathematical differential equations with initial-boundary value in 1984. Differing from FDM and FEM, QAM deals with the differential equation by finding a approximate integral expression directly rather than discreting and solving a large linear algebratic equation.In this paper, a quasi-analytical numerical model for 2-D convection-diffusion equation has been set up to calculate a real convection-diffusion problem by splitting the equation into three parts: convection, diffusion and source, and calculating the analytic expressions of every splitted equations seperaterly. The computation is performed on the nodes of triangular mesh.An example is given to solve the heating water distribution from a power station. Advantages of QAM have been proved both over FDM, which subjects to grids restriction, and over FEM which suffers from larger computer time. Therefore, QAM can be considered as a better approach for solving hydromechanical problems.更多还原