Meshfree models for simulation of reactive transport in groundwater systems

Groundwater is the largest source for freshwater which plays an important role in the hydrological cycle. The pollution of groundwater is on the rise due to various natural and anthropogenic sources such as landfills, agricultural lands, and underground waste storage facilities etc. These pollutants can be subjected to reactions depending on the contaminant type and the subsurface environment along with advection and dispersion processes.  As groundwater is used in various human activities such as drinking, agriculture and industrial activities, it is essential to track the contaminants in groundwater for assessing possible environmental impacts. The complex phenomena of flow and contaminant transport are represented by partial differential equations (PDEs) which are solved numerically throughout the problem domain. Although Finite Difference method (FDM) and Finite Element Method (FEM) based models are conventionally used for these simulations, these methods suffer from certain instabilities due to the presence of mesh/grid, for example, numerical dispersion and artificial oscillation for advection and reaction dominant problems. Moreover, these methods are not suitable for adaptive analysis which requires meshing and re-meshing in each simulation making the problem highly computationally expensive. Here, we present a strong form meshfree method named Radial Point Collocation Method (RPCM) for modelling flow and transport in groundwater. In contrast to mesh-based methods, the problem domain is discretised using only nodes in the proposed method. Moreover, unlike the mesh-based methods, it produces stable solutions for advection and reaction dominant problems without using special techniques such as up-winding, adaptive re-meshing or, operator splitting. The performance of the model is tested against analytical solutions, FDM and FEM based models for different reactive transport problems in groundwater involving adsorption, decay, multi-species decay network and biodegradation.