A scalable well-balanced numerical scheme for the simulation of fast landslides with efficient time stepping

We consider a single-phase depth-averaged model for the numerical simulation of fast-moving landslides with the goal of constructing a well-balanced, yet scalable and efficient, second-order time-stepping algorithm. We apply a Strang splitting approach to distinguish between parabolic and hyperbolic problems. For the parabolic contribution, we adopt a second-order Implicit- Explicit Runge-Kutta-Chebyshev scheme, while we use a two-stage Taylor discretization combined with a path-conservative strategy, to deal with the purely hyperbolic contribution. The proposed strategy allows to decouple hyperbolic from parabolic-reaction stiff contributions resulting in an overall well-balanced scheme subject just to stability restrictions of the hyperbolic term. The spatial discretization we adopt is based on a standard finite element method, associated with a hierarchically refined Cartesian grid. After providing numerical evidence of the well-balancing property, we demonstrate the capability of the proposed approach to select time steps larger than the ones adopted by a classical Taylor-Galerkin scheme. Finally, we provide some meaningful scaling results on ideal and realistic scenarios.