A stabilized POD model for turbulent flows over a range of Reynolds numbers: Optimal parameter sampling and constrained projection

JOURNAL OF COMPUTATIONAL PHYSICS

卷:371

Article

Fick, Lambert¹  Maday, Yvon^2,3  Patera, Anthony T.⁴  Taddei, Tommaso² 

[1] Texas A&M Univ, Dept Nucl Engn, College Stn, TX 77843 USA

[2] UPMC Univ Paris 06, Sorbonne Univ, Lab Jacques Louis Lions, F-75005 Paris, France

[3] Brown Univ, Div Appl Math, Providence, RI 02906 USA

[4] MIT, Dept Mech Engn, Cambridge, MA 02139 USA

关键词: Model order reduction;    Reduced basis method;    CFD;    Proper orthogonal decomposition;    A posteriori error estimation;   

DOI  :  10.1016/j.jcp.2018.05.027

来源: Elsevier

【 摘 要 】

We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained Galerkin formulation that corrects the standard Galerkin statement by incorporating prior information about the long-time attractor. For explicit and semi-implicit time discretizations, our statement reads as a constrained quadratic programming problem where the objective function is the Euclidean norm of the error in the reduced Galerkin (algebraic) formulation, while the constraints correspond to bounds for the maximum and minimum value of the coefficients of the N-term expansion. Second, we propose an a posteriori error indicator, which corresponds to the dual norm of the residual associated with the time-averaged momentum equation. We demonstrate that the error indicator is highly-correlated with the error in mean flow prediction, and can be efficiently computed through an offline/online strategy. Third, we propose a Greedy algorithm for the construction of an approximation space/procedure valid over a range of parameters; the Greedy is informed by the a posteriori error indicator developed in this paper. We illustrate our approach and we demonstrate its effectiveness by studying the dependence of a two-dimensional turbulent lid-driven cavity flow on the Reynolds number. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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