Two-dimensional meshfree modelling of contaminant transport through saturated porous media using RPIM

• Published in: Environmental earth sciences Vol. 61; no. 2; pp. 341 - 353
• Main Authors: Praveen Kumar, R., Dodagoudar, G. R.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.07.2010; Springer; Springer Nature B.V
• Subjects: Anisotropy; Biogeosciences; Bioremediation; Contaminants; Contaminated sediments; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Environmental Science and Engineering; Exact sciences and technology; Geochemistry; Geology; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Landfills; Mathematical models; Original Article; Pollution, environment geology; Porosity; Porous media; Terrestrial Pollution; Waste disposal sites; Canada; Ontario; Eastern Canada; Contaminant transport; Radial point interpolation method; Meshfree method; Thin plate spline radial basis functions; Landfill liners; advection; diffusion; ground water; pore fluid; case studies; transport; finite element analysis; pollution; North America; sorption; interpolation; landfills; solution; human waste; solid waste; two-dimensional models; saturated zone; dispersion; porous media
• ISSN: 1866-6280; 1866-6299
• DOI: 10.1007/s12665-009-0346-4

This paper presents a new numerical tool to model the two-dimensional contaminant transport through saturated porous media using a meshfree method, called radial point interpolation method (RPIM) with polynomial reproduction. In RPIM, an approximate solution is constructed entirely in terms of a set of nodes and no characterisation of the interrelationship of the nodes is needed. The advection–dispersion equation with sorption is considered to illustrate the applicability of the RPIM. The Galerkin weak form of the governing equation is formulated using 2D meshfree shape functions constructed using thin plate spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Three numerical examples are presented and the results are compared with those obtained from the finite element method and analytical solutions. In order to test the practical applicability and performance of the RPIM, two case studies of contaminant transport through landfill liners are presented. A good agreement is obtained between the results of the RPIM and the field investigation data.