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arXiv · 1709.00243

On a certified Smagorinsky reduced basis turbulence model

Tomás Chacón Rebollo·Enrique Delgado Ávila·Macarena Gómez Mármol·Francesco Ballarin·Gianluigi Rozza
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Abstract

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.

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Tomás Chacón Rebollo, Enrique Delgado Ávila, Macarena Gómez Mármol, Francesco Ballarin, Gianluigi Rozza. 2017-09-01. On a certified Smagorinsky reduced basis turbulence model. https://doi.org/10.1137/17m1118233

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