Modeling Groundwater Flow in Unconfined Conditions: Numerical Model and Solvers’ Efficiency

被引:7
作者
Anuprienko D.V. [1 ]
Kapyrin I.V. [1 ,2 ]
机构
[1] Nuclear Safety Institute of the Russian Academy of Sciences, ul. Bol’shaya Tul’skaya 52, Moscow
[2] Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, ul. Gubkina 8, Moscow
关键词
Groundwater flow; nonlinear solvers; unconfined conditions;
D O I
10.1134/S1995080218070053
中图分类号
学科分类号
摘要
A mathematical model for variably saturated flow in unconfined conditions is presented. The model is based on pseudo-unsaturated approach using Richards equation with piecewise linear dependencies between hydraulic head, water content and relative permeability. It is implemented in GeRa (Geomigration of Radionuclides) software package, which is designed for modeling groundwater flow and contaminant transport in porous media and uses finite volume methods on unstructured grids. We consider two nonlinear solvers for nonlinear equations arising from discretization of the Richards equation, namely Newton and Picard methods. A special method for correction of hydraulic head values within the iterations of nonlinear solvers is proposed. The developed numerical techniques are applied to two test cases: dam seepage and real-world groundwater flow problems. © 2018, Pleiades Publishing, Ltd.
引用
收藏
页码:867 / 873
页数:6
相关论文
共 16 条
[1]  
Richards L., Capillary conduction of liquids through porous mediums, J. Appl. Phys., 1, pp. 318-333, (1931)
[2]  
Kapyrin I.V., Ivanov V.A., Kopytov G.V., Utkin S.S., Integral code GeRa for RAW disposal safety validation, Gorn. Zh., 10, pp. 44-50, (2015)
[3]  
Diersch H.J., FEFLOW: Finite Element Modeling of Flow, Mass and Heat Transport in Porous and Fractured Media, (2013)
[4]  
Simunek J., van Genuchten M.T., Modeling nonequilibrium flow and transport processes using HYDRUS, Vadose Zone J., 7, pp. 782-797, (2008)
[5]  
Harbaugh A.W., Banta E.R., Hill M.C., McDonald M.G., MODFLOW-2000, The U. S. Geological Survey modular ground-water model-user guide to modularization concepts and the ground-water flow process, (2000)
[6]  
Kapyrin I.V., Suskin V.V., Rastorguev A.V., Nikitin K.D., Verification of unsaturated flow and transport in vadose zone models using the computational code GeRa, Vopr. At. Nauki Tekh., Ser.: Mat. Model. Fiz. Protsess., 1, pp. 60-75, (2017)
[7]  
Plenkin A.V., Chernyshenko A.Y., Chugunov V.N., Kapyrin I.V., Adaptive unstructured mesh generation methods for hydrogeological problems, Vychisl. Metody Programm., 16, pp. 518-533, (2015)
[8]  
Aavatsmark I., Interpretation of a two-point flux stencil for skew parallelogram grids, Comput. Geosci., 11, pp. 199-206, (2007)
[9]  
Aavatsmark I., Barkve T., Boe O., Mannseth T., Discretization on unstructured grids for inhomogeneous, anizotropic media. Part I: Derivation of the methods, SIAM J. Sci. Comput., 19, pp. 1700-1716, (1998)
[10]  
Danilov A., Vassilevski Y., A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes, Russ. J. Numer. Anal.Math. Model., 24, pp. 207-227, (2009)