A generalized multi-dimensional saturated-unsaturated flow model based on spatial linkers
-
摘要: 多维饱和-非饱和流方程离散后生成的系数矩阵中常存在零系数，这将影响求解过程中的存储空间和计算效率。合理的系数矩阵优化方法既能保证模拟精度，又能提高模型在大规模网格单元中的计算效率及通用性。文章在多维饱和-非饱和流有限差分法基础上，预先记录不同方向上有效单元间的连接关系，避免了零系数的计算和存储，并结合矩阵标识法建立了空间链接器式多维通用饱和-非饱和流模型。通过模拟地下水位起涨、渗流面排水等四个经典案例及田间三场长历时小雨入渗过程，验证了该模型的模拟精度及计算效率。对比结果表明：该模型在多维度、不同边界条件（包括天然降雨、渗流面等）下的模拟精度与Hydrus、VSF等成熟软件相当，计算效率略低于Hydrus软件。田间模拟结果表明：VG模型中的参数n敏感性最强，需优先率定；因模型中尚未考虑大孔隙流影响，各层土壤水分响应时间滞后于实测过程；三场降雨计算时段末期，超过80%的入渗水量仍滞蓄在表层40 cm的土壤中，仅有约4%~12%的水量已转化为潜水。本文模型有望成为传统多维饱和-非饱和流模型的重要补充。Abstract: There are often some zero coefficients in the coefficient matrix after the multi-dimensional saturated-unsaturated flow equation is discretized, which will affect the storage space and calculation efficiency in the solution process. A reasonable coefficient matrix optimization method can not only guarantee the simulation accuracy, but also improve the calculation efficiency and universality of the model when it is applied in large-scale grid cells. This paper proposed a generalized multi-dimensional saturated-unsaturated flow model based on spatial linkers. Finite difference method is used to solve the multi-dimensional saturated-unsaturated flow equation. The connections between each two effective units in different directions were pre-recorded, which will avoid the calculation and storage of zero coefficients. The matrix marking method is applied to further simplify the coefficient matrix. The simulation accuracy and efficiency of the model are verified by simulating four classic cases, such as groundwater level rise and seepage surface drainage, as well as three long periods of light rain infiltration in the field. The comparison results show that the simulation accuracy of the model is comparable to some mature softwares, such as Hydrus and VSF, under multiple dimensions and different boundary conditions (including natural rainfall, seepage surface, etc.), while the efficiency is slightly lower than that with Hydrus. Field simulation results also show that the parameter n in VG model can make greatest changes in simulation results with smallest variation and needs to be calibrated in priority. Because the effect of macropore flow has not been considered in the model, the soil moisture response time of each layer lags behind the measured process. At the end of the three rainfall calculation periods, more than 80% of the infiltration water is still stored in the upper 40 cm soil layer, and only about 4%—12% of the infiltration water has been converted to phreatic water. The model in this paper is expected to be an important supplement to the traditional multi-dimensional saturated-unsaturated flow models.
-
Key words:
- spatial linker /
- saturated-unsaturated flow /
- numerical simulation /
- VG model /
- parameter sensititity
-
-
[1] LIAKOPOULOS A C. Retention and distribution of moisture in soils after infiltration has ceased[J]. International Association of Scientific Hydrology Bulletin, 1965, 10(2):58-69.
[2] 吴梦喜, 高莲士. 饱和-非饱和土体非稳定渗流数值分析[J]. 水利学报, 1999, 30(12):38-42.[WU M X, GAO L S. Saturated-unsaturated unsteady seepage numerical analysis[J]. Journal of Hydraulic Engineering, 1999, 30(12):38-42.(in Chinese)]
[3] 李信,高骥,汪自力,等. 饱和-非饱和土的渗流三维计算[J]. 水利学报, 1992, 23(11):63-68.[LI X, GAO J, WANG Z L, et al. Three-dimensional seepage simulation in saturated-unsaturated soil[J]. Journal of Hydraulic Engineering, 1992, 23(11):63-68.(in Chinese)]
[4] ZHA Y Y, YANG J Z, ZENG J C, et al. Review of numerical solution of Richardson-Richards equation for variably saturated flow in soils[J/OL]. Wiley Interdisciplinary Reviews:Water, 2019, 6(5):e1364. DOI:10.1002/wat2.1364.
