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充型流动数值模拟的研究，是计算机在铸造生产中应用的最重要的内容之一，积极开发这一领域的研究对于优化工艺设计、提高铸件质量、降低生产成本、促进铸造学科的发展，跟踪和赶超国际上最新成果有重要科学价值和实际意义。本文通过伽辽金加权余量有限元法在利用有限元进行充型流动数值模拟方面做了深入的研究。将三维实体建模、流动数值模拟和动态图形显示处理有机地结合起来。在流动数值模拟有限元分析方面，完成了二维和三维的基本理论推导和应用程序的开发，向实用化跨出了关键的一步。在研究过程中发现用有限元法构造的三维流场数值解析数学模型可以得到大量的数学论据支持，使三维流场数值解析理论推导的正确性得到极大的保证。研究结果表明：用有限元法开发的应用程序可以十分方便地与实体造型软件连接在一起，使复杂零件的数值模拟变得非常容易。即开发的程序结构，可以方便地扩展。实践证明，将二维有限元主体程序扩展到三维是十分方便和可行的。同时预测用有限元方法开发的应用程序可以将速度场分析与温度场和应力场分析统一起来。本研究利用有限元法在充型流动数值模拟研究方面做了大量的实质性工作，完成了充型流动数值模拟的主体部分，并证明用有限元法进行充型流动数值模拟是强而有效的?
The study of numerical simulation of filling flow is one of the most important contents of the application of computer in foundry production. The research of active development in this field is very important for optimizing process design, improving casting quality, reducing production cost and promoting the development of foundry discipline. And catch up with the latest international achievements have important scientific value and practical significance. In this paper, by using finite element method of Galerkin weighted residuals, the finite element method is used to conduct the numerical simulation of filling flow. The three-dimensional solid modeling, flow numerical simulation and dynamic graphics display processing organically combined. In the field of flow numerical simulation, the two-dimensional and three-dimensional basic theoretical derivation and application development have been completed, which leads to a crucial step toward practical application. In the process of research, it is found that the mathematical model of numerical simulation of three-dimensional flow field constructed by finite element method can get a lot of support for mathematical arguments, and the correctness of numerical derivation theory of three-dimensional flow field is greatly guaranteed. The results show that the application program developed by the finite element method can be easily connected with the solid modeling software, making the numerical simulation of the complex parts very easy. That is, the program structure developed can be easily expanded. Practice has proved that it is very convenient and feasible to extend the 2D finite element main program to 3D. At the same time, it is predicted that the application developed by finite element method can unify speed field analysis with temperature field and stress field analysis. In this study, a great deal of substantive work has been done on the numerical simulation of filling flow using finite element method, and the main part of numerical simulation of filling flow has been completed. It is also proved that the numerical simulation of filling flow with finite element method is strong and effective ?