In 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 lets us obtain an affine 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 different parameter configuration.

%B Computers and Mathematics with Applications %V 80 %P 973-989 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085843368&doi=10.1016%2fj.camwa.2020.05.013&partnerID=40&md5=7c6596865ec89651319c7dd97159dd77 %R 10.1016/j.camwa.2020.05.013 %0 Journal Article %J SIAM Journal on Numerical Analysis %D 2017 %T On a certified smagorinsky reduced basis turbulence model %A Rebollo, T.C. %A E.D. Ávila %A Marmol, M.G. %A F. Ballarin %A Gianluigi Rozza %B SIAM Journal on Numerical Analysis %V 55 %P 3047-3067 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c %R 10.1137/17M1118233