A new MOX report entitled “A positivity-preserving well-balanced numerical scheme for the simulation of fast landslides with efficient time stepping” by Gatti, F.; Perotto, S.; de Falco, C.; Formaggia, L. has appeared in the MOX Report Collection.
The report can be donwloaded at the following link:
https://www.mate.polimi.it/biblioteca/add/qmox/11/2023.pdf
Abstract: We consider a single phase depth–averaged model for the numerical simulation of fast–moving landslides with the goal of constructing a well-balanced positivitypreserving, 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 case, 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 combine these schemes in such a way that the corresponding absolute stability regions remain unbiased, while guaranteeing positivity-preserving and well-balancing property to the overall implementation. 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 in selecting time steps larger with respect to the ones adopted by a classical Taylor-Galerkin scheme. Finally, we provide some meaningful scaling results, both on ideal and realistic scenarios.
