本文選題：地下水?dāng)?shù)值模擬 + 自適應(yīng)格網(wǎng)�。� 參考：《南京師范大學(xué)》2015年碩士論文

【摘要】：有限元法(Finite Element Method,簡(jiǎn)稱FEM)是孔隙地下水流主要數(shù)值模擬方法,模擬區(qū)域三角形格網(wǎng)空間離散的精度直接影響模擬結(jié)果的正確性�？臻g離散的重要準(zhǔn)則之一是：“地下水水力梯度大的模擬區(qū)域,離散格網(wǎng)的密度也較大”。目前,二維孔隙地下水流有限元數(shù)值模擬模型主要采用固定不變的三角形空間離散格網(wǎng)。由于孔隙地下水流的水力梯度直接受地下水開采強(qiáng)度、補(bǔ)給強(qiáng)度與開采時(shí)間的影響,屬于動(dòng)態(tài)變量,不同的模擬時(shí)步,水力梯度的空間分布特征也不同。模擬過程中各個(gè)時(shí)步若仍采用固定不變的三角形空間離散格網(wǎng),則與孔隙地下水流有限元數(shù)值模擬的空間離散準(zhǔn)則不相符。因此需要針對(duì)孔隙地下水流有限元數(shù)值模擬特點(diǎn)研究自適應(yīng)離散格網(wǎng)生成方法。主要研究?jī)?nèi)容與方法為：(1)孔隙地下水流有限元模擬的三角形空間離散格網(wǎng)生成方法研究。結(jié)合孔隙地下水流數(shù)值模擬的模擬區(qū)域邊界復(fù)雜、對(duì)格網(wǎng)自適應(yīng)要求高的特點(diǎn),選擇采用邊界適應(yīng)能力以及格網(wǎng)節(jié)點(diǎn)控制能力強(qiáng)的前沿推進(jìn)法作為有限元格網(wǎng)生成算法。對(duì)前沿推進(jìn)法進(jìn)行分析前沿邊內(nèi)向推進(jìn)過程中,形態(tài)特征的變化情況及其對(duì)格網(wǎng)單元構(gòu)建過程發(fā)生的影響,將其歸納為不同的情境,通過幾何論證的方法,對(duì)每種情境給出相應(yīng)的解決策略,從自動(dòng)化程度、格網(wǎng)單元質(zhì)量、算法通用性等角度對(duì)現(xiàn)有的前沿推進(jìn)法進(jìn)行改進(jìn),提出適用于孔隙地下水流有限元模擬的三角形空間離散格網(wǎng)生成方法。(2)水文地質(zhì)參數(shù)自動(dòng)提取方法研究。根據(jù)水文地質(zhì)參數(shù)空間分布特征,將孔隙地下水?dāng)?shù)值模擬中涉及的地下水位、導(dǎo)水系統(tǒng)、儲(chǔ)水系數(shù)、越流系數(shù)、地下水開采強(qiáng)度等水文地質(zhì)參數(shù)劃分為“點(diǎn)”、“線”、“面”三類矢量數(shù)據(jù),利用GIS的空間分析功能,結(jié)合孔隙地下水流有限元模擬的三角形空間離散方法,實(shí)現(xiàn)孔隙地下水流數(shù)值模擬參數(shù)的自動(dòng)提取。(3)隨水力梯度時(shí)空變化三角形空間離散格網(wǎng)的自適應(yīng)生成方法研究。結(jié)合模擬區(qū)域孔隙地下水?dāng)?shù)值模擬精度要求,對(duì)有限元模擬結(jié)果進(jìn)行誤差估算,將估算出的誤差作為啟發(fā)式參數(shù),對(duì)不滿足精度要求的區(qū)域進(jìn)行再次剖分,實(shí)現(xiàn)離散格網(wǎng)隨水力梯度時(shí)空變化的自適應(yīng)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.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：P641.2

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