【作者】 冯民权；

【导师】 周孝德；

【作者基本信息】 西安理工大学 ， 水力学及河流动力学， 2003， 博士

【摘要】 由于实际工程中湖泊、水库、河流、河口区域边界几何形状的不规则，以及水动力学方程的非线性性质，使得理论分析解难以作出，只能求助于数值解。数值模拟具有成本低、速度快、资料完备、具有改变各种参数、模拟真实条件及理想条件的能力。计算水力学中所求解的是非线性偏微分(积分)方程组，其数值方法的现有数学理论尚不够充分，严格的稳定性分析、误差估计和收敛性证明等理论工作的发展还跟不上数值模拟方法的进展。所以，需依靠对非线性数学方程的数值实验及数值解与试验或典型算例结果的比较和物理特性分析，验证数值计算结果，进一步改进计算方法。大多数生产实践问题要求进行二维水流水质数值模拟。在海岸、河口、湖泊、大型水库等广阔水域地区，水平尺度远大于垂向尺度，水力参数(如流速等)在垂直方向变化要小于水平方向的变化，其流场可用沿水深的平均流动量来表示，可采用平面二维水流流场与水质数值模拟技术。而在另外一些水域，如窄深潮汐通道、窄深型河谷水库如三峡、窄深河口地区，有关参量(如流速、温度、浓度等)的垂向变化要比水平横向的变化为大，应采用垂向二维水流水质数值模拟技术。西安理工大学博士学位论文 本文主要工作:对二维非恒定流，既处理了不规则域，又研究了各种算法;不仅做了平面二维，而且做了垂向二维;不仅计算了水流流场，也计算了水质变化;包括了算例算法的研究和应用，也结合了Gls技术;平面二维模型采用了边界拟合坐标变换，适应不规则的区域形状;垂向二维模型结合口坐标变换，可精确跟踪自由表面与非规则的地形边界。对水平尺度远大于垂向尺度，水力参数(如流速等)在垂直方向变化要小于水平方向变化的广阔水域地区，其流场可用沿水深的平均流动量来表示。考虑自由水面与水深的影响，建立坐标变换、交替方向、交错网格、线性递推、隐格式的平面二维水流与水质模型。对宽深比较小，有关参量(如流速、温度、浓度)的垂向变化比水平横向的变化为大的窄深型河谷水库等区域，建立垂向二维水流与水温数学模型。垂向做叮变换将可变域变为规则区域，使计算精确拟合自由面与底部边界。采用算子分裂法、交错网格法、有限差分法进行计算。 所建立的平面二维模型和垂向二维模型均在实际工程中得到应用，其中: 在大庆市洪水模拟中采用平面二维非恒定流模型，ro天洪水可在1小时内计算完毕，实现洪水演进的快速预报，为指挥防洪提供科学依据;采用贴体坐标技术，可完全适应不规则的区域、河流边界;同时将GIS、遥感技术和洪水模拟技术有机地结合起来，实现实时动态地显示、率定模型参数，显示洪水演进过程、实时地查询洪水演进过程的参数等。 在博斯腾湖大水体研究中采用平面二维水流与水质模型，可完全适应不规则的湖岸边界，考虑表面风应力，对吞吐量、风力、泵站位置、水位四种因素的多种组合情况下的博斯腾湖风生环流、矿化度分布及出流水质进行了模拟计算，获得了一些有意义的研究成果。 糯扎渡水库属峡谷型高坝大库，对糯扎渡水电站，采用垂向二维水流数学模型，模拟了水电站机组启动过程的非恒定水流流动，模拟结果是合理的。这对于中国西南地区类似的峡谷型高坝大库的水电站与三峡水电站垂向二维非恒定流模拟具有参考价值。更多还原

【Abstract】 In practical projects, the boundary shape irregularity of the lake, reservoir, river and estuary area and the non-linear character of hydrodynamic equation make it difficult to get the theoretical solution of the equation, so the numerical solution has to be the only a choice. The numerical simulation is of some advantages such as low cost, quick speed, complete data, and being capable to change parameters and simulate both the real and the ideal conditions. The non-linear partial differential (integral) equation often needs to be solved in the computational hydraulics, however, the mathematical theory of its numerical method has yet not been sufficient at present, for example, the development of some theories such as the strict stability analysis, error estimate and convergence proof has been unable to keep pace with the development of the numerical simulation method. Therefore, it is necessary to test the computation results and further modify the computation method based on the comparison between the numerical solution of the linear or non-linear equations and the trial value or the computation results of typical cases. The two-dimension numerical simulation of water flow and water quality is required in most practical projects, in which two types aredivided according to the different water area. In the broad water area such as the coast, estuary, lake and large reservoir, the horizontal scale is far larger than the vertical scale, the variation of the hydraulic parameters (for instance, velocity) is smaller in the vertical direction than in the horizontal direction, and the flow field can be expressed as the average flowing value along the water depth, so the two-dimension plane numerical simulation technique of the water flow and water quality may be used in these areas. But, in some other water areas such as the narrow-deep tide channel, narrow-deep valley reservoir and narrow-deep estuary area, the vertical varies of parameters such as the velocity, temperature and concentration is far greater than that in the horizontal direction, so the two-dimension vertical numerical simulation technique should be adopted in these areas.The main contents in this paper are as follows: simulated irregular boundary and researched varies of algorithms; studied the two-dimension plane and two-dimension vertical computing; simulated water flow filed and water quality; researched algorithms and it’s examples and combined with GIS tech. In two-dimension plane model the boundary fitted coordinate transformation were adopted to fit in with irregular area shape. In two-dimension vertical model a coordinate transformation were used to following the tracks of free surface and irregular topography boundary. In this paper, in order to fit in with the irregular boundary shape, and further to realize the quick forecast of the water flow and water quality, the two-dimension plane water flow and water quality model were built, in which the techniques of the coordinate transformation, alternate direction, staggered grid, linear recursion and implicit schemes were included. As for the reservoir of which the width to depth ratio is smaller, and the vertical variation of the parameters related such as the velocity, temperature and concentration is greater than their variation in the horizontal direction, the vertical two- dimension water flow model were set up, in which the water depth may change with the time and space, and when the coordinate transformation was made along the vertical direction, the variable area could be changedinto the regular one. In this model, the operator splitting technique, staggered grid technique and finite difference method were used.The two-dimension plane model and two-dimension vertical model developed have been used in practical projects, in which:In the flood simulation of Daqing City, the two-dimension plane unsteady flow model has been built to fit in with the irregular river boundary and realize the rapid forecast of the water flow. In this model, the geographic information sys更多还原