Three Dimensional Godunov Mixed Methods on tetrahedra for the advection-dispersion equation

Godunov Mixed Methods on triangular grids has been shown to be an effective tool for the solution of the two-dimensional advection-dispersion equation. The method is based on the discretization of the dispersive flux by means of the mixed hybrid finite element approach, while a high resolution Godunov-like finite volume scheme discretizes advection. The two techniques are combined together through a time-splitting algorithm that achieves formal second order accuracy if a corrective term is added in the finite volume stencil. In this paper we develop and study the extension of this approach to three dimensions employing tetrahedral elements and a fully 3D limiter. The numerical characteristics of the proposed method will be studied both theoretically and numerically using simple test problems.