Mathematical analysis of water and air flow in the life and its computer simulation.

该研究项目的目的是研究与我们的生活密切相关的水和空气流动的数学方面，并开发一个在PC上实现的计算机模拟程序。其目的如下：1.采用有限元方法数值求解流动方程，以处理所述流动区域的复杂几何形状。对不可压缩粘性流体流动采用分步法离散控制方程，对浅水流动采用Taylor-Galerkin方法离散。利用线性三角形单元对未知量进行内插。2.针对生活中的水和空气流动，开发了一个前后处理的计算机模拟集成软件包，方便实用地对流动环境进行评价。根据初步用户提交的索赔反映的易于使用的基础上对计算机程序进行了修改。3.流动被表示为偏微分方程组的初边值问题的解。流动模拟中的区域往往存在所谓的开放边界，这种边界是通过对真实流动区域进行人为切割而形成的。开边界上的边界条件不是先验给定的。结果表明：1.开发了一种在PC机上运行的计算机模拟程序，并以书本形式公布。2.在开边界条件下，发现了一种适合于特征曲线的迎风格式。这篇论文对此进行了讨论，并提交给了一家期刊发表。

The purpose of the research project is to investigate mathematical aspects of the flow of water and air closely connected to our life, and develop a computer simulation program implemented on PC.The objectives are set as fol lows :1.The finite element method is used for numerical solution of flow equations in order to cope with the complex geometry of the flow domian in question. The governing equations are discretized by using the fractional step method for incompressible viscous fluid flow and using the Taylor-Galerkin's method for flow in shallow waters. The unknowns are interpolated by using the linear triangular element.2.An integrated package of computer simulation with pre- and post-processors is developed concerning the flow of water and air in the life for handy and practical use to assess the flow environment. The computer program is revised on the easy-to-use base reflected from the claims served by tentative users.3.The flows are presented as solutions of initial-boundary value problems of partial differential equations. Domain in the flow simulation often has a so-called open boundaries, which are formed by cutting artificially the real flow domain. The boundary condition on the open boundaries are not a priori given. Suitable boundary conditions are crucial for the success of the computer simulation.We obtained the following results :1.A novel computer simulation program running on PC was developed, and publicised in a book form.2.An upwind-type scheme along the characteristic curves was found appropriate for the condition on the open boundary. The related discussion is presented in the paper, which is submitted to a journal for publication.