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

Federico Gatti, Carlo de Falco, Simona Perotto and Luca Formaggia

Applied Mathematics and Computation, 2024, vol. 468, issue C

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, 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.

Keywords: Taylor-Galerkin scheme; Depth-integrated models; Implicit-explicit Runge-Kutta-Chebyshev scheme; C-property; Path-conservative methods; Parallel simulations (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:468:y:2024:i:c:s009630032300694x

DOI: 10.1016/j.amc.2023.128525

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