Least square-based finite volumes for solving the advection–diffusion of contaminants in porous media

Abstract

A second-order cell-centered finite-volume method is proposed to solve the steady advection–diffusion equation for contaminant transport in porous media. This method is based on a linear least square reconstruction that maintains the approximate cell-average values. The reconstruction is combined with an appropriate slope limiter to prevent the formation of spurious oscillations in the convection-dominated case. The theoretical convergence rate is investigated on a boundary layer problem, and the preliminar results show that the method is promising in the numerical simulation of more complex groundwater flow problems.