2026-05-30T07:07:46Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/308342026-02-03T11:07:12Zcom_10630_2254col_10630_37953

Vertically averaged and moment equations: new derivation, efficient numerical solution and comparison with other physical approximations for modeling non-hydrostatic free surface flows Escalante-Sánchez, Cipriano Morales-de-Luna, Tomás Cantero-Chinchilla, Francisco Nicolás Castro-Orgaz, Óscar Ecuaciones Mecánica de fluidos Dinámica de fluidos Efficient modeling of flow physics is a prerequisite for a reliable computation of free-surface environmental flows. Non-hydrostatic flows are often present in shallow water environments, making the task challenging. In this work, we use the method of weighted residuals for modeling non-hydrostatic free surface flows in a depth-averaged framework. In particular, we focus on the Vertically Averaged and Moment (VAM) equations model. First, a new derivation of the model is presented using expansions of the field variables in sigma-coordinates with Legendre polynomials basis. Second, an efficient two-step numerical scheme is proposed: the first step corresponds to solving the hyperbolic part with a second-order path-conservative PVM scheme. Then, in a second step, non-hydrostatic terms are corrected by solving a linear Poisson-like system using an iterative method, thereby resulting in an accurate and efficient algorithm. The computational effort is similar to the one required for the well-known Serre-Green-Naghdi (SGN) system, while the results are largely improved. Finally, the physical aspects of the model are compared to the SGN system and a multilayer model, demonstrating that VAM is comparable in physical accuracy to a two-layer model. 2024-03-14T13:27:13Z 2024-03-14T13:27:13Z 2024-03-14T13:27:13Z 2024-02-27 journal article C. Escalante, T. Morales de Luna, F. Cantero-Chinchilla, O. Castro-Orgaz, Vertically averaged and moment equations: New derivation, efficient numerical solution and comparison with other physical approximations for modeling non-hydrostatic free surface flows, Journal of Computational Physics, Volume 504, 2024, 112882, ISSN 0021-9991, https://doi.org/10.1016/j.jcp.2024.112882 https://hdl.handle.net/10630/30834 10.1016/j.jcp.2024.112882 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier