Ballarin, FrancescoChacón Rebollo, TomásDelgado Ávila, EnriqueGómez Mármol, María MacarenaRozza, Gianluigi2023-11-032023-11-032020-02-03Ballarin, F., Chacón Rebollo, T., Delgado Ávila, E., Gómez Mármol, M.M. y Rozza, G. (2020). Certified Reduced Basis VMS-Smagorinsky model for natural convection ow in a cavity with variable height. Computers & Mathematics with Applications, 80 (5), 973-989. https://doi.org/10.1016/j.camwa.2020.05.013.1873-76680898-1221https://hdl.handle.net/11441/150073In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical parametrizations, considering the Rayleigh number as a parameter, so as the height of the cavity. We perform an Empirical Interpolation Method to approximate the sub-grid eddy viscosity term that let us obtain an a ne decomposition with respect to the parameters. We construct an a posteriori error estimator, based upon the Brezzi-Rappaz-Raviart theory, used in the greedy algorithm for the selection of the basis functions. Finally we present several numerical tests for di erent parameter con guration.application/pdf16 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Reduced basis methodEmpirical interpolation methoda pos- teriori error estimationBoussinesq equationsSmagorinsky turbulence modelinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.camwa.2020.05.013