Application of radial basis function collocation method in groundwater flow and solute transport problems

Abstract

Groundwater is a vital source for potable water demand, irrigation and industrial activities. For more than a century many studies in the field of hydrogeology have focused on feasible supply of groundwater. For the last five decades, the research focus has shifted to the protection and remediation of groundwater. All these research issues bring the requirement to work with mathematical models describing groundwater flow and solute transport processes. Many investigators attempted to solve the governing flow and transport equations analytically. However, the majority of the proposed analytical models are applicable for quite simplified problems and hence, do not reflect real-world conditions. The emergence of computer technology in 1960s, brought about the derivation of new numerical techniques which provide more realistic flow and transport predictions. This thesis focuses on the numerical solution of fundamental groundwater flow and solute transport equations with the use of the radial basis function collocation method (RBFCM), which is comparably a new meshless numerical technique. Through this study, groundwater flow and solute transport in saturated soil zone, vertical infiltration in vadose zone and coupled density-driven flow and solute transport processes were modeled with the use of RBFCM. Different test cases were employed with homogeneous as well as spatially varying model parameters. For the validation of the proposed RBF models, relevant analytical solutions and some leading finite difference and finite element based numerical softwares were employed. Different RBF options augmented with polynomials of different orders were tested in the developed models using regularly as well as randomly placed nodes. In the light of the existing analytical and numerical solution schemes, for both homogeneous and heterogeneous test cases, RBFCM is seen to provide accurate results irrespectve of the node selection scheme.