On a certified Smagorinsky reduced basis turbulence model
Numerical Analysis
2023-08-08 v1
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.
Cite
@article{arxiv.1709.00243,
title = {On a certified Smagorinsky reduced basis turbulence model},
author = {Tomás Chacón Rebollo and Enrique Delgado Ávila and Macarena Gómez Mármol and Francesco Ballarin and Gianluigi Rozza},
journal= {arXiv preprint arXiv:1709.00243},
year = {2023}
}