Fully Implicit Form of Differential Quadrature Method for Multi-Species Solute Transport in Porous Media

Yıl 2022, Cilt: 33 Sayı: 4, 12265 - 12282, 01.07.2022

Amin Gharehbaghı

https://doi.org/10.18400/tekderg.975457

Cited By: 2

Öz

Solute transport problems, including sequential multi-species transport phenomena, frequently occur in soil systems. The goal of this paper is to present a novel one-dimensional numerical model with a fully implicit form of differential quadrature method for solving multi-species solute transport equations. The analytical results of three multi-species solute dispersion problems with three- and four-chain members are used to analyse the developed model. Simultaneously, the outcomes of the developed model are compared with the performance of the fully implicit fourth-order finite difference method. Finally, the accuracy of the established model is discussed and evaluated. According to the numerical experiments, the derived model is very useful and widely applicable.

Anahtar Kelimeler

Multi-species, Solute transport, Porous media, Fully-Implicit Differential Quadrature Method, Fully-Implicit Fourth-Order Finite Difference Method

Kaynakça

• Bagalkot, N., Kumar, G.S., 2015. Effect of nonlinear sorption on multispecies radionuclide transport in a coupled fracture-matrix system with variable fracture aperture: a numerical study. ISH Journal of Hydraulic Engineering. 21(3) 242–254, http://dx.doi.org/10.1080/09715010.2015.1016125
• Bauer, P., Attinger, S., Kinzelbach, W., 2001. Transport of a decay chain in homogenous porous media: analytical solutions, Journal of Contaminant Hydrology. 49, 217–239.
• Bellman, R., Casti, J., 1971. Differential quadrature and long-term integration. J. Math. Anal. Appl. 34 (2), 235–238.
• Chaudhary, M., Singh, M.K. 2020, Study of multispecies convection-dispersion transport equation with variable parameters, Journal of Hydrology 591 (2020), https://doi.org/10.1016/j.jhydrol.2020.125562
• Chen, W. and Zhong, T., 1997, The study on the nonlinear computations of the DQ and DC methods. Numerical Methods for Partial Differential Equations, 13, 57–75
• Chen-Charpentier, B.M., Dimitrov, D.T., Kojouharov H.V., 2009. Numerical simulation of multi-species biofilms in porous media for different kinetics, Mathematics and Computers in Simulation, 79, 1846–1861.
• Ciftci, E., 2017. Modelling coupled density-dependent flow and solute transport with the differential quadrature method, Geosciences Journal, 21(5), 807817, http://dx.doi.org/10.1007/s12303-017-0009-5
• Konikow, L.F., and Bredehoeft, J.D., 1978, Computer model of two-dimensional solute transport and dispersion in ground water: U.S. Geological Survey, Techniques of Water-Resources Investigations, Book 7, Chap. C2.
• Civalek, O. 2004, Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns, Engineering Structures, 26,171–186.
• Das, P., Akhter, A., Singh, M.K., 2018. Solute transport modelling with the variable temporally dependent boundary, Sadhana, 43, 1-12, https://doi.org/10.1007/s12046-017-0778-6
• Essaid, H.I. and Bekins, B.A., 1997, BIOMOC, A Multispecies Solute-Transport Model with Biodegradation, U.S. GEOLOGICAL SURVEY, Water-Resources Investigations Report 97-4022.
• Gharehbaghi, A., 2016. Explicit and implicit forms of differential quadrature method for advection–diffusion equation with variable coeffcients in semi-infnite domain, J. Hydrol. 541 (1), 935–940, http://dx.doi.org/10.1016/j.jhydrol.2016.08.002
• Gharehbaghi, A., 2017. Third- and fifth-order finite volume schemes for advection–diffusion equation with variable coefficients in semi-infinite domain. Water and Environment Journal. 31 (2), 184–193. doi:10.1111/wej.12233
• Gharehbaghi, A., Kaya, B., Saadatnejadgharahassanlou, H., 2017. Two-dimensional bed variation models under nonequilibrium conditions in turbulent streams. Arabian Journal for Science and Engineering. 42 (3), 999–1011.
• Kaya, B., 2010. Solution of the advection-diffusion equation using the differential quadrature method. KSCE J. Civil Eng. 14 (1), 69–75.
