基于有限体积法的二维水流水质模拟
摘要
近几十年来，我国经济迅速发展，人口急剧增长，工业化、城市化进程加速，同时大量工业废水、生活污水进入江河、湖泊或近海，造成了严重的水体污染，使我国本来就短缺的水资源日趋短缺，威胁人类的生存和经济社会的可持续发展。因此保护、改善水环境成为一项紧迫而又艰巨的任务。研究水流水质的数值模拟技术，可以模拟水流运动及污染物的输移扩散，为水环境的保护和改善提供技术支持，因而具有十分重要的理论意义和实用价值。
基于间断思想的非结构网格有限体积法因守恒性好，自动逆风，具备处理间断问题及复杂几何边界的能力，在浅水水流的数值模拟中取得了巨大的成功，目前正逐渐应用到水质和泥沙的模拟中。本文对基于有限体积法的二维水流水质数值模拟技术进行研究。首先介绍二维水流水质方程的离散方法，接着对求解的关键技术如控制体界面数值通量的计算、不规则地形的处理、开边界及陆地边界的处理、动边界及扩散项的处理等进行了详细论述。采用“斜底”模型处理不规则的水下地形，对计算控制通界面平均通量的中点公式和高斯三点公式进行了数值验证，提出用高斯两点公式计算控制通界面平均通量，提出了一种新的适合于有限体积法的动边界处理技术。接着，对数值模拟软件的集成和实现技术进行研究，提出采用基于组件的软件架构来实现数值模拟软件，用面向对象的思想来开发核心计算组件，用Map WinGIs组件为平台进行计算结果的可视化。最后，用实验数据对开发的模型进行验证，并将其应用到广东台山核电站温排水模拟研究中。模型的验证和应用表明：模型具备了对复杂地形、复杂边界的水流、水质进行模拟的能力，具有良好的应用前景。
During the past decades, with the development of the economics, the industrialization and urbanization process have speed up in China. Meanwhile, abundant industrial and municipal wastewater is discharged into surface water bodies like rivers and lakes, which results in the serious water pollution, and aggravates the shortage of the water resources and even threatens the exist of mankind and sustainable development of the society and economics. Therefore, the protection and improvement of water environment became an urgent and arduous task. The research on numerical simulation technology for modeling the contaminant transport problems is of great interest for the practical engineering because it could provide technology support for the protection and improvement of water environment.
The unstructured mesh Finite Volume Method (FVM) based on discontinuous theory has gained tremendous success in the simulation of shallow water, because it has virtues of conservation, automatically upwinded and abilities of dealing with discontinuous problems and complex geometry boundary. Now, the FVM is applied to the simulation of contaminant transport step by step. It is intended to study the 2D flow and contaminant transport by using the new technology which is based on FVM. Firstly, it introduces the numerical approximation method to 2D flow and water quality equation. Then it is to study the key technologies of solving 2D flow and water quality equation, such as flux computation at the boundary of Finite Volume, the approach of dealing with the irregular topography, open boundary and land boundary, moving boundary and the diffusion term of equation and et. al. In this paper the gradient bottom model is modified to deal with the complicated topography, and three formulas for the flux computation through boundary of control volume are validated. Moreover, the Two-Point Gauss formula is employed to calculate the average flux at the boundary of finite volume. A new approach is proposed to deal with moving boundary which is fitted for the finite volume method. Next, the integration technology of simulation software is carried out, and it is to build the simulation software based on the Component Technology, in which the key Calculation Component based on the OOP Method and implement visualization based on the MapWinGIS Component is applied. At last, the developed numerical model is verified not only by using the experimental data and numerical test, but also using the field measurement of the cooling water of Taishan nuclear power station. From the verification, it is found that the proposed model is powerful to deal with the complex boundary conditions and is feasible to simulate the flow and contaminat transport in surface water bodies.
基于间断思想的非结构网格有限体积法因守恒性好，自动逆风，具备处理间断问题及复杂几何边界的能力，在浅水水流的数值模拟中取得了巨大的成功，目前正逐渐应用到水质和泥沙的模拟中。本文对基于有限体积法的二维水流水质数值模拟技术进行研究。首先介绍二维水流水质方程的离散方法，接着对求解的关键技术如控制体界面数值通量的计算、不规则地形的处理、开边界及陆地边界的处理、动边界及扩散项的处理等进行了详细论述。采用“斜底”模型处理不规则的水下地形，对计算控制通界面平均通量的中点公式和高斯三点公式进行了数值验证，提出用高斯两点公式计算控制通界面平均通量，提出了一种新的适合于有限体积法的动边界处理技术。接着，对数值模拟软件的集成和实现技术进行研究，提出采用基于组件的软件架构来实现数值模拟软件，用面向对象的思想来开发核心计算组件，用Map WinGIs组件为平台进行计算结果的可视化。最后，用实验数据对开发的模型进行验证，并将其应用到广东台山核电站温排水模拟研究中。模型的验证和应用表明：模型具备了对复杂地形、复杂边界的水流、水质进行模拟的能力，具有良好的应用前景。
During the past decades, with the development of the economics, the industrialization and urbanization process have speed up in China. Meanwhile, abundant industrial and municipal wastewater is discharged into surface water bodies like rivers and lakes, which results in the serious water pollution, and aggravates the shortage of the water resources and even threatens the exist of mankind and sustainable development of the society and economics. Therefore, the protection and improvement of water environment became an urgent and arduous task. The research on numerical simulation technology for modeling the contaminant transport problems is of great interest for the practical engineering because it could provide technology support for the protection and improvement of water environment.
The unstructured mesh Finite Volume Method (FVM) based on discontinuous theory has gained tremendous success in the simulation of shallow water, because it has virtues of conservation, automatically upwinded and abilities of dealing with discontinuous problems and complex geometry boundary. Now, the FVM is applied to the simulation of contaminant transport step by step. It is intended to study the 2D flow and contaminant transport by using the new technology which is based on FVM. Firstly, it introduces the numerical approximation method to 2D flow and water quality equation. Then it is to study the key technologies of solving 2D flow and water quality equation, such as flux computation at the boundary of Finite Volume, the approach of dealing with the irregular topography, open boundary and land boundary, moving boundary and the diffusion term of equation and et. al. In this paper the gradient bottom model is modified to deal with the complicated topography, and three formulas for the flux computation through boundary of control volume are validated. Moreover, the Two-Point Gauss formula is employed to calculate the average flux at the boundary of finite volume. A new approach is proposed to deal with moving boundary which is fitted for the finite volume method. Next, the integration technology of simulation software is carried out, and it is to build the simulation software based on the Component Technology, in which the key Calculation Component based on the OOP Method and implement visualization based on the MapWinGIS Component is applied. At last, the developed numerical model is verified not only by using the experimental data and numerical test, but also using the field measurement of the cooling water of Taishan nuclear power station. From the verification, it is found that the proposed model is powerful to deal with the complex boundary conditions and is feasible to simulate the flow and contaminat transport in surface water bodies.
引文
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