Description of the depth-averaged two-phase flow code in hpGEM

In this note we give a description of the implementation of the discontinuous Galerkin finite element discretization of the depth-averaged two-phase flow equations as formulated in Rhebergen et al. [9]. The equations are of hyperbolic type (depending, however, on the parameters required if parameters are chosen such that the equations are not hyperbolic, this code does not work). Furthermore, the PDE’s have nonconservative products and we deal with these terms as described in [8] based on the theory of Dal Maso, LeFloch and Murat [1]. To deal with overand undershoots, a WENO slope limiter is applied [6, 9] in conjunction with a discontinuity detector [4, 9].