• Kaya, B., Arisoy, Y., 2011. Differential quadrature solution for one-dimensional aquifer flow, Mathematical and Computational Applications, 16(2), 524-534.
• Kaya, B., Gharehbaghi., A., 2014. Implicit Solutions of Advection Diffusion Equation by Various Numerical Methods. Aust. J. Basic & Appl. Sci., 8(1): 381-391.
• Kumar, A., Kumar, D., Kumar, J.N., 2010. Analytical solutions to one-dimensional advection–diffusion equation with variable coefficients in semi-infinite media. J. Hydrol. 380, 330–337.
• Massoudieh, A., Ginn, T.R., 2007, Modeling colloid-facilitated transport of multi-species contaminants in unsaturated porous media, Journal of Contaminant Hydrology 92, 162–183, doi:10.1016/j.jconhyd.2007.01.005
• Engdahl N.B., Aquino, T., 2018, Considering the utility of backward-in-time simulations of multi-component reactive transport in porous media, Advances in Water Resources, 119, 17–27. https://doi.org/10.1016/j.advwatres.2018.06.003
• Natarajan N., Kumar S.G., 2010. Finite difference approach for modeling multispecies transport in porous media, International Journal of Engineering Science and Technology. 2(8), 3344-3350.
• Pathania, T., Eldho, T.I., Bottacin-Busolin, A. 2020. Coupled simulation of groundwater flow and multispecies reactive transport in an unconfined aquifer using the element-free Galerkin method. Engineering Analysis with Boundary Elements. 121, 31–49.
• Pérez Guerrero, J.S., Skaggs, T.H., van Genuchten, M.Th., 2009. Analytical Solution for Multi-Species Contaminant Transport Subject to Sequential First-Order Decay Reactions in Finite Media. Transp Porous Med. 80, 373–387, DOI 10.1007/s11242-009-9368-3
• Ramos, T.B., Šimůnek, J., Gonçalves, M.C., Martins, J.C., Prazeres, A., Castanheira, N.L., Pereira, L.S., 2011, Field evaluation of a multicomponent solute transport model in soils irrigated with saline waters, Journal of Hydrology, 407(1–4), 129-144, https://doi.org/10.1016/j.jhydrol.2011.07.016.
• Savovic, S., Djordjevich, A., 2012. Finite difference solution of the one-dimensional advection–diffusion equation with variable coefficients in semi-infinite media. Int. J. Heat Mass Transf. 55, 4291–4294. http://dx.doi.org/10.1016/j. ijheatmasstransfer.2012.03.073
• Sharma A., Guleria, A., Swami D., 2016. Numerical modelling of multispecies solute transport in porous media. Hydro 2016 international conference. 159-169.
• Shu, C., 2000. Differential Quadrature and its Application in Engineering. first ed.Springer-Verlag, London Limited.
• Šimůnek, J., Šejna, M., Saito, H., Sakai, M., and van Genuchten, M. Th., 2012, The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media, university of california riverside riverside, California
• Singh, M.K., Ahamad S., and Singh, V.P., 2012. Analytical Solution for One-Dimensional Solute Dispersion with Time-Dependent Source Concentration along Uniform Groundwater Flow in a Homogeneous Porous Formation. Journal of Engineering Mechanics. 138(8).
• Sun, Y., Petersen, J. N., Clement, T. P., and Skeen, R. S., 1999, Development of analytical solutions for multispecies transport with serial and parallel reactions, water resources research, 35(1), 185-190.
• Torlapati, J., 2013. Development and Application of One Dimensional Multi-component Reactive Transport Models. Phd dissertation, Auburn, Alabama, USA, May 4, 2013
• Van Genuchten, M.Th., 1985, Convective-dispersive transport of solutes involved in sequential first-order decay reactions, Computers & Geosciences, 11(2), 129-147, https://doi.org/10.1016/0098-3004(85)90003-2.
• Verma, K., Wille, R., High Performance Simulation for Industrial Paint Shop Applications, Springer Nature, 2021
• Zhang, Z., Zhang, J., Ju, Z. Zhu, M. 2018, A one-dimensional transport model for multi-component solute in saturated soil, Water Science and Engineering, 11(3), 236-242, https://doi.org/10.1016/j.wse.2018.09.007.
• Zong, Z., Zhang, Y., 2009. Advanced Differential Quadrature Methods, first ed. CRC Press, Taylor and Francis Group, New York.