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00925njm 22002777a 4500 dc Garres-Díaz, José author Escamilla-Sánchez, Alejandro author Morales-de-Luna, Tomás author Castro-Díaz, Manuel Jesús author 2022-09-13 In this work, we present a general framework for vertical discretizations of Euler equations. It generalizes the usual moment and multilayer models and allows to obtain a family of multilayer-moment models. It considers a multilayer-type discretization where the layerwise velocity is a polynomial of arbitrary degree N on the vertical variable. The contribution of this work is twofold. First, we compare the multilayer and moment models in their usual formulation, pointing out some advantages/disadvantages of each approach. Second, a family of multilayer-moment models is proposed. As particular interesting case we shall consider a multilayer-moment model with layerwise linear horizontal velocity. Several numerical tests are presented, devoted to the comparison of multilayer and moment methods, and also showing that the proposed method with layerwise linear velocity allows us to obtain second order accuracy in the vertical direction. We show as well that the proposed approach allows to correctly represent the vertical structure of the solutions of the hydrostatic Euler equations. Moreover, the measured efficiency shows that in many situations, the proposed multilayer-moment model needs just a few layers to improve the results of the usual multilayer model with a high number of vertical layers. J. Garres-Díaz, C. Escalante, T. Morales de Luna, M.J. Castro Díaz, A general vertical decomposition of Euler equations: Multilayer-moment models, Applied Numerical Mathematics, Volume 183, 2023, Pages 236-262, ISSN 0168-9274, https://doi.org/10.1016/j.apnum.2022.09.004 https://hdl.handle.net/10630/25779 10.1016/j.apnum.2022.09.004 Multilayer-moment models Vertical discretizations Shallow water flows Free surface Euler equations A general vertical decomposition of Euler equations: Multilayer-moment models