ON A CERTIFIED SMAGORINSKY REDUCED BASIS TURBULENCE MODEL
ON A CERTIFIED SMAGORINSKY REDUCED BASIS TURBULENCE MODEL
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DOI：
10.1137/17m1118233
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发表时间：
2017-01-01
影响因子：
2.9
通讯作者：
Rozza, Gianluigi
中科院分区：
文献类型：
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作者：
Chacon Rebollo, Tomas;Delgado Avila, Enrique;Rozza, Gianluigi
在这项工作中，我们提出了一个定常流动的减基Smagorinsky湍流模型。我们使用经验插值法来逼近非线性涡旋扩散项(参见。作者声明：[M.A.Grepl等，ESAIM Math.模特。诺默。Anan.，41(2007)，pp.575-605；Barrault等人，C.R.Acad。SCI。巴黎爵士。I Math，339(2004)，pp.667-672])和速度-压力未知数。该模型基于对Smagorinsky湍流模型的后验误差估计。后验误差估计的理论发展是基于[S.Deparis，SIAM J.Sci.计算机，46(2008)，2039-2067页]和[A.Manzoni，ESAIM Math.模特。诺默。Anan.，48(2014)，pp.1199-1226]，根据Brezzi-Rappaz-Raviart稳定性理论，并适用于非线性涡旋扩散项。我们给出了一些数值测试，用的是FreeFem++(参见访问数/每百万人：Reach for[F.数学，20(2012)，pp.251-265])，其中我们展示了在基准二维流动中计算的加速比大于1000的因子。
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 Ser. 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.