Journal:
SIAM Journal on Numerical Analysis, 55(6), p. pp. 3047–3067
Date:
2017
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}, }