Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height


Computers and Mathematics with Applications




Ballarin, F. and Chacón Rebollo, T. and Delgado Ávila, E. and Gómez Mármol, M. and Rozza, G.

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.