Abstract
First-order reaction networks are often encountered in groundwater pollution problems. The members of the network transform/degrade from one species to another. In this paper a strong form meshfree numerical method named radial point collocation method (RPCM) is introduced to model such reactions. In the proposed method, the entire domain is decomposed into a number of overlapping local support domains surrounding each node. The concentrations of species at each node and its directional derivatives are approximated using multiquadrics radial basis functions (MQ-RBF) within the local support domain. 1D models are verified against existing analytical solutions. Further, the 2D model simulations are compared with widely used RT3D (Reactive Transport in 3 Dimensions) for a benchmark problem. Sensitivity analysis is also performed for model parameters. The proposed model solves species-wise governing equations and boundary conditions without operator splitting, unlike the popular grid/mesh-based models. The RPCM-based models are found to be very effective in modeling first-order reaction network problems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Anshuman, A., Eldho, T.I., Singh, L.: G: Simulation of reactive transport in porous media using radial point collocation method. Eng. Anal. Bound. Elem. 104, 8–25 (2019)
Batu, V.: Applied flow and solute transport modeling in aquifers: fundamental principles and analytical and numerical methods. CRC Press, Boca Raton (2005)
Bauer, P., Attinger, S., Kinzelbach, W.: Transport of a decay chain in homogenous porous media: analytical solutions. J. Contam. Hydrol. 49(3-4), 217–239 (2001)
Bear, J., Cheng, A.H.: Modeling groundwater flow and contaminant transport. Springer Science & Business Media, Berlin (2010)
Boddula, S., Eldho, T.I.: Groundwater management using a new coupled model of meshless local Petrov-Galerkin method and modified artificial bee colony algorithm. Comput. Geosci. 22(3), 657–675 (2018)
Chen, C.S., Ganesh, M., Golberg, M.A., Cheng, A.D.: Multilevel compact radial functions based computational schemes for some elliptic problems. Comput. Math. Appl. 43(3-5), 359–378 (2002)
Clement, T.P.: RT3D—a modular computer code for simulating reactive multi-species transport in 3-dimensional groundwater aquifers. In: Pacific Northwest National Laboratory, Richland, Washington, pp. 1–59 (1997)
Hardy, R.L.: Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res. 76(8), 1905–1915 (1971)
Kansa, E.J.: Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates. Comput. Math. Appl. 19(8-9), 127–145 (1990)
Kansa, E.J.: Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput. Math. Appl. 19(8-9), 147–161 (1990)
Kansa, E.J., Hon, Y.C.: Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comput. Math. Appl. 39(7-8), 123–138 (2000)
Liu, G.R., Gu, Y.T.: An introduction to meshfree methods and their programming. Springer Science & Business Media, Berlin (2005)
Meenal, M., Eldho, T.I.: Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method. Eng. Anal. Bound. Elem. 35(4), 700–707 (2011)
Meenal, M., Eldho, T.I.: Two-dimensional contaminant transport modeling using meshfree point collocation method (PCM). Eng. Anal. Bound. Elem. 36(4), 551–561 (2012)
Meenal, M., Eldho, T.I.: Multiobjective groundwater remediation design using a coupled MFree point collocation method and particle swarm optimization. J. Hydrol. Eng.19(6), 1259–1263 (2014)
Oliphant, T.E.: A guide to NumPy (Vol. 1, p. 85). Trelgol Publishing, USA (2006)
Perez, F., Granger, B.E., Hunter, J.D.: Python: an ecosystem for scientific computing. Comput. Sci. Eng. 13(2), 13–21 (2010)
Quezada, C.R., Clement, T.P., Lee, K.K.: Generalized solution to multidimensional multi-species transport equations coupled with a first-order reaction network involving distinct retardation factors. Adv. Water Resour. 27(5), 507–520 (2004)
Rastogi, A.K.: Numerical groundwater hydrology. Penram International Publication, India (2007)
Šarler, B., Vertnik, R.: Meshfree explicit local radial basis function collocation method for diffusion problems. Comput. Math. Appl. 51(8), 1269–1282 (2006)
Simunek, J., Van Genuchten, M.T., Sejna, M.: 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 Research Reports. 3, 1–240 (2005)
Singh, L.G., Eldho, T.I., Kumar, A.V.: 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 (2016)
Singh, L.G., Eldho, T.I., Kumar, A.V.: Identification of Groundwater Contamination Sources Using Meshfree RPCM Simulation and Particle Swarm Optimization. Water Resour. Manag. 32(4), 1517–1538 (2018)
Stevens, D., Power, H., Meng, C.Y., Howard, D., Cliffe, K.: A: An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functio22ns. J. Comput. Phys. 254, 52–75 (2013)
Suk, H.: Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction network with spatially or temporally variable transport and decay coefficients. Adv. Water Resour. 94, 412–423 (2016)
Sun, Y., Petersen, J.N., Clement, T.P.: Analytical solutions for multiple species reactive transport in multiple dimensions. J. Contam. Hydrol. 35(4), 429–440 (1999)
Therrien, R., McLaren, R.G., Sudicky, E.A., Panday, S.M.: HydroGeoSphere: a three-dimensional numerical model describing fully-integrated subsurface and surface flow and solute transport. Groundwater Simulations Group, University of Waterloo, Waterloo, ON (2010)
Thomas, A., Majumdar, P., Eldho, T.I., Rastogi, A.K.: Simulation optimization model for aquifer parameter estimation using coupled meshfree point collocation method and cat swarm optimization. Eng. Anal. Bound. Elem. 91, 60–72 (2018)
Van Genuchten, M.T.: Convective-dispersive transport of solutes involved in sequential first-order decay reactions. Comput. Geosci. 11(2), 129–1479 (1985)
Zheng, C., Wang, P.P.: MT3DMS: a modular three-dimensional multispecies transport model for simulation of advection, dispersion, and chemical reactions of contaminants in groundwater systems; documentation and user's guide. Alabama University (1999)
Acknowledgments
The work reported in this paper is supported by a project sanctioned by Board of Research in Nuclear Sciences (BRNS) titled “Modelling of reactive transport in groundwater using meshfree based numerical methods” (Project no. 16BRNS002). Authors are thankful to BRNS for their support. Authors also thank the anonymous reviewers for their constructive comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
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
Anshuman, A., Eldho, T.I. Modeling of transport of first-order reaction networks in porous media using meshfree radial point collocation method. Comput Geosci 23, 1369–1385 (2019). https://doi.org/10.1007/s10596-019-09906-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-019-09906-8