湖泊群水环境数学模型及其应用研究
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摘要
湖泊作为陆地上最为重要的水资源载体之一，是人类赖以生存和可持续发展的自然依托，但以湖泊富营养化为代表的诸多水环境问题，已成为我国经济发展的瓶颈。近年来，江（河）湖连通作为人们遏制湖泊富营养化的新途径，在长江中下游湖群中进行了大量尝试，并被确定我国在新时期的重要水利发展战略。对于连通工程形成的“自然－人工”复合水系，连通方式的选择和连通效应的评估是两大核心问题，直接关系到连通工程对湖泊水环境的改善效果，而湖泊水环境数学模型作为解决这两个问题的重要途径，一直是江（河）湖连通研究领域的热点和前沿。
湖泊水环境数学模型是以湖泊水动力学模型为基础，并与水质模型和水温模型耦合后得到的。本文首先以武汉“大东湖生态水网构建工程”所涉及的湖泊群为对象，基于静压水动力学模型建立了湖泊群水环境数学模型，对连通工程的引水调度模式和水环境效应进行了研究。鉴于静压模型无法模拟地形突变区的水流和短波等存在明显垂向流动的水流现象，应用对象的范围有限，本文又分别建立了平面二维和垂向二维的非静压水动力学模型，并对模型的多种求解方法和计算效率作了创新性的科学研究工作。主要工作和创新性成果如下：
（1）以沙湖、东湖、严西湖和北湖组成的大型城市湖泊群为研究对象，建立了平面二维湖泊群水动力－水质模型，模拟分析了三种引水调度模式的湖泊群水质改善效果，提出了推荐调度模式。然后对推荐调度模式的三种引水规模进行了模拟，分析了引水规模与水质改善效果之间的关系，为连通工程的实施提供了科学的决策依据。
（2）以沙湖和东湖为研究对象，建立了三维湖泊水动力－水温－水质模型，以气温典型年为背景，模拟了江湖连通前和江湖连通后（推荐调度模式）两种情景，通过对比两种情景下的湖流运动规律、子湖间水体交换和温度场，分析了江湖关系变化的水动力与水环境效应。此外，通过分析江湖连通后湖泊群的水体置换率和总磷变化情况，探索性的提出了“三循环”调度策略。
（3）推导了非静压的平面二维水动力学控制方程，并分别采用显格式法、θ法和新ADI法对其进行求解。其中新ADI法不仅避免了前两种求解方法中须将开边界动压设为零的通行做法，更加符合真实情况，而且还具有极高的计算效率。
（4）针对目前已有的非静压垂向二维水动力学模型将水体进行分层而求解效率低的问题，提出了一种单层模式的非静压垂向二维水动力学模型，大大提高了模型的计算效率，同时也具有较高的精度。
最后，总结了本文的研究成果，提出了今后进一步研究的方向。
As an important water carrier on land, lakes are the natural basement on which people liveand keep sustainable development. However, lake eutrophication, the typical one of manyenvironmental issues, has become a bottleneck of Chinese economy. In the past few years,river-lake connection, a new way to prevent the lake eutrophication, has been tried in thelake group located in the middle and lower reaches of Changjiang River and also beendetermined as a significant hydraulic development stragety in China. In thenatural-artificial river systems formed by connection projects, the way of connecting andits effect are the two essential problems, which directively involve the improvement effectof the projects. Lake water environment mathematical models, an important approach tosolving the two problems, are always the focus and front field.
A lake water environment mathematical model often consists of a hydrodynamicmodel which is the basement and a water quality and temperature model. In thedissertation, the project of East lakes ecological water network in Wuhan is the object, anda lake group water environment mathematical model based on hydrostatic models wasdeveloped. The water diversion scheme and environmental effects of the project werestudied using this model. Because hydrostatic models have a limited application range,they are unable to simulate the flows with significant vertical velocity, such as flows overabruptly changed bottom, short wave, and so on, a depth-integrated and a verticalnon-hydrostatic model were developed, respectively. Multiple innovative solution methodsand their computational efficiency are studied. The main work and innovations are asfollows.
(1) A depth-integrated hydrodynamic and water quality model was developed, whichincluded Sha lake, East lake, Yanxi lake, and Bei lake. Using the model, the improvementeffects of three water diversion schemes were simulated and one of them wasrecommended. After that, three sizes of inflow of the recommended scheme were alsosimulated, and the relationship between its inflow and improvement effect wasinvestigated. The obtained results provided a scientific support to the project.
(2) A three dimensional hydrodynamic model which was coupled with water temperature and quality model was established, including Sha lake and East lake. Usingthe data from a typical temperature year, two scenes, which are before and aftern theproject, respectively, were simulated using the model. By comparing the lake current,water exchange between sub-lakes, and water temperature field in the two scenes, thehydrodynamical and environmental effects induced by the change of river-lakerelationship were analyzed. In addition, by analyzing the water exchange rate and totalphosphorus in the second scene, an exploratory diversion tactics―three cycles‖wasproposed.
(3) The governing equations of a depth-integrated, non-hydrostatic model werederivated. Three solution method, an explicit method, a θ method, and a new ADI method,were applied to solve the equations. The new ADI method not only avoids the conventionthat the dynamic pressure at the open boundary is set as zero, but also has a highefficiency.
