A solution for unconfined groundwater flow: An innovative approach based on the lattice Boltzmann method

Document Type : Article

Authors

1 Department of Civil and Environmental Engineering, School of Engineering, Shiraz University, Shiraz, Iran

2 Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, P.O. Box 71555-313, Iran

Abstract

Lattice Boltzmann method (LBM) has emerged as a fast, precise, and efficient numerical solution to solve differential equations. There seems to be a dearth of research regarding the solution for groundwater flow in unconfined aquifer using LBM. Accordingly, in this study, an innovative numerical solution based on LBM was introduced to solve groundwater flow in unconfined aquifers, taking into account D2Q9 scheme. The solutions obtained from the proposed LBM were compared to results stemmed from three different unconfined groundwater problems with known solutions. Both steady and transient conditions for groundwater flow were considered in simulations. It was deduced that the proposed LBM could simulate the unconfined groundwater flow satisfactorily.

Keywords

References

References:
1.             Zhou, J.G. “Lattice Boltzmann method for advection and anisotropic dispersion equation”, J. Appl. Mech., 78(2), pp. 1-5 (2011).
2.             Hekmatzadeh, A.A., Adel, A., Zarei, F. and Haghighi, A.T. “Probabilistic simulation of advection-reaction-dispersion equation using random lattice Boltzmann method”, Int. J. Heat Mass Transf., 144, pp. 118647 (2019).
3.             Hekmatzadeh, A.A. “ Keshavarzi, H., Talebbeydokhti, N. and T.Haghighi, A., Lattice Boltzmann solution of advection-dominated mass transport problem: a comparison”, Sci. Iran., 27(2), pp. 625-638 (2020).
4.             Wang, H. “Numerical simulation for solitary wave of Klein–Gordon–Zakharov equation based on the lattice Boltzmann model”, Comput. Math. with Appl., 78 (12), pp. 3941-3955 (2019).
5.             Zhao, Y., Wu, Y., Chai, Z. and Shi, B. “A block triple-relaxation-time lattice Boltzmann model for nonlinear anisotropic convection–diffusion equations”, Comput. Math. with Appl., 79(9), pp. 2550-2573 (2020).
6.             Salinas, Á., Torres, C. and Ayala, O. “A fast and efficient integration of boundary conditions into a unified CUDA Kernel for a shallow water solver lattice Boltzmann Method”, Comput. Phys. Commun., 249, pp. 107009 (2020).
7.             Chen, Y. and Müller, C. “A Dirichlet boundary condition for the thermal lattice Boltzmann method”, Int. J. Multiph. Flow, 123, pp. 103184 (2020.).
8.             Aristov, V.V., Ilyin, O.V. and Rogozin, O.A. “Kinetic multiscale scheme based on the discrete-velocity and lattice-Boltzmann methods”, J. Comput. Sci., 40, pp. 101064 (2020).
9.             Vandekerckhove, C., Van Leemput, P. and Roose, D. “Acceleration of lattice Boltzmann models through state extrapolation: a reaction–diffusion example”, Appl. Numer.  Math., 58, pp. 1742–1757 (2008).
10.          Yu, X., Regenauer-Lieb, K. and Tian, F.-B. “A hybrid immersed boundary-lattice Boltzmann/finite difference method for coupled dynamics of fluid flow, advection, diffusion and adsorption in fractured and porous media”, Comput. Geosci., 128, pp. 70-78 (2019).
11.          Mohamad, A. “Lattice Boltzmann Method”, Springer, 70, pp. 21-100 (2011).
12.          Perumal, D.A. and Dass, A.K. “A Review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer”, Alex. Eng. J., 54(4), pp. 955-971 (2015).
13.          Li, L., Mei, R. and Klausner, J.F. “Lattice Boltzmann models for the convection-diffusion equation: D2Q5 vs D2Q9”, Int. J. Heat Mass Transf., 108, pp. 41-62 (2017).
14.          Xia, Y., Wu, J. and Zhang, Y. “Lattice-Boltzmann simulation of two-dimensional super-diffusion”, Eng. Appl. Comput. Fluid Mech., 6 (4), pp. 581-594 (2012).
15.          Perko, J. and Patel, R.A. “Single-relaxation-time lattice Boltzmann scheme for advection-diffusion problems with large diffusion-coefficient heterogeneities and high-advection transport”, Phys. Rev. E., 89 (5), pp. 053309 (2014).
16.          Chopard, B., Falcone, J.-L. and Latt, J. “The lattice Boltzmann advection-diffusion model revisited”, The Eur. Phys. J. Spec. Top., 171(1), pp. 245-249 (2009).
17.          Guo, X., Shi, B. and Chai, Z “General propagation lattice Boltzmann model for nonlinear advection-diffusion equations”, Phy. Rev. E., 97(4), pp. 043310 (2018).
18.          Zhang, M., Zhao, W. and Lin, P. “Lattice Boltzmann method for general convection-diffusion equations: MRT model and boundary schemes”, J. Comput. Phys., 389, pp. 147-163 (2019).
19.          Xing, H., Dong, X., Sun, D. and Han, Y. “Anisotropic lattice Boltzmann-phase-field modeling of crystal growth with melt convection induced by solid-liquid density change”, J. Mater. Sci. Technol., 57, pp. 26-32 (2020).
