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oai:riuma.uma.es:10630/385362026-02-03T10:56:45Zcom_10630_2254col_10630_37953
RIUMA. Repositorio Institucional de la Universidad de Málaga author Caballero Cárdenas, Celia author Gómez Bueno, Irene author Del Grosso, A. author Koellermeier, J. author Morales-de-Luna, Tomás 2025-05-08T11:12:05Z 2025-05-08T11:12:05Z 2025-01-30 Caballero-Cárdenas, C., Gómez-Bueno, I., del Grosso, A., Koellermeier, J., & Morales de Luna, T. (2025). A semi-implicit exactly fully well-balanced relaxation scheme for the Shallow Water Linearized Moment Equations. Computer Methods in Applied Mechanics and Engineering, 437, 117788. 0045-7825 https://hdl.handle.net/10630/38536 10.1016/j.cma.2025.117788 When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we deal with the Shallow Water Linearized Moment Equations (SWLME), in which the velocity is no longer constant in the vertical direction, where a polynomial expansion around the mean value is considered. The linearized version implies neglecting the non-linear terms of the basis coefficients in the higher order equations. As a result, the model is always hyperbolic and the stationary solutions can be more easily computed. Then, our objective is to propose an efficient, accurate and robust numerical scheme for the SWLME model, specially adapted for low Froude number situations. Hence, we describe a semi-implicit second order exactly fully well-balanced method. More specifically, a splitting is performed to separate acoustic and material phenomena. The acoustic waves are treated in an implicit manner to gain in efficiency when dealing with subsonic flow regimes, whereas the second order of accuracy is achieved thanks to a polynomial reconstruction and Strang-splitting method. We also exploit a reconstruction operator to achieve the fully well-balanced character of the method. Extensive numerical tests demonstrate the well-balanced properties and large speed-up compared to traditional methods. eng Atribución-NoComercial 4.0 Internacional Análisis numérico Magnetohidrodinámica A semi-implicit exactly fully well-balanced relaxation scheme for the Shallow Water Linearized Moment Equations journal article 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 URL https://riuma.uma.es/bitstreams/b1ade52b-a33d-490b-922e-5da1fbe976ce/download File MD5 b217ebdf87e18f1d2f305dc601f23322 1466191 application/pdf 1-s2.0-S004578252500060X-main.pdf