Castro Díaz, M. J.Escalante, C.Garres-Díaz, JoséMorales de Luna, T.2025-04-242025-04-242025Castro Díaz, M.J., Escalante, C., Garres-Díaz, José y Morales de Luna, T. (2025). High-order well-balanced schemes for shallow models for dry avalanches. Applied Numerical Mathematics, 215, 138-145. https://doi.org/10.1016/j.apnum.2025.04.008.0168-92741873-5460https://hdl.handle.net/11441/172048© 2025 The Author(s). Published by Elsevier B.V. on behalf of IMACS. This is an open access article under the CC BY-NC-ND licenseIn this work we consider a depth-averaged model for granular flows with a Coulomb-type friction force described by the rheology. In this model, the so-called lake-at-rest steady states are of special interest, where velocity is zero and the slope is under a critical threshold defined by the angle of repose of the granular material. It leads to a family with an infinite number of lake-at-rest steady states. We describe a well-balanced reconstruction procedure that allows to define well-balanced finite volume methods for such problem. The technique is generalized to high-order space/time schemes. In particular, the second and third-order schemes are considered in the numerical tests section. An accuracy test is included showing that second and third-order are achieved. A well-balanced test is also considered. The proposed scheme is well-balanced for steady states with non-constant free surface, and it is exactly well-balanced for those steady states given by a simple characterization.application/pdf8 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Finite volume methodWell-balanced schemesHigh-order schemeSavage-Hutter modelGranular flowsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.apnum.2025.04.008