On a certified Smagorinsky reduced basis turbulence model

Journal: 

SIAM Journal on Numerical Analysis, 55(6), p. pp. 3047–3067

Date: 

2017

Authors: 

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

In this work we present a reduced basis Smagorinsky turbulence model for steady flows. We approximate the non-linear eddy diffusion term using the Empirical Interpolation Method, and the velocity-pressure unknowns by an independent reduced-basis procedure. This model is based upon an a posteriori error estimation for Smagorinsky turbulence model. The theoretical development of the a posteriori error estimation is based on previous works, according to the Brezzi-Rappaz-Raviart stability theory, and adapted for the non-linear eddy diffusion term. We present some numerical tests, programmed in FreeFem++, in which we show an speedup on the computation by factor larger than 1000 in benchmark 2D flows.

@article{ChaconDelgadoGomezBallarinRozza2017,
author = {Chacón Rebollo, Tomás and Delgado Ávila, Enrique and Gómez Mármol, Macarena and Ballarin, Francesco
and Rozza, Gianluigi},
title = {On a certified Smagorinsky reduced basis turbulence model},
year = {2017},
journal = {SIAM Journal on Numerical Analysis},
doi = {10.1137/17M1118233},
year = {2017},
volume = {55},
number = {6},
pages = {3047--3067},
}

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