A scalable well-balanced numerical scheme for the modeling of two-phase shallow granular landslide consolidation

We introduce a new method to efficiently solve a variant of the Pitman-Le two-phase depth-integrated system of equations, for the simulation of a fast landslide consolidation process. In particular, in order to cope with the loss of hyperbolicity typical of this system, we generalize Pelanti's proposition for the Pitman-Le model to the case of a non-null excess pore water pressure configuration. The variant of the Pitman-Le model is numerically solved by relying on the approach the authors set to discretize the corresponding single-phase model, jointly with a fictitious inter-phase drag force which avoids arising the spurious numerical oscillations induced by the loss of hyperbolicity. To verify the reliability of the proposed simulation tool, we first assess the accuracy and efficiency of the new method in ideal scenarios. In particular, we investigate the well-balancing property and provide some relevant scaling results for the parallel implementation of the method. Successively, we challenge the procedure on real configurations from the available literature.