Numerical Modeling of Contamination Transport Equation in Porous Media for Transient Flow Regime by Finite Volume Method

Document Type : Original Research

Authors
Department of Civil Engineering, K.N. Toosi University of Technology, Tehran, Iran
Abstract
Groundwater is an essential source of fresh water, which is less prone to pollution in comparison to surface water, and access to this valuable resource is affordable. These issues make groundwater a viable source during surface water shortages such as drought, especially in arid and semi-arid countries. In this research, the equation of contamination transport in groundwater is modeled by a novel dual discrete finite volume method (DDFVM). Using this numerical method, the contamination concentrations are obtained at the center and vertices of each element. This model has been applied to an unstructured triangular mesh that could be fitted to complex geometric boundaries. For the transient flow regimes, the flow equation has been coupled with the contaminant transport problem, and the results of the numerical model are validated with the model of Modflow. Finally, the flow and transport FV coupled model has been applied in a porous media with strong heterogeneity. The free-oscillation results for the two parameters of head and concentration demonstrate the stability of the model.

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عطایی آشتیانی، بهزاد، و حامد کتابچی، هیدرولیک و آلودگی آب‌های زیرزمینی. تهران، موسسه انتشارات علمی دانشگاه صنعتی شریف، چاپ اول.1393.
Ray S.S. & Elango L. 2019 Deterioration of groundwater quality: implications and management,. In: Water Governance: Challenges and Prospects. Springer, 87–101.
Gao Y., Shuping Y., & Chunmiao Z. 2021 Efficient simulation of groundwater solute transport using the multipoint flux approximation method with arbitrary polygon grids. Journal of Hydrology, 601 ,126637.
Elrick D.E., Mermoud A. & Monnier, T. 1994 An analysis of solute accumulation during steady-state evaporation in an initially contaminated soil. Journal of Hydrology, 155, 27–38.
Connell L.D. 2007 Simple models for subsurface solute transport that combine unsaturated and saturated zone pathways. Journal of Hydrology, 332, 361–373.
Diersch H.J.G. 2005 Reference Manual. DHI-WASY Software FEFLOW-Finite Element Subsurface Flow & Transport Simulation System. DHI-WASY GmbH, Berlin, German.
Zhu Y., Liangsheng S., Jinzhong Y., Jingwei W., & Deqiang M. 2013 Coupling methodology and application of a fully integrated model for contaminant transport in the subsurface system. Journal of hydrology, 501, 56-72.
Wang H.F. & Anderson M.P. 1995 Introduction to groundwater modeling: finite difference and finite element methods. Academic Press.
Zhu Y., Shi L., Lin L., Yang J., & Ye M. 2012 A fully coupled numerical modeling for regional unsaturated-saturated water flow. Journal of hydrology. 475, 188–203.
Gao Y., Pu S., Zheng C. & Yi S. 2019 An improved method for the calculation of unsaturated–saturated water flow by coupling the FEM and FDM. Scientific Reports, 9(1), 1-9.
Mehl S. & Hill M.C. 2004 Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: a new method of interpolation and analysis of errors. Advances in Water Resources, 27(9), 899-912.
Di Giammarco P., Todini E. & Lamberti P. 1996 A conservative finite elements approach to overland flow: the control volume finite element formulation. Journal of Hydrology, 175(1-4), 267-291.
Asadi R., Ataie-Ashtiani B. & Simmons C.T. 2014 Finite volume coupling strategies for the solution of a Biot consolidation model. Computers and Geotechnics, 55, 494-505.
Asadi R. & Ataie-Ashtiani B. 2016 Numerical modeling of subsidence in saturated porous media: A mass conservative method. Journal of hydrology, 542, 423-436.
Asadi R. & Ataie-Ashtiani B. 2021 Hybrid finite volume-finite element methods for hydro-mechanical analysis in highly heterogeneous porous media. Computers and Geotechnics, 132, 103996.
Loudyi D., Falconer R.A. & Lin, B. 2007 Mathematical development and verification of a non-orthogonal finite volume model for groundwater flow applications. Advances in water resources, 30(1), 29-42.
Aavatsmark I. 2002 An introduction to multipoint flux approximations for quadrilateral grids. Computational Geosciences, 6(3), 405-432.
Aavatsmark I. 2008 Comparison of monotonicity for some multipoint flux approximation methods. In Finite Volumes for Complex Applications. New York: 5, Wiley‐ISTE.
Droniou J. & Eymard, R. 2006 A mixed finite volume scheme for anisotropic diffusion problems on any grid. Numerische Mathematik, 105(1), 35-71.
Lewis R.W., Masters I. & Rees, I. 2006 Coupled and uncoupled contaminant transport using advanced finite volume methods. Computational Mechanics, 37(4), 292-310.
Coudière Y., Vila J.P. & Villedieu P. 1999 Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem. ESAIM: Mathematical Modelling and Numerical Analysis, 33(3), 493-516.
Coudière Y. & Villedieu, P. 2000 Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes. ESAIM: Mathematical Modelling and Numerical Analysis, 34(6), 1123-1149.
Manzini G. & Ferraris S. 2004 Mass-conservative finite volume methods on 2-D unstructured grids for the Richards’ equation. Advances in Water Resources, 27(12), 1199-1215.
Bevilacqua I., Canone D. & Ferraris S. 2011 Acceleration techniques for the iterative resolution of the Richards equation by the finite volume method. International Journal for Numerical Methods in Biomedical Engineering, 27(8), 1309-1320.
Milašinović M., Ranđelović A., Jaćimović N. & Prodanović, D. 2019 Coupled groundwater hydrodynamic and pollution transport modelling using Cellular Automata approach. Journal of Hydrology, 576, 652-666.
Gambolati G., Paniconi C. & Putti M. 1993 Numerical modeling of contaminant transport in groundwater. In Migration and Fate of Pollutants in Soils and Subsoils. Springer, Berlin, Heidelberg.