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.

VL - 80 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85085843368&doi=10.1016%2fj.camwa.2020.05.013&partnerID=40&md5=7c6596865ec89651319c7dd97159dd77 ER - TY - JOUR T1 - On a certified smagorinsky reduced basis turbulence model JF - SIAM Journal on Numerical Analysis Y1 - 2017 A1 - Rebollo, T.C. A1 - E.D. Ávila A1 - Marmol, M.G. A1 - F. Ballarin A1 - Gianluigi Rozza VL - 55 UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c ER -