Discontinuous Galerkin finite element method for shallow two-phase flows

We present a discontinuous Galerkin finite element method for a depth-averaged two-phase flow model. This model contains nonconservative products for which we developed a discontinuous Galerkin finite element formulation in Rhebergen et al. [S. Rhebergen, O. Bokhove, J.J.W. van der Vegt, Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations, J. Comput. Phys. 227 (2008) 1887]. The goal is to qualitatively validate the model against a laboratory experiment and to show the abilities of the model to capture physical phenomena. To be able to perform these test cases, a WENO slope limiter is investigated in conjunction with a discontinuity detector to detect regions where spurious oscillations appear.