Parallel simulations for fast-moving landslides: Space-time mesh adaptation and sharp tracking of the wetting front

We propose a highly scalable solver for a two-dimensional depth-integrated fluid dynamic model in order to simulate flow-like landslides, such as debris or mud flows. The governing equations are discretized on quadtree meshes by means of a two-step second-order Taylor-Galerkin scheme, enriched by a suitable flux correction in order to avoid spurious oscillations, in particular near discontinuities and close to the wetting-drying interface. A mesh adaptation procedure based on a gradient-recovery a posteriori error estimator allows us to efficiently deal with a discretization of the domain customized to the phenomenon under investigation. Moreover, we resort to an adaptive scheme also in time to prevent filtering out the landslide dynamics, and to an interface tracking algorithm to avoid an excessive refinement in noninterfacial regions while preserving details along the wetting-drying front. Finally, after verifying the performance of the proposed numerical method on idealized settings, we carry out a scalability analysis of the code both on idealized and real scenarios, to check the efficiency of the overall implementation.