On a certified Smagorinsky reduced basis turbulence model

In this work we present a reduced basis Smagorinsky turbulence model for steady flows. 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...

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Detalles Bibliográficos
Autores: Chacón Rebollo, Tomás, Delgado Ávila, Enrique, Gómez Mármol, María Macarena, Ballarin, Francesco, Rozza, Gianluigi
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/69698
Acceso en línea:https://hdl.handle.net/11441/69698
https://doi.org/10.1137/17M1118233
Access Level:acceso abierto
Palabra clave:Reduced basis method
Empirical interpolation method
A posteriori error estimation
Steady Smagorinsky model
Descripción
Sumario:In this work we present a reduced basis Smagorinsky turbulence model for steady flows. 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 Sér. 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 flows.