On a certified smagorinsky reduced basis turbulence model

Francesco Ballarin, Tomás Chacón Rebollo, Enrique Delgado Ávila, Macarena Gómez Marmol, Gianluigi Rozza

Risultato della ricerca: Contributo in rivistaArticolo in rivista

22 Citazioni (Scopus)


In this work we present a reduced basis Smagorinsky turbulence model for steady ows. We approximate the nonlinear eddy diffusion term using the empirical interpolation method (cf. [M. A. Grepl et al., ESAIM Math. Model. Numer. Anal., 41 (2007), pp. 575-605; Barrault et al., C. R. Acad. Sci. Paris Sffer. I Math., 339 (2004), pp. 667-672]) and the velocity-pressure unknowns by an independent reduced-basis procedure. This model is based upon an a posteriori error estimation for a Smagorinsky turbulence model. The theoretical development of the a posteriori error estimation is based on [S. Deparis, SIAM J. Sci. Comput., 46 (2008), pp. 2039-2067] and [A. Manzoni, ESAIM Math. Model. Numer. Anal., 48 (2014), pp. 1199-1226], according to the Brezzi-Rappaz-Raviart stability theory, and adapted for the nonlinear eddy diffusion term. We present some numerical tests, programmed in FreeFem++ (cf. [F. Hecht, J. Numer. Math., 20 (2012), pp. 251-265]), in which we show a speedup on the computation by factor larger than 1000 in benchmark two-dimensional ows.
Lingua originaleEnglish
pagine (da-a)3047-3067
Numero di pagine21
RivistaSIAM Journal on Numerical Analysis
Stato di pubblicazionePubblicato - 2017


  • A posteriori error estimation
  • Empirical interpolation method
  • Reduced basis method
  • Steady Smagorinsky model

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