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

本课题的目的是研究与我们生活密切相关的水和空气流动的数学问题，并开发一个在PC机上实现的计算机模拟程序，其目标如下：1.为了科普所讨论的流动域的复杂几何形状，采用有限元法对流动方程进行数值求解。对于不可压缩粘性流体流动，采用分步法离散控制方程;对于浅水沃茨，采用泰勒-伽辽金法离散控制方程。2.开发了一套完整的前、后处理器的计算机模拟软件包，用于生活中水和空气的流动，以方便和实用地评估流动环境。根据试用用户的要求，在易于使用的基础上对计算机程序进行了修改。3.流场表示为偏微分方程初边值问题的解。流动模拟中的区域往往存在所谓的开边界，它是通过人为地切割真实的流动区域而形成的。开边界上的边界条件不是先验给定的。合适的边界条件是计算机模拟成功的关键，我们得到了以下结果：1.开发了一个新的计算机模拟程序，并在PC上运行，并出版在一本书的形式。2.发现一个迎风型格式沿着的特征曲线适合于开边界的条件。相关的讨论在论文中提出，这是提交给期刊出版。

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.