NUMERICAL SIMULATION OF A SINGLE RING INFILTRATION EXPERIMENT WITH hp-ADAPTIVE SPACE-TIME DISCONTINUOUS GALERKIN METHOD

Vít Dolejší; Michal Kuráž; Pavel Solin

doi:10.14311/AP.2021.61.0059

Authors

Vít Dolejší Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Prague, Czech Republic
Michal Kuráž Czech University of Life Sciences Prague, Faculty of Environmental Sciences, Department of Water Resources and Environmental Modeling, Kamýcká 129, 165 00 Prague, Czech Republic
Pavel Solin University of Nevada, College of Science, Department of Mathematics and Statistics, 1664 N Virginia St, NV 89557 Reno, USA

DOI:

https://doi.org/10.14311/AP.2021.61.0059

Keywords:

Richards equation, porous media flow, space-time discontinuous Galerkin method

Abstract

We present a novel hp-adaptive space-time discontinuous Galerkin (hp-STDG) method for the numerical solution of the nonstationary Richards equation equipped with Dirichlet, Neumann and seepage face boundary conditions. The hp-STDG method presented in this paper is a generalization of a hp-STDG method which was developed for time dependent non-linear convective-diffusive problems. We describe the method and the single ring experiment, and then we present a numerical experiment which clearly demonstrates the superiority of the hp-STDG method over a discontinuous Galerkin method based on a static fine mesh.

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References

X. Xu, C. Lewis, W. Liu, et al. Analysis of single-ring infiltrometer data for soil hydraulic properties estimation: Comparison of best and wu methods. Agricultural Water Management 107:34 – 41, 2012. doi:10.1016/j.agwat.2012.01.004.

M. Nakhaei, J. Šimunek. Parameter estimation of soil hydraulic and thermal property functions for unsaturated porous media using the hydrus-2d code. Journal of Hydrology and Hydromechanics 62(1):7–15, 2014. doi:10.2478/johh-2014-0008.

L. A. Richards. Capillary conduction of liquids through porous mediums. Journal of Applied Physics 1(5):318–333, 1931. doi:10.1063/1.1745010.

S. C. Iden, J. R. Blöcher, E. Diamantopoulos, et al. Numerical test of the laboratory evaporation method using coupled water, vapor and heat flow modelling. Journal of Hydrology 570:574 – 583, 2019. doi:10.1016/j.jhydrol.2018.12.045.

A. Binley, K. Beven. Vadose zone flow model uncertainty as conditioned on geophysical data. Ground Water 41(2):119–127, 2003. doi:10.1111/j.1745-6584.2003.tb02576.x.

S. Würzer, N. Wever, R. Juras, et al. Modelling liquid water transport in snow under rain-on-snow conditions – considering preferential flow. Hydrology and Earth System Sciences 21(3):1741–1756, 2017. doi:10.5194/hess-21-1741-2017.

M. Kuraz, P. Mayer, V. Havlicek, et al. Dual permeability variably saturated flow and ontaminant transport modeling of a nuclear waste repository with capillary barrier protection. Applied Mathematics and Computation 219(13):7127 – 7138, 2013. ESCO 2010 Conference in Pilsen, June 21- 25, 2010, doi:10.1016/j.amc.2011.08.109.

H. Alt, S. Luckhaus. Quasilinear elliptic-parabolic differential equations. Mathematische Zeitschrift 183(3):311–341, 1983. doi:10.1007/BF01176474.

F. Otto. L1-contraction and uniqueness for quasilinear elliptic-parabolic equations. Journal of Differential Equations 131(1):20–38, 1996.

F. Otto. L1–contraction and uniqueness for unstationary saturated-unsaturated porous media flow. Adv Math Sci Appl 7(2):537–553, 1997.

L. Lam, D. Fredlund. Saturated-unsaturated transient finite element seepage model for geotechnical engineering. Advances in Water Resources 7(3):132 – 136, 1984. doi:10.1016/0309-1708(84)90042-3.

C. Kees, M. Farthing, C. Dawson. Locally conservative, stabilized finite element methods for variably saturated flow. Computer Methods in Applied Mechanics and Engineering 197(51):4610 – 4625, 2008. doi:10.1016/j.cma.2008.06.005.

