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Mathematical analysis of flows directly associated with environmental problems.

对与环境问题直接相关的流量进行数学分析。

基本信息

批准号：
10640100
负责人：
ONISHI Kazuei
金额：
$ 1.92万
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：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

The purpose of the research project is to investigate mathematical problems in the flow analysis closely connected with the problems of environmental pollution. The research aimes at the development of computer simulation techniques for the protection of the environment in the aquious and atmospheric fields. For the objectives, we obtain the following results :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 scheme for incompressible viscous fluid flow and using the Taylor-Galerkin's method for the flow in shallow waters.2. Boundary conditions are discussed from the view points of the domain decomposition method and the inverse problems. When relatively small areas are considered for numerical simulation of environmental flow problems, artificial boundaries need to be introduced in the formulation, on which some for … More ms of fictitious boundary values should be prescribed. The values to be prescribed on the artificial boundaries play the crucial role for the success of the simulation. However the boundary values are not known a priori, in fact they constitute unknowns of the problem itself. We found from our numerical experiment on the flow simulation around airfoils that appropriate boundary values can be obtained by the Dirichlet-Neumann alternating method after quite a few times of iteration.3. Laminar flow model turns out to be insufficient for the numerical simulation of flows in the environmental study. We extended our analysis to turbulent models. We concluded that the κ-ε model is the most suitable from the stand points of practical use ; (1) the model is easy-to-use, and (2) data requisite for the implementation of the model are easily accessible. For flows at high Reynolds numbers or order 10^5 in turbulent regime, the finite analytical method was applied for the numerical simulation. The simulation showed good agreement with the corresponding results in physical experiment. Less

该研究项目的目的是研究与环境污染问题密切相关的流动分析中的数学问题。该研究旨在开发用于保护水和大气领域环境保护的计算机模拟技术。对于目标，我们得到以下结果： 1．有限元方法用于流动方程的数值求解，以应对所讨论的流动域的复杂几何形状。不可压缩粘性流体流动采用分数阶格式，浅水流动采用Taylor-Galerkin法对控制方程进行离散化。 2．从域分解法和反问题的角度讨论了边界条件。当考虑相对较小的区域进行环境流问题的数值模拟时，需要在公式中引入人为边界，并在其上规定一些毫秒的虚拟边界值。在人工边界上规定的值对于模拟的成功起着至关重要的作用。然而，边界值不是先验已知的，事实上它们构成了问题本身的未知数。通过对翼型周围流动的数值模拟实验发现，采用狄利克雷-诺依曼交替法经过多次迭代即可得到合适的边界值。 3．事实证明，层流模型不足以对环境研究中的流动进行数值模拟。我们将分析扩展到湍流模型。我们的结论是，从实际应用的角度来看，κ-ε模型是最合适的； (1) 该模型易于使用，(2) 易于获取实施该模型所需的数据。对于湍流状态下高雷诺数或10^5阶的流动，采用有限解析方法进行数值模拟。模拟结果与物理实验的相应结果吻合良好。较少的