Abstract
In this study, a meshless simulation model based on the element-free Galerkin method (EFGM) is proposed for the coupled simulation of groundwater flow and contaminant transport (GFCT) in the two-dimensions. EFGM discretizes the governing GFCT equations using the Galerkin integral approach and shape functions generated through the moving least squares (MLS) approximation method. It results into the stable system of equations for estimating the groundwater head and contaminant concentration values. EFGM computes the several global matrices using the spatial information of the scattered and unconnected field nodes and hence, terminates the meshing procedure unlike the finite difference (FDM) and finite element (FEM) methods. The Kronecker delta function property is missing in EFGM shape functions and hence, the Dirichlet boundary conditions are enforced with some special methods. We have used the penalty method to include them into the presented EFGM model. This method is straightforward and computationally useful for the real field simulations. The proposed model is first validated using both the one- and two-dimensional analytical solutions. The developed coupled model is then applied to solve the hypothetical and real field problems. EFGM results for both the problems are compared with the MODFLOW and MT3DMS results for the head and concentration values respectively. EFGM results are found to be satisfactory for both the cases, and it shows the potential of the proposed approach for the coupled GFCT simulations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bear J (1972) Dynamics of fluids in porous media. Elsevier, New York
Bear J (1979) Hydraulics of groundwater. McGraw Hill Publishing, New York
Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37(2):229–256. https://doi.org/10.1002/nme.1620370205
Boddula S, Eldho TI (2018) Groundwater management using a new coupled model of meshless local Petrov-Galerkin method and modified artificial bee colony algorithm. Comput Geosci 22:657–675. https://doi.org/10.1007/s10596-018-9718-8
Boddula S, Eldho TI (2017) A moving least squares based meshless local Petrov-Galerkin method for the simulation of contaminant transport in porous media. Eng Anal Bound Elem 78:8–19. https://doi.org/10.1016/j.enganabound.2017.02.003
Dhar RL, Singh VS, Rao G, VVS, Rao A, Sarma V, MRK, Prakash BA, Krishnan V (1999) Assessment of the impact of red mud stacking on groundwater regime around INDAL Alumina plant, Belgaum, Karnataka. Tech. Rep. No. NGRI- 99 – GW- 256, p 79
Dolbow J, Belytschko T (1998) An introduction to programming the meshless Element Free Galerkin method. Arch Comput Methods Eng 5(3):207–241. https://doi.org/10.1007/BF02897874
Guneshwor L, Eldho TI, Vinod Kumar A (2018) Identification of groundwater contamination sources using meshfree RPCM simulation and particle swarm optimization. Water Resour Manag 32(4):1517–1538. https://doi.org/10.1007/s11269-017-1885-1
Guneshwor Singh L, Eldho TI, Vinod Kumar A (2016) Coupled groundwater flow and contaminant transport simulation in a confined aquifer using meshfree radial point collocation method (RPCM). Eng Anal Bound Elem 66:20–33. https://doi.org/10.1016/j.enganabound.2016.02.001
Harbaugh AW (2005) MODFLOW-2005, the U.S. Geological Survey modular ground-water model – the ground-water flow process: U.S. Geological Survey Techniques and Methods 6-A16
Liu GR, Gu YT (2005) An introduction to meshfree methods and their programming. Springer, Dordrecht
Majumder Partha, Eldho TI (2017) Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking. Hydrolog Process 31(5):1144–1160. https://doi.org/10.1002/hyp.11106
Mategaonkar M, Eldho TI (2014) Multiobjective groundwater remediation design using a coupled mfree point collocation method and particle swarm optimization. J Hydrolog Eng 19(6):1259–1263. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000899
Meenal M, Eldho TI (2011) Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method. Eng Anal Bound Elem 35(4):700–707. https://doi.org/10.1016/j.enganabound.2010.12.003
Meenal M, Eldho TI (2012) Two-dimensional contaminant transport modeling using meshfree point collocation method (PCM). Eng Anal Bound Elem 36(4):551–561. https://doi.org/10.1016/j.enganabound.2011.11.001
Park Y-C, Leap DI (2000) Modeling groundwater flow by the element-free Galerkin (EFG) method. Geosci J 4(3):231–241. https://doi.org/10.1007/BF02910141
Pathania T, Bottacin-Busolin A, Rastogi AK, Eldho TI (2019) Simulation of groundwater flow in an unconfined sloping aquifer using the element-free Galerkin method. Water Resour Manag 33(8):2827–2845. https://doi.org/10.1007/s11269-019-02261-4
Pinder GF, Gray WG (1977) Finite element simulation in surface and subsurface hydrology. Academic Press, New York
Praveen Kumar R, Dodagoudar GR (2010) Meshfree analysis of two-dimensional contaminant transport through unsaturated porous media using EFGM. Int J Numer Method Biomed Eng 26(12):1797–1816. https://doi.org/10.1002/cnm.1266
Qin X, Duan X, Hu G, Su L, Wang X (2018) An Element-free Galerkin method for solving the two-dimensional hyperbolic problem. Appl Math Comput 321:106–120. https://doi.org/10.1016/J.AMC.2017.10.040
Samimi S, Pak A (2012) Three-dimensional simulation of fully coupled hydro-mechanical behavior of saturated porous media using Element Free Galerkin (EFG) method. Comput Geotech 46:75–83. https://doi.org/10.1016/j.compgeo.2012.06.004
Singh A, Singh IV, Prakash R (2007) Meshless element free Galerkin method for unsteady nonlinear heat transfer problems. Int J Heat Mass Transfer 50(5-6):1212–1219. https://doi.org/10.1016/j.ijheatmasstransfer.2006.08.039
Swathi B, Eldho TI (2014) Groundwater flow simulation in unconfined aquifers using meshless local Petrov–Galerkin method. Eng Anal Bound Elem 48:43–52. https://doi.org/10.1016/j.enganabound.2014.06.011
Van Genuchten MTh, Alves WJ (1982) Analytical solutions of the one-dimensional convective-dispersive solute transport equation. Technical Bulletin Number 1661, United States Department of Agriculture, Economic Research Service
Wang HF, Anderson MP (1982) Introduction to groundwater modeling: finite difference and finite element methods. W.H. Freeman and Company, New York
Zheng C, Wang PP (1999) MT3DMS: A modular three-dimensional multi-species transport model for simulation of advection, dispersion, and chemical reactions of contaminants in groundwater systems. Documentation and user’s guide. In: Contract Report SERDP-99-1, U.S. Army Engineer Research and Development. Vicksburg, Mississippi, USA
Zhu T, Atluri SN (1998) A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput Mech 21(3):211–222. https://doi.org/10.1007/s004660050296
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
There is no conflict of interest in this manuscript.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Pathania, T., Eldho, T.I. A Moving Least Squares Based Meshless Element-Free Galerkin Method for the Coupled Simulation of Groundwater Flow and Contaminant Transport in an Aquifer. Water Resour Manage 34, 4773–4794 (2020). https://doi.org/10.1007/s11269-020-02689-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-020-02689-z