(4) A new vertical two dimensional non-hydrostatic model with a single layer wasproposed. Unlike the other established vertical models which have multiple vertical layersand need much time to solve the equations, the present model has only one layer. As aresult, it’s accurate and highly efficient.
At last, the achievement in the dissertation was summarized and some worthyresearch orientations were proposed.
湖泊水环境数学模型是以湖泊水动力学模型为基础，并与水质模型和水温模型耦合后得到的。本文首先以武汉“大东湖生态水网构建工程”所涉及的湖泊群为对象，基于静压水动力学模型建立了湖泊群水环境数学模型，对连通工程的引水调度模式和水环境效应进行了研究。鉴于静压模型无法模拟地形突变区的水流和短波等存在明显垂向流动的水流现象，应用对象的范围有限，本文又分别建立了平面二维和垂向二维的非静压水动力学模型，并对模型的多种求解方法和计算效率作了创新性的科学研究工作。主要工作和创新性成果如下：
（1）以沙湖、东湖、严西湖和北湖组成的大型城市湖泊群为研究对象，建立了平面二维湖泊群水动力－水质模型，模拟分析了三种引水调度模式的湖泊群水质改善效果，提出了推荐调度模式。然后对推荐调度模式的三种引水规模进行了模拟，分析了引水规模与水质改善效果之间的关系，为连通工程的实施提供了科学的决策依据。
（2）以沙湖和东湖为研究对象，建立了三维湖泊水动力－水温－水质模型，以气温典型年为背景，模拟了江湖连通前和江湖连通后（推荐调度模式）两种情景，通过对比两种情景下的湖流运动规律、子湖间水体交换和温度场，分析了江湖关系变化的水动力与水环境效应。此外，通过分析江湖连通后湖泊群的水体置换率和总磷变化情况，探索性的提出了“三循环”调度策略。
（3）推导了非静压的平面二维水动力学控制方程，并分别采用显格式法、θ法和新ADI法对其进行求解。其中新ADI法不仅避免了前两种求解方法中须将开边界动压设为零的通行做法，更加符合真实情况，而且还具有极高的计算效率。
（4）针对目前已有的非静压垂向二维水动力学模型将水体进行分层而求解效率低的问题，提出了一种单层模式的非静压垂向二维水动力学模型，大大提高了模型的计算效率，同时也具有较高的精度。
最后，总结了本文的研究成果，提出了今后进一步研究的方向。
As an important water carrier on land, lakes are the natural basement on which people liveand keep sustainable development. However, lake eutrophication, the typical one of manyenvironmental issues, has become a bottleneck of Chinese economy. In the past few years,river-lake connection, a new way to prevent the lake eutrophication, has been tried in thelake group located in the middle and lower reaches of Changjiang River and also beendetermined as a significant hydraulic development stragety in China. In thenatural-artificial river systems formed by connection projects, the way of connecting andits effect are the two essential problems, which directively involve the improvement effectof the projects. Lake water environment mathematical models, an important approach tosolving the two problems, are always the focus and front field.
A lake water environment mathematical model often consists of a hydrodynamicmodel which is the basement and a water quality and temperature model. In thedissertation, the project of East lakes ecological water network in Wuhan is the object, anda lake group water environment mathematical model based on hydrostatic models wasdeveloped. The water diversion scheme and environmental effects of the project werestudied using this model. Because hydrostatic models have a limited application range,they are unable to simulate the flows with significant vertical velocity, such as flows overabruptly changed bottom, short wave, and so on, a depth-integrated and a verticalnon-hydrostatic model were developed, respectively. Multiple innovative solution methodsand their computational efficiency are studied. The main work and innovations are asfollows.
(1) A depth-integrated hydrodynamic and water quality model was developed, whichincluded Sha lake, East lake, Yanxi lake, and Bei lake. Using the model, the improvementeffects of three water diversion schemes were simulated and one of them wasrecommended. After that, three sizes of inflow of the recommended scheme were alsosimulated, and the relationship between its inflow and improvement effect wasinvestigated. The obtained results provided a scientific support to the project.
(2) A three dimensional hydrodynamic model which was coupled with water temperature and quality model was established, including Sha lake and East lake. Usingthe data from a typical temperature year, two scenes, which are before and aftern theproject, respectively, were simulated using the model. By comparing the lake current,water exchange between sub-lakes, and water temperature field in the two scenes, thehydrodynamical and environmental effects induced by the change of river-lakerelationship were analyzed. In addition, by analyzing the water exchange rate and totalphosphorus in the second scene, an exploratory diversion tactics―three cycles‖wasproposed.
(3) The governing equations of a depth-integrated, non-hydrostatic model werederivated. Three solution method, an explicit method, a θ method, and a new ADI method,were applied to solve the equations. The new ADI method not only avoids the conventionthat the dynamic pressure at the open boundary is set as zero, but also has a highefficiency.
(4) A new vertical two dimensional non-hydrostatic model with a single layer wasproposed. Unlike the other established vertical models which have multiple vertical layersand need much time to solve the equations, the present model has only one layer. As aresult, it’s accurate and highly efficient.
At last, the achievement in the dissertation was summarized and some worthyresearch orientations were proposed.
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