Modeling of transport of first-order reaction networks in porous media using meshfree radial point collocation method

  • Aatish Anshuman
  • T. I. EldhoEmail author
Original Paper


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.


Point collocation method Meshfree method Decay chain transport Reversible reaction Porous media 


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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.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dept. of Civil EngineeringIndian Institute of Technology BombayMumbaiIndia
  2. 2.Dept. of Civil EngineeringIndian Institute of Technology BombayMumbaiIndia

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