Mathematical analysis of flows directly associated with environmental problems.

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。本研究旨在发展水和大气领域环境保护的计算机模拟技术。针对这一目标，我们得到了以下结果：1.为了科普流动区域的复杂几何形状，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格式离散，对于浅水流动采用Taylor-Galerkin方法离散.从区域分解法和反问题的角度讨论了边界条件。当环境流问题的数值模拟考虑相对较小的区域时，需要在公式中引入人工边界， 关于我们 应规定虚拟边界值的ms。在人工边界上规定的值对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。通过对翼型绕流模拟的数值实验发现，用Dirichlet-Neumann交替法进行多次迭代后，可以得到合适的边界值.层流模型已不能满足环境研究中水流数值模拟的需要。我们将分析扩展到湍流模型。从实际应用的角度来看，我们得出结论，κ-ε模型是最合适的：（1）该模型易于使用，（2）实施该模型所需的数据很容易获得。对于高雷诺数或10^5阶湍流区的流动，采用有限分析方法进行数值模拟。模拟结果与物理实验结果吻合较好。少

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