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.

On a Certified Smagorinsky Reduced Basis Turbulence Model / Rebollo, Tomás Chacón; Ávila, Enrique Delgado; Mármol, Macarena Gómez; Ballarin, Francesco; Rozza, Gianluigi. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 55:6(2017), pp. 3047-3067. [10.1137/17M1118233]

On a Certified Smagorinsky Reduced Basis Turbulence Model

Ballarin, Francesco;Rozza, Gianluigi
2017-01-01

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.
2017
55
6
3047
3067
https://doi.org/10.1137/17M1118233
https://arxiv.org/abs/1709.00243
Rebollo, Tomás Chacón; Ávila, Enrique Delgado; Mármol, Macarena Gómez; Ballarin, Francesco; Rozza, Gianluigi
File in questo prodotto:
File Dimensione Formato  
17m1118233.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 649.86 kB
Formato Adobe PDF
649.86 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/63605
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 36
  • ???jsp.display-item.citation.isi??? 32
social impact