A meshless solution for two dimensional density-driven groundwater flow

Density-driven groundwater flow is a complicated nonlinear problem in groundwater hydraulics. The local boundary integral method is a promising meshless scheme that is used for solving several difficult problems in different areas. This method applies the boundary integral equations to the local domain around every node. The nodes can be randomly distributed in the domain and on the global boundary. Therefore, this method is characterised as meshless. The unknown potentials and concentrations in all of the nodes are approximated by interpolation to obtain a system of linear equations. Solving this system of equations leads to the numerical solution for the main problem. In this paper, a combination of the radial basis function interpolation and the local boundary element method is used to solve groundwater flow problem combined with the transport of pollution, which also influences the density of groundwater.