面向孔隙地下水流有限元模拟的二维空间离散格网自适应生成方法

发布时间：2018-05-16 00:42

本文选题：地下水数值模拟 + 自适应格网　；参考：《南京师范大学》2015年硕士论文

【摘要】：有限元法(Finite Element Method,简称FEM)是孔隙地下水流主要数值模拟方法,模拟区域三角形格网空间离散的精度直接影响模拟结果的正确性。空间离散的重要准则之一是：“地下水水力梯度大的模拟区域,离散格网的密度也较大”。目前,二维孔隙地下水流有限元数值模拟模型主要采用固定不变的三角形空间离散格网。由于孔隙地下水流的水力梯度直接受地下水开采强度、补给强度与开采时间的影响,属于动态变量,不同的模拟时步,水力梯度的空间分布特征也不同。模拟过程中各个时步若仍采用固定不变的三角形空间离散格网,则与孔隙地下水流有限元数值模拟的空间离散准则不相符。因此需要针对孔隙地下水流有限元数值模拟特点研究自适应离散格网生成方法。主要研究内容与方法为：(1)孔隙地下水流有限元模拟的三角形空间离散格网生成方法研究。结合孔隙地下水流数值模拟的模拟区域边界复杂、对格网自适应要求高的特点,选择采用边界适应能力以及格网节点控制能力强的前沿推进法作为有限元格网生成算法。对前沿推进法进行分析前沿边内向推进过程中,形态特征的变化情况及其对格网单元构建过程发生的影响,将其归纳为不同的情境,通过几何论证的方法,对每种情境给出相应的解决策略,从自动化程度、格网单元质量、算法通用性等角度对现有的前沿推进法进行改进,提出适用于孔隙地下水流有限元模拟的三角形空间离散格网生成方法。(2)水文地质参数自动提取方法研究。根据水文地质参数空间分布特征,将孔隙地下水数值模拟中涉及的地下水位、导水系统、储水系数、越流系数、地下水开采强度等水文地质参数划分为“点”、“线”、“面”三类矢量数据,利用GIS的空间分析功能,结合孔隙地下水流有限元模拟的三角形空间离散方法,实现孔隙地下水流数值模拟参数的自动提取。(3)随水力梯度时空变化三角形空间离散格网的自适应生成方法研究。结合模拟区域孔隙地下水数值模拟精度要求,对有限元模拟结果进行误差估算,将估算出的误差作为启发式参数,对不满足精度要求的区域进行再次剖分,实现离散格网随水力梯度时空变化的自适应生成方法。
[Abstract]:Finite Element method (Element) is the main numerical simulation method for pore groundwater flow. The accuracy of spatial dispersion of triangular grid in simulation region directly affects the correctness of simulation results. One of the important criteria of spatial dispersion is: "the density of the discrete grid is also larger in the simulation area with large hydraulic gradient of groundwater." At present, the finite element numerical simulation model of two-dimensional pore groundwater flow mainly adopts the fixed triangle space discrete grid. Because the hydraulic gradient of pore groundwater flow is directly affected by groundwater exploitation intensity, recharge intensity and mining time, it belongs to dynamic variable, and the spatial distribution characteristics of hydraulic gradient are different with different simulation time steps. If the fixed triangular spatial discrete grid is still used in each time step of simulation, it is inconsistent with the spatial discretization criterion of finite element numerical simulation of pore groundwater flow. Therefore, it is necessary to study the adaptive discrete grid generation method according to the characteristics of finite element numerical simulation of pore groundwater flow. The main research contents and methods are the generation of triangular spatial discrete grid for finite element simulation of pore groundwater flow. Considering the complex boundary of the simulated region of the numerical simulation of pore groundwater flow and the high demand for grid adaptation, the forward propulsion method with strong boundary adaptability and grid node control ability is chosen as the finite element mesh generation algorithm. This paper analyzes the change of morphological characteristics and its influence on the construction process of grid units in the process of forward edge inward propulsion, and sums it up into different situations, through the method of geometric demonstration. The corresponding solution strategies are given for each situation, and the existing frontier propulsion methods are improved from the aspects of automation degree, grid element quality, algorithm generality and so on. This paper presents a method of generating triangular spatial discrete grid for finite element simulation of pore groundwater flow. The method of automatic extraction of hydrogeological parameters is studied. According to the spatial distribution characteristics of hydrogeological parameters, the hydrogeological parameters, such as groundwater level, water conductivity system, water storage coefficient, overcurrent coefficient, groundwater exploitation intensity and so on, are divided into "points" and "lines" in numerical simulation of pore groundwater. Using the spatial analysis function of GIS and the triangular spatial discretization method of finite element simulation of pore groundwater flow, three kinds of vector data of "surface" are used. Automatic extraction of numerical simulation parameters for porous groundwater flow. Research on adaptive generation of triangular spatial discrete grid with hydraulic gradient. According to the precision requirement of numerical simulation of pore groundwater in simulated area, the error of finite element simulation result is estimated, and the estimated error is used as heuristic parameter to subdivide the area that does not meet the precision requirement again. The adaptive generation method of discrete grid with time and space variation of hydraulic gradient is realized.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P641.2

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