[5] NGO-CONG D, MAI-DUY N, ANTILLE D L, et al. A control volume scheme using compact integrated radial basis function stencils for solving the Richards equation[J]. Journal of Hydrology, 2020, 580:124240.
[6] HUYAKORN P S, THOMAS S D, THOMPSON B M. Techniques for making finite elements competitve in modeling flow in variably saturated porous media[J].Water Resources Research, 1984, 20(8):1099-1115.
[7] ZHA Y Y, YANG J Z, YIN L H, et al. A modified Picard iteration scheme for overcoming numerical difficulties of simulating infiltration into dry soil[J]. Journal of Hydrology, 2017, 551:56-69.
[8] ZENG J C, ZHA Y Y, YANG J Z. Switching the Richards' equation for modeling soil water movement under unfavorable conditions[J]. Journal of Hydrology, 2018, 563:942-949.
[9] CELIA M A, BOULOUTAS E T, ZARBA R. A general mass-conservative numerical solution for the unsaturated flow equation[J].Water Resources Research, 1990, 26(7):1483-1496.
[10] KIRKLAND M R, HILLS R G, WIERENGA P J. Algorithms for solving Richards' equation for variably saturated soils[J]. Water Resources Research, 1992, 28(8):2049-2058.
[11] DOGAN A, MOTZ L H. Saturated-unsaturated 3D groundwater model. I:development[J]. Journal of Hydrologic Engineering, 2005, 10(6):492-504.
[12] 李光炽,王船海. 大型河网水流模拟的矩阵标识法[J]. 河海大学学报(自然科学版), 1995, 23(1):36-43.[LI G Z, WANG C H. Matrix mark method for large-scale river network flow modeling[J]. Journal of Hohai University (Natural Sciences), 1995,23(1):36-43.(in Chinese)]
[13] 李光炽, 王船海, 周晶晏. 二维流场模拟的矩阵标识法[J]. 河海大学学报(自然科学版), 2002, 30(3):80-84.[LI G Z, WANG C H, ZHOU J Y. Matrix mark method for modelling 2D flow pattern[J]. Journal of Hohai University(Natural Sciences), 2002,30(3):80-84.(in Chinese)]
[14] 施小清, 张可霓, 吴吉春. TOUGH2软件的发展及应用[J]. 工程勘察, 2009, 37(10):29-34.[SHI X Q, ZHANG K N, WU J C. The history and application of TOUGH2 code[J]. Geotechnical Investigation & Surveying, 2009,37(10):29-34.(in Chinese)]
[15] 陈景波, 王船海, 杜世鹏, 等. 平原区饱和-非饱和土壤水运动模型及数值算法研究[J]. 水力发电, 2016, 42(9):13-16.[CHEN J B, WANG C H, DU S P, et al. Study on flow model and numerical simulation of unsaturated and saturated soil water in plain area[J]. Water Power, 2016,42(9):13-16.(in Chinese)]
[16] COOLEY R L. Some new procedures for numerical solution of variably saturated flow problems[J]. Water Resources Research, 1983, 19(5):1271-1285.
[17] van GENUCHTEN M Th. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J]. Soil Science Society of America Journal, 1980, 44(5):892-898.
[18] DIERSCH H J G.. FEFLOW:Finite element modeling of flow, mass and heat transport in porous and fractured media[M]. Berlin:Springer Press, 2014.
[19] HUYAKORN P S, SPRINGER E P, GUVANASEN V, et al. A three-dimensional finite-element model for simulating water flow in variably saturated porous media[J]. Water Resources Research, 1986, 22(13):1790-1808.
[20] DAVIS L A, NEUMAN S P. Documentation and user's guide:UNSAT2-Variably saturated flow model[R]. Fort Collins, Colorado:Water, Waste & Land, Incorporation, 1983.
[21] VAUCLIN M, KHANJI D, VACHAUD G. Experimental and numerical study of a transient, two-dimensional unsaturated-saturated water table recharge problem[J]. Water Resources Research, 1979, 15(5):1089-1101.
[22] ZHA Y Y, SHI L S, YE M, et al. A generalized Ross method for two-and three-dimensional variably saturated flow[J]. Advances in Water Resources, 2013, 54:67-77.
[23] CLEMENT T P, WISE W R, MOLZ F J. A physically based, two-dimensional, finite-difference algorithm for modeling variably saturated flow[J]. Journal of Hydrology, 1994, 161(1):71-90.