20.          Gawas, A.S. and Patil, D.V. “Axisymmetric thermal-lattice Boltzmann method for Rayleigh-Bénard convection with anisotropic thermal diffusion”, J. Comput. Sci., 45, pp. 101185 (2020).
21.          Cartalade, A., Younsi, A. and Neel, M.C. “Multiple-Relaxation-Time Lattice Boltzmann scheme for fractional advection–diffusion equation”, Comput. Phys. Commun., 234, pp. 40-54 (2019).
22.          Chai, Z. and Shi, B. “Multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: Modeling, analysis, and elements”, Phys. Rev. E., 102(2), pp. 023306 (2020).
23.          Yan, Z., Yang, X., Li, S. and Hilpert, M. “Two-relaxation-time lattice Boltzmann method and its application to advective-diffusive-reactive transport”, Adv. Water Resour., 109, pp. 333-342 (2017).
24.          Guo, C., Zhao, W. and Lin, P. “On the collision matrix of the lattice Boltzmann method for anisotropic convection-diffusions equations”, Appl. Math. Lett., 105, p. 106304 (2020).
25.          Zhang, H. and Misbah, C. “Lattice Boltzmann simulation of advection-diffusion of chemicals and applications to blood flow”, Comput. Fluids., 187, pp. 46-59 (2019).
26.          Du, R. and Liu, Z. “A lattice Boltzmann model for the fractional advection–diffusion equation coupled with incompressible Navier–Stokes equation”, Appl. Math. Lett., 101, pp. 106074 (2020).
27.          Wolf-Gladrow, D. “A lattice Boltzmann equation for diffusion”, J. Stat. Phys., 79(5-6), pp. 1023-1032 (1995).
28.          Lin, Y., Yang, C., Choi, C., et al. “ Lattice Boltzmann simulation of multicomponent reaction-diffusion and coke formation in a catalyst with hierarchical pore structure for dry reforming of methane”, Chem. Eng. Sci., 229, pp. 116105 (2020).
29.          Zhou, J.G. “A lattice Boltzmann model for groundwater flows”, Int. J. Mod. Phys. C., 18 (06), pp. 973-991 (2007).
30.          Zhou, J.G. “A rectangular lattice Boltzmann method for groundwater flows”,  Mod. Phys. Lett. B., 21 (09), pp. 531-542 (2007).
31.          Anwar, S. and Sukop, M.C. “Regional scale transient groundwater flow modeling using Lattice Boltzmann methods”, Comput. Math. With Appl., 58(5), pp. 1015-1023 (2009).
32.          Budinski, L., Fabian, J. and Stipić, M. “Lattice Boltzmann method for groundwater flow in non-orthogonal structured lattices”, Comput. Math. with Appl., 70, pp. 2601–2615 (2015).
33.          Anwar, S. and Sukop, M.C. “Lattice Boltzmann models for flow and transport in saturated karst”,  Groundw., 47(3), pp. 401-413 (2009).
34.          Abdelaziz, R., Pearson, A.J. and Merkel, B.J. “Lattice Boltzmann modeling for tracer test analysis in a fractured Gneiss aquifer”, Nat. Sci., 5(3), pp. 368-374 (2013).
35.          Liu, X., Huang, Y., Wang, C.H. and Zhu, K. “Solving steady and transient radiative transfer problems with strong inhomogeneity via a lattice Boltzmann method”, Int. J. Heat Mass Transf., 155, pp. 119714 (2020).
36.          Todd, D.K. and Mays, L.W. “Groundwater hydrology”, John Wiley & Sons, (2004).
37.          Zhou, J.G. “Lattice Boltzmann methods for shallow water flows”, Springer, 4, (2004).
38.          Girimaji, S. “Lattice Boltzmann Method: Fundamentals and Engineering Applications With Computer Codes. 2013”,  AIAA J., 51(1), pp. 278-279 (2013).
39.          El-Ghandour, H.A. and Elsaid, A. “Groundwater management using a new coupled model of flow analytical solution and particle swarm optimization”, Int. J. Water Resour. Environ. Eng., 5 (1), pp. 1-11 (2013).
40.          Malama, B. “Alternative linearization of water table kinematic condition for unconfined aquifer pumping test modeling and its implications for specific yield estimates”, J. Hydrol., 399(3-4), pp. 141-147 (2011).
41.          Moench, A.F. “Combining the Neuman and Boulton models for flow to a well in an unconfined aquifer”, Groundw., 33(3), pp. 378-385 (1995).
42.          Moench, A.F. “Flow to a well in a water-table aquifer: an improved Laplace transform solution”, Groundw., 34(4), pp. 593-597 (1996).
43.          Moench, A.F. “Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer. Water Resour. Res., 33(6), pp. 1397-1407 (1997).
44.          Blumenthal, B.J. and Zhan, H. “Rapid computation of directional wellbore drawdown in a confined aquifer via Poisson resummation”, Adv. Water Resour., 94, pp. 238-250 (2016).
45.          Malama, B., Kuhlman, K.L. and Barrash, W. “Semi-analytical solution for flow in leaky unconfined aquifer–aquitard systems”, J. Hydrol., 346(1-2), pp. 59-68 (2007).
46.          Chiang, W. “Processing Modflow: an integrated modeling environment for the simulation of groundwater flow, transport and reactive processes, Users manual, manuscript”, Simcore Software, (2010).
Scientia Iranica
Volume 28, Issue 5
Transactions on Civil Engineering (A)
September and October 2021
Pages 2493-2503

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