Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping

Abstract

In this work we present and analyze a reliable and robust approximation scheme for biochemically reacting transport in the subsurface following Monod type kinetics. Water flow is modeled by the Richards equation. The proposed scheme is based on higher order finite element methods for the spatial discretization and the two step backward differentiation formula for the temporal one. The resulting nonlinear algebraic systems of equations are solved by a damped version of Newton's method. For the linear problems of the Newton iteration Krylov space methods are used. In computational experiments conducted for realistic subsurface (groundwater) contamination scenarios we show that the higher order approximation scheme significantly reduces the amount of inherent numerical diffusion compared to lower order ones. Thereby an artificial transverse mixing of the species leading to a strong overestimation of the biodegradation process is avoided. Finally, we present a robust adaptive time stepping technique for the coupled flow and transport problem which allows efficient long-term predictions of biodegradation processes.