[24] SIMUNEK J, VAN GENUCHTEN M T, SEJNA M. The HYDRUS software package for simulating two-and three-dimensional movement of water, heat, and multiple solutes in variably saturated media[R]. Prague, Czech Republic:PC Progress, 2006.
[25] THOMS R B, JOHNSON R L, HEALY R W. User's guide to the variably saturated flow (VSF) process for MODFLOW[R]. Reston, Virginia:US Geological Survey, 2006.
[26] DOGAN A. Variably saturated three-dimensional rainfall-driven groundwater flow model[D]. Gainesville, Florida:University of Florida, 1999.
[27] VAUCLIN M, VACHAUD G, KHANJI J. Two dimensional numerical analysis of transient water transfer in saturated-unsaturated soils[C]//VANSTEENKISTE G C. Modeling and simulation of water resources systems. Amsterdam:North-Holland Publishing Company, 1975:299-323.
[28] HAVERKAMP R, VAUCLIN M, TOUMA J, et al. A comparison of numerical simulation models for one-dimensional infiltration1[J]. Soil Science Society of America Journal, 1977, 41(2):285-294.
[29] 吴礼舟,黄润秋.非饱和土渗流及其参数影响的数值分析[J].水文地质工程地质,2011,38(1):94-98.[WU L Z, HUANG R Q. A numerical analysis of the infiltration and parameter effects in unsaturated soil[J].Hydrogeology & Engineering Geology,2011,38(1):94-98. (in Chinese)]
[30] 陈卫金,程东会,陶伟.van Genuchten模型参数的物理意义[J].水文地质工程地质,2017,44(6):147-153.[CHEN W J, CHENG D H, TAO W. Physical significance of the parameters in the van Genuchten model[J].Hydrogeology & Engineering Geology,2017,44(6):147-153. (in Chinese)]
[31] 范严伟, 赵文举, 毕贵权. Van Genuchten模型参数变化对土壤入渗特性的影响分析[J]. 中国农村水利水电, 2016(3):52-56.[FAN Y W, ZHAO W J, BI G Q. The influence analysis of parameters variations in van Genuchten model on the soil infiltration characteristics[J]. China Rural Water and Hydropower, 2016(3):52-56.(in Chinese)]
[32] 高志鹏, 屈吉鸿, 陈南祥, 等. 一维水流及溶质运移对VG模型参数的敏感性分析[J]. 节水灌溉, 2017(11):65-71.[GAO Z P, QU J H, CHEN N X, et al. Sensitivity analysis of VG model parmneters to one dimensional water flows and solute transport[J]. Water Saving Irrigation, 2017(11):65-71.(in Chinese)]
[33] 霍思远, 靳孟贵. Van Genuchten模型参数对降水入渗数值模拟的敏感性[J]. 地球科学, 2017, 42(3):447-452.[HUO S Y, JIN M G. Effect of parameter sensitivity of van Genuchten model on numerical simulation of rainfall recharge[J]. Earth Science, 2017, 42(3):447-452.(in Chinese)]
[34] 张海阔, 姜翠玲, 李亮, 等. 基于HYDRUS-1D模拟的变水头入渗条件下VG模型参数敏感性分析[J]. 河海大学学报(自然科学版), 2019, 47(1):32-40.[ZHANG H K, JIANG C L, LI L, et al. Parameter sensitivity analysis of VG model in the varying-head infiltration based on HYDRUS-1D simulation[J]. Journal of Hohai University(Natural Sciences), 2019, 47(1):32-40.(in Chinese)]
[35] 李昊旭,邵景力,崔亚莉,等.不同作物覆盖对农业区地下水入渗补给的影响分析[J].水文地质工程地质,2019,46(2):57-65.[LI H X, SHAO J L, CUI Y L, et al. Effects of different crop covers on vertical groundwater recharge[J].Hydrogeology & Engineering Geology,2019,46(2):57-65. (in Chinese)]
[36] 霍思远,靳孟贵.不同降水及灌溉条件下的地下水入渗补给规律[J].水文地质工程地质,2015,42(5):6-13.[HUO S Y, JIN M G. Effects of precipitation and irrigation on vertical groundwater recharge[J].Hydrogeology & Engineering Geology,2015,42(5):6-13. (in Chinese)]
-
计量
- 文章访问数: 547
- PDF下载数: 81
- 施引文献: 0
下载: