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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (7): 1385-1393    DOI: 10.3785/j.issn.1008-973X.2022.07.014
土木工程、水利工程、交通工程     
任意多边形网格剖分的潜水层水流模型
高玉龙1,2(),刘志杰3,韩玉2,易树平2,*()
1. 哈尔滨工业大学 环境学院，黑龙江 哈尔滨 150090
2. 南方科技大学 环境科学与工程学院，广东 深圳 518055
3. 深圳市南科环保科技有限公司，广东 深圳 518055
Numerical model for groundwater flow simulation in unconfined aquifer with arbitrary polygon grids
Yu-long GAO1,2(),Zhi-jie LIU3,Yu HAN2,Shu-ping YI2,*()
1. School of Environment, Harbin Institute of Technology, Harbin 150090, China
2. School of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
3. Shenzhen Sustech Environmental Incorporation, Shenzhen 518055, China
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摘要：

为了提高潜水含水层水流数值模型网格剖分的灵活性，利用多点通量近似方法，建立适用于任意多边形网格剖分的潜水层水流数值模型. 通过4个案例验证模型的有效性，将新模型与通用软件MODFLOW的模拟结果进行对比. 结果显示，新模型计算结果与MODFLOW的结果有良好的一致性. 在具有复杂边界形状的案例中，新模型的均方根误差均小于对应的MODFLOW的均方根误差，说明使用任意多边形网格剖分的新模型表现优于MODFLOW模型. 研究结果表明，新模型有潜力应用于具有复杂边界形状的潜水层的水流过程模拟.
关键词： 地下水流模型;  任意多边形网格;  有限体积法;  多点通量近似;  潜水含水层    
Abstract:

An improved groundwater flow model was developed by using the multipoint flux approximation method in order to improve the flexibility of discretizing aquifers for groundwater flow numerical model in unconfined aquifer. The arbitrary-shaped polygon grids were used to discretize the aquifer. The availability of the new model was verified by comparing the output between our model and MODFLOW in four cases. Results showed that the calculation results of the new model accorded well with the results of MODFLOW model. All the root mean square errors calculated by the new models were smaller than those of MODFLOW models in real watershed cases with complex boundaries, which indicated that the new model performed better than MODFLOW. The research results show that the new model has the potential to simulate groundwater flow processes in the unconfined aquifer with complex boundaries.
Key words: groundwater flow model    arbitrary polygon grid    finite volume scheme    multipoint flux approximation    unconfined aquifer
收稿日期: 2021-08-27 出版日期: 2022-07-26
CLC:  P 641  
基金资助: 国家自然科学基金资助项目(41877193)；深圳市高层次人才科研启动经费资助项目(Y01296126)
通讯作者: 易树平     E-mail: gyulong@qq.com;yisp@sustech.edu.cn
作者简介: 高玉龙（1990—）男，博士生，从事地下水模拟的研究. orcid.org/0000-0003-2833-1509. E-mail： gyulong@qq.com
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引用本文:

高玉龙,刘志杰,韩玉,易树平. 任意多边形网格剖分的潜水层水流模型[J]. 浙江大学学报(工学版), 2022, 56(7): 1385-1393.

Yu-long GAO,Zhi-jie LIU,Yu HAN,Shu-ping YI. Numerical model for groundwater flow simulation in unconfined aquifer with arbitrary polygon grids. Journal of ZheJiang University (Engineering Science), 2022, 56(7): 1385-1393.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.07.014    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I7/1385

图 1  顶点A周围的符号
图 2  不规则网格和规则网格剖分含水层
图 3  不同时刻模型模拟结果的对比
图 4  不同时刻下在含水层剖线（x = 75 m）的模拟结果对比
图 5  不同时刻模型模拟结果的对比
图 6  新桥河流域模型的输入
图 7  新模型与MODFLOW模型和参考模拟结果的对比
图 8  不同时刻的模拟结果对比
图 9  平谷盆地模型的输入
图 10  新模型、MODFLOW模型和参考模型模拟结果的对比
图 11  不同时刻的模拟结果对比
1 任杰, 程嘉强, 杨杰, 等. 潜流交换温度示踪方法研究进展[J]. 水科学进展. 2018, 29(4): 597-606.
REN Jie, CHENG Jia-qiang, YANG Jie, et al. Advances in temperature tracer method of hyporheic exchange [J]. Advances in Water Science, 2018, 29(4): 597-606.
2 陈飞, 徐翔宇, 羊艳, 等 中国地下水资源演变趋势及影响因素分析[J]. 水科学进展, 2020, 31 (6): 811- 819
CHEN Fei, XU Xiang-yu, YANG Yan, et al Investigation on the evolution trends and influencing factors of groundwater resources in China[J]. Advances in Water Science, 2020, 31 (6): 811- 819
3 MCDONALD M G, HARBAUGH A W. A modular three-dimensional finite-difference ground-water flow model [M]. Reston: US Geological Survey, 1988.
4 HARBAUGH A W. MODFLOW-2005, the US geological survey modular ground-water model: the ground-water flow process[M]. Reston: US Geological Survey, 2005.
5 MA L, HE C, BIAN H, et al MIKE SHE modeling of ecohydrological processes: Merits, applications, and challenges[J]. Ecological Engineering, 2016, 96: 137- 149
doi: 10.1016/j.ecoleng.2016.01.008
6 TREFRY M G, MUFFELS C FEFLOW: a finite-element ground water flow and transport modeling tool[J]. Ground Water, 2010, 45 (5): 525- 528
7 AAVATSMARK I An introduction to multipoint flux approximations for quadrilateral grids[J]. Computational Geosciences, 2002, 6 (3): 405- 432
8 AAVATSMARK I, EIGESTAD G T, KLAUSEN R A. Numerical convergence of the MPFA O-method for general quadrilateral grids in two and three dimensions [M]. New York: Springer, 2006: 1-21.
9 AAVATSMARK I, BARKVE T, MANNSETH T Control-volume discretization methods for 3D quadrilateral grids in inhomogeneous, anisotropic reservoirs[J]. SPE Journal, 1998, 3 (2): 146- 154
doi: 10.2118/38000-PA
10 AAVATSMARK I, BARKVE T, BØE Ø, et al Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media[J]. Journal of Computational Physics, 1996, 127 (1): 2- 14
doi: 10.1006/jcph.1996.0154
11 EDWARDS M G Unstructured, control-volume distributed, full-tensor finite-volume schemes with flow based grids[J]. Computational Geosciences, 2002, 6 (3/4): 433- 452
doi: 10.1023/A:1021243231313
12 YOUNES A, FAHS M, BELFORT B Monotonicity of the cell-centred triangular MPFA method for saturated and unsaturated flow in heterogeneous porous media[J]. Journal of Hydrology, 2013, 504: 132- 141
doi: 10.1016/j.jhydrol.2013.09.041
13 YOUNES A, MAKRADI A, ZIDANE A, et al A combination of Crouzeix-Raviart, discontinuous Galerkin and MPFA methods for buoyancy-driven flows[J]. International Journal of Numerical Methods for Heat and Fluid Flow, 2014, 24 (3): 735- 759
doi: 10.1108/HFF-07-2012-0156
14 DRONIOU J, POTIER C L Construction and convergence study of schemes preserving the elliptic local maximum principle[J]. SIAM Journal on Numerical Analysis, 2011, 49 (2): 459- 490
doi: 10.1137/090770849
15 AAVATSMARK I, EIGESTAD G T, KLAUSEN R A, et al Convergence of a symmetric MPFA method on quadrilateral grids[J]. Computational Geosciences, 2007, 11 (4): 333- 345
doi: 10.1007/s10596-007-9056-8
16 KLAUSEN R A, RUSSELL T F Relationships among some locally conservative discretization methods which handle discontinuous coefficients[J]. Computational Geosciences, 2004, 8 (4): 341- 377
doi: 10.1007/s10596-005-1815-9
17 KLAUSEN R A, RADU F A, EIGESTAD G T Convergence of MPFA on triangulations and for Richards' equation[J]. International Journal for Numerical Methods in Fluids, 2008, 58 (12): 1327- 1351
doi: 10.1002/fld.1787
18 SHENG Z, YUAN G An improved monotone finite volume scheme for diffusion equation on polygonal meshes[J]. Journal of Computational Physics, 2012, 231 (9): 3739- 3754
doi: 10.1016/j.jcp.2012.01.015
19 ZHOU Y. Parallel general-purpose reservoir simulation with coupled reservoir models and multisegment wells [D]. Stanford: Stanford University, 2012.
20 WONG Z Y, KWOK F, HORNE R N, et al Sequential-implicit Newton method for multiphysics simulation[J]. Journal of Computational Physics, 2019, 391: 155- 178
doi: 10.1016/j.jcp.2019.04.023
21 JIN Z L, LIU Y, DURLOFSKY L J Deep-learning-based surrogate model for reservoir simulation with time-varying well controls[J]. Journal of Petroleum Science and Engineering, 2020, 192: 107273
doi: 10.1016/j.petrol.2020.107273
22 DOTLIĆ M, POKORNI B, PUŠIĆ M, et al Non-linear multi-point flux approximation in the near-well region[J]. Filomat, 2018, 32 (20): 6857- 6867
doi: 10.2298/FIL1820857D
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