J. Šembera, M. Beneš. Nonlinear Galerkin method for reaction-diffusion systems admitting invariant regions. Journal of Computational and Applied Mathematics 136(1):163 – 176, 2001. doi:10.1016/S0377-0427(00)00582-3.

P. Solin, M. Kuraz. Solving the nonstationary Richards equation with adaptive hp-FEM. Advances in Water Resources 34(9):1062 – 1081, 2011. New Computational Methods and Software Tools, doi:10.1016/j.advwatres.2011.04.020.

M. Tocci, C. Kelley, C. Miller. Accurate and economical solution of the pressure-head form of Richards’ equation by the method of lines. Advances in Water Resources 20(1):1 – 14, 1997. doi:10.1016/S0309-1708(96)00008-5.

C. Miller, C. Abhishek, M. Farthing. A spatially and temporally adaptive solution of Richards’ equation. Advances in Water Resources 29(4):525 – 545, 2006. doi:10.1016/j.advwatres.2005.06.008.

M. Kuraz, P. Mayer, V. Havlicek, P. Pech. Domain decomposition adaptivity for the Richards equation model. Computing 95(1):501–519, 2013. doi:10.1007/s00607-012-0279-8.

M. Kuraz, P. Mayer, P. Pech. Solving the nonlinear Richards equation model with adaptive domain decomposition. Journal of Computational and Applied Mathematics 270:2 – 11, 2014. Fourth International Conference on Finite Element Methods in Engineering and Sciences (FEMTEC 2013), doi:10.1016/j.cam.2014.03.010.

M. Kuraz, P. Mayer, P. Pech. Solving the nonlinear and nonstationary Richards equation with two-level adaptive domain decomposition (dd-adaptivity). Applied Mathematics and Computation 267:207 – 222, 2015. The Fourth European Seminar on Computing (ESCO 2014), doi:10.1016/j.amc.2015.03.130.

V. Dolejší, M. Kuráž, P. Solin. Adaptive higher-order space-time discontinuous galerkin method for the computer simulation of variably-saturated porous media flows. Applied Mathematical Modelling 72:276 – 305, 2019. doi:10.1016/j.apm.2019.02.037.

M. T. van Genuchten. Closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44(5):892–898, 1980. doi:10.2136/sssaj1980.03615995004400050002x.

Y. Mualem. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12(3):513–522, 1976. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/WR012i003p00513. doi:10.1029/WR012i003p00513.

M. Kuraz, P. Mayer, M. Leps, D. Trpkosova. An adaptive time discretization of the classical and the dual porosity model of Richards’ equation. Journal of Computational and Applied Mathematics 233(12):3167 – 3177, 2010. Finite Element Methods in Engineering and Science (FEMTEC 2009), doi:10.1016/j.cam.2009.11.056.

V. Dolejší, M. Feistauer. Discontinuous Galerkin Method – Analysis and Applications to Compressible Flow. Springer Series in Computational Mathematics 48. Springer, Cham, 2015.

H. F. Walker, P. Ni. Anderson acceleration for fixed-point iterations. SIAM J Numer Anal 49(4):1715–1735, 2011. doi:10.1137/10078356X.

V. Dolejší. Anisotropic hp-adaptive method based on interpolation error estimates in the Lq-norm. Appl Numer Math 82:80–114, 2014. doi:10.1016/j.apnum.2014.03.003.

V. Dolejší. Anisotropic hp-adaptive method based on interpolation error estimates in the H1-seminorm. Appl Math 60(6):597–616, 2015. doi:10.1007/s10492-015-0113-7.

M. Kuraz, J. R. Bloecher. Hydrodynamic of porous media. CULS in Prague, 2017. Http://drutes.org/documents/notes.pdf.

J. Dusek, M. Dohnal, T. Vogel. Numerical analysis of ponded infiltration experiment under different experimental conditions. Soil and Water Research 4(SPECIAL ISSUE 2):22–27, 2009. doi:10.17221/1368-SWR.