An exponential integrator for advection-dominated reactive transport in heterogeneous porous media

We present an exponential time integrator in conjunction with a finite volume discretisation in space for simulating transport by advection and diffusion including chemical reactions in highly heterogeneous porous media representative of geological reservoirs. These numerical integrators are based on the variation of constants solution and solving the linear system exactly. This is at the expense of computing the exponential of the stiff matrix comprising the finite volume discretisation. Using real Léja points or a Krylov subspace technique to approximate the exponential makes these methods competitive compared to standard finite difference-based time integrators. We observe for a variety of example applications that numerical solutions with exponential methods are generally more accurate and require less computational cost. They hence comprise an efficient and accurate method for simulating ∗Corresponding author Email addresses: [email protected] (A. Tambue), [email protected] (G. J. Lord), [email protected] (S. Geiger) Preprint submitted to Journal of Computational Physics January 24, 2010 non-linear advection dominated transport in geological formations.