Research progress on the application of dynamic grids in the numerical simulation of unsaturated-saturated interfaces
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摘要:
为了探讨结构和非结构动网格技术在地下水非饱和-饱和数值模拟领域未来的发展趋势, 总结了非饱和-饱和耦合数值模拟研究现状, 介绍了动网格技术原理及运动边界结构和非结构网格的变形方法, 综述了动网格技术在非饱和-饱和分界面的应用现状及存在的不足, 探讨了相关研究的未来发展趋势。综合分析表明: 结构动网格和非结构动网格均存在其固有优缺点, 结构、非结构混合网格以及多种动边界处理方法的结合使用在非饱和-饱和耦合数值模拟研究中具有重要的应用价值。在模拟潜水面的变动时, 可将多种网格变形方法结合使用, 当潜水面位置和形状变动较小时, 采用弹簧法更新网格; 当潜水面位置变化较大但形状变化较小时, 采用重叠结构动网格技术或铺层法更新网格; 当潜水面形状变动较大时, 则采用网格重构法更新网格, 从而更精确地模拟非饱和-饱和分界面的变化和移动。相关研究为场地非饱和带土壤与饱和带地下水协同防治工作提供了科学指导。
Abstract:In order to discuss the future development trend of structural and unstructured dynamic grid technology in the field of unsaturated-saturated groundwater numerical simulation, this paper summarizes the research status of unsaturated-saturated coupled numerical simulation, introduces the principle of dynamic grid technology and the deformation method of moving boundary structure and unstructured grid, summarizes the application status and shortcomings of dynamic grid technology in the unsaturated-saturated interface, and discusses the future development trend of related research. The review shows that both structural dynamic grids and unstructured dynamic grids have their inherent advantages and disadvantages, and the combination of structural/unstructured hybrid grids and multiple dynamic boundary treatment methods has important application value in the research of unsaturated-saturated coupling numerical simulation. When simulating the change of phreatic surface, a variety of mesh deformation methods can be combined. When the change of the position and shape of the phreatic surface is small, the spring method is used to update the mesh; When the position of the water table changes significantly but the shape changes little, the overlapping structure dynamic grid technology or the overlay method is used to update the grid; If the shape of the water table changes greatly, the grid reconstruction method is used to update the grid, so as to more accurately simulate the change and movement of the unsaturated-saturated interface. Relevant research provides scientific guidance for the coordinated prevention and control of unsaturated zone soil and saturated zone groundwater of the site.
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图 1 非饱和模拟与MODFLOW耦合模型网格示意图[63]
Figure 1. Grid diagram of unsaturated-simulation and MODFLOW coupling model
图 2 区域非饱和-饱和带水流运动及溶质运移模型网格示意图[89]
Figure 2. Grid diagram of regional unsaturated-saturated flow movement and solute transport model
表 1 结构网格动边界处理方法
Table 1. Processing method of moving boundary of structured grid
原理 优点 缺点 刚性运动网格法[37-38] 网格随物体一起做刚性运动 计算量小 仅适用于单个刚性物体运动 超限插值动网格生成法[39-41] 外边界保持静止,物面边界由物体运动规律或运动方程得到,内场网格由超限插值的方法代数生成 计算量小 网格正交性难以保证 重叠结构动网格技术[42-45] 在计算域的各个子域采用区域共享(重叠部分)的方法来实现信息交换 减轻了子域网格生成的难度且能够保证子域的网格品质 计算量较大 滑移结构动网格技术[46-47] 在物体运动轨迹周围预先划出一个滑移子区域,在子区域和其他区域分别生成多块结构网格;在二者连接处,利用搭接边界与其他区域对接,从而实现整个流场的计算 计算效率高、适用性强 划分子域的多少会影响网格变形质量和计算量 表 2 非结构网格动边界处理方法
Table 2. Processing method of moving boundary of unstructured grid
原理 优点 缺点 弹簧法[48-51] 将整个网格区域看作一个弹性区域,在边界发生移动且变形较小的情况下,网格发生轻微变形 无需插值,可以保证流场中解的守恒,保证了计算精度 边界位移过大时会使网格严重变形,导致计算出错 扩散法[52-53] 对扩散方程进行求解,基于扩散方程结果更新网格节点位置 网格质量好、计算精度高 不适用时间较长的计算 铺层法[54] 在一个时间步长内,动边界扫过固定的网格,对运动边界周围变形的网格,进行合并或分割 无需对控制方程进行坐标转换,即可实现对复杂动边界的追踪拟合 应用贴体网格及求解N-S方程比较困难 网格重构法[55-58] 利用网格变形前后的变形率来判断网格是否符合要求;对于严重变形的网格区域则重新生成网格 对网格拓扑结构没有限制,同时可以保证边界周围网格单元的质量,对于任意的边界变形也可以得到很好的处理 在重新生成以后,空腔内的网格节点的流场参数必须通过插值的方法得到 -
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