On a certified Smagorinsky reduced basis turbulence model


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




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.

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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