A second order time-splitting technique for advection-dispersion equation on unstructured grids

In this paper we present a time-splitting approach for advection-di\-sper\-sion equations. We split the dispersive and advective fluxes into two separate partial differential equations (PDEs) one containing the dispersive term and the other one the advective term, respectively. On triangular elements we combine a triangle-based high resolution Finite Volume (FV) scheme for advection with a Mixed Hybrid Finite Element (MHFE) technique to solve dispersion. In this work we consider a development of the time-splitting technique to obtain second order accuracy in space and time. This is obtained by means of the combination of the Crank-Nicolson scheme for the MHFE and the explicit midpoint rule for FV and by adding a correction term in the linear reconstruction of the FV discretization of the advective term. Numerical results are used to validate the theory presented.