An efficient parallel depth-integrated adaptive numerical framework with application to flow-type landslides

Hydrogeological instability is among the effects of climate change with major impact on people and built environments security. Among instabilities, landslides are responsible for significant human and economic losses worldwide.

Landslide dynamic is characterized by a broad range of velocity-scales, from the steady creeping slip to a catastrophic avalanche passing through the intermittent rapid slip. During these phases, the landslide undergoes different mechanical behaviours. In particular, during the triggering phase, the landslide behaves roughly like a rigid body and the driving process is the pore-pressure diffusion that causes the intermittent slipping of the involved material. Once the landslide is initiated, it follows various behaviours, e.g. we may have a flow-like motion typical of debris and mud flows, where the landslide follows a visco-plastic behaviour and the overall process becomes advection dominated.

We propose an efficient multi-core numerical framework solving a two-dimensional depth-integrated fluid dynamic model for the simulation of flow-type landslides such as debris and mud flows. The governing equations are solved on adaptive quadtree meshes via the classical two-step second order Taylor-Galerkin scheme with a classical flux correction finite element strategy to avoid spurious oscillations near discontinuities and wetting-drying interface. Possible extensions considered by the author, such as an implicit-explicit operator splitting strategy, to deal with stiff diffusion and source terms will be discussed. Extensions that however do not affect the data locality of the scheme so do not affect the efficiency of the parallel implementation. To avoid excessive refinement in non-interfacial regions, we implement an interface tracking strategy that ensures detail preservation at the wetting-drying interface. We test the numerical framework on a real case study located in the Northern Italy to show its ability to deal with real problems.