RT Journal Article
T1 Vertically averaged and moment equations: new derivation, efficient numerical solution and comparison with other physical approximations for modeling non-hydrostatic free surface flows
A1 Escalante-Sánchez, Cipriano
A1 Morales-de-Luna, Tomás
A1 Cantero-Chinchilla, Francisco Nicolás
A1 Castro-Orgaz, Óscar
K1 Ecuaciones
K1 Mecánica de fluidos
K1 Dinámica de fluidos
AB 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.
PB Elsevier
YR 2024
FD 2024-02-27
LK https://hdl.handle.net/10630/30834
UL https://hdl.handle.net/10630/30834
LA eng
NO 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
NO Funding for open access charge: Universidad de Málaga/CBUA.This work is partially supported by projects RTI2018-096064-B-C2(1-2), PID2020-114688RB-I00, and PID2022-137637NB-C21 funded by Ministry of Science, Innovation and Universities MCIN/AEI/10.13039/501100011033 and “ERDF A way of making Europe”. F. Cantero-Chinchilla was partially supported by the grant IJC2020-042646-I, funded by CIN/AEI/10.13039/501100011033 and by the European Union “NextGenerationEU/PRTR”, through the Spanish Ministry of Science, Innovation and Universities Juan de la Cierva program 2020.”
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 26 ene 2026