Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height
Abstract
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 let us obtain an affine decomposition with respect to the parameters. We construct an a posterior 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.
Keywords
Cite
@article{arxiv.1902.05729,
title = {Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height},
author = {Francesco Ballarin and Tomás Chacón Rebollo and Enrique Delgado Ávila and Macarena Gómez Mármol and Gianluigi Rozza},
journal= {arXiv preprint arXiv:1902.05729},
year = {2023}
}