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

生活中水和空气流动的数学分析及其计算机模拟。

基本信息

批准号：
08640305
负责人：
ONISHI Kazuei
金额：
$ 1.41万
依托单位：
Ibaraki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640305/
关键词：
Water environment Computational fluid dynamics Navier-Stokes equations Shallow water equations Finite element method Computer simulation Environmental problem

项目摘要

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.

本研究项目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方面，并开发一个在PC上实现的计算机模拟程序。目标设定如下：1。本文采用有限元法对流动方程进行数值求解，以解决流动区域的复杂几何问题。对不可压缩粘性流体流动采用分步法离散，对浅水流动采用泰勒-伽辽金法离散。用线性三角元插值未知量。为了方便实际地评估生活中水和空气的流动环境，开发了一套具有前后处理器的综合计算机模拟软件包。计算机程序在易于使用的基础上进行了修改，这反映了暂定用户所提供的要求。这些流动被表示为偏微分方程初边值问题的解。流动模拟中的流域通常有一个所谓的开放边界，它是通过人为切割真实流域而形成的。开放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。开发了一种在PC机上运行的新颖的计算机模拟程序，并以书的形式出版。在开放边界条件下，沿特征曲线找到了适合的逆风型方案。相关讨论已在论文中提出，并已提交期刊发表。