TY - JOUR

T1 - Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height

AU - Ballarin, Francesco

AU - Chacón Rebollo, Tomás

AU - Delgado Ávila, Enrique

AU - Gómez Mármol, Macarena

AU - Rozza, Gianluigi

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Boussinesq equations

KW - Empirical interpolation method

KW - Reduced basis method

KW - Smagorinsky LES model

KW - a posteriori error estimation

KW - Boussinesq equations

KW - Empirical interpolation method

KW - Reduced basis method

KW - Smagorinsky LES model

KW - a posteriori error estimation

UR - http://hdl.handle.net/10807/174177

U2 - 10.1016/j.camwa.2020.05.013

DO - 10.1016/j.camwa.2020.05.013

M3 - Article

VL - 80

SP - 973

EP - 989

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

ER -