2D Burgers equation with large Reynolds number using POD/DEIM and calibration. (1st June 2016)

• Record Type: Journal Article
• Authors: Wang, Yuepeng; Navon, Ionel M.; Wang, Xinyue; Cheng, Yue
• Is Part Of: International journal for numerical methods in fluids. Volume 82:Number 12(2016)
• Page Start: 909
• Page End: 931
• Publication Date: 2016-06-01
• Subjects: Burgers equation -- POD/DEIM‐reduced order model -- Tikhonov regularization -- calibration; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4249
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: Model order reduction of the two‐dimensional Burgers equation is investigated. The mathematical formulation of POD/discrete empirical interpolation method (DEIM)‐reduced order model (ROM) is derived based on the Galerkin projection and DEIM from the existing high fidelity‐implicit finite‐difference full model. For validation, we numerically compared the POD ROM, POD/DEIM, and the full model in two cases of R e = 100 and R e = 1000, respectively. We found that the POD/DEIM ROM leads to a speed‐up of CPU time by a factor of O (10). The computational stability of POD/DEIM ROM is maintained by means of a careful selection of POD modes and the DEIM interpolation points. The solution of POD/DEIM in the case of R e = 1000 has an accuracy with error O (10 −3 ) versus O (10 −4 ) in the case of R e = 100 when compared with the high fidelity model. For this turbulent flow, a closure model consisting of a Tikhonov regularization is carried out in order to recover the missing information and is developed to account for the small‐scale dissipation effect of the truncated POD modes. It is shown that the computational results of this calibrated ROM exhibit considerable agreement with the high fidelity model, which implies the efficiency of the closure model used. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : For the 2D Burgers equation with large Reynolds number (turbulent flow case), we have developed the proper orthogonal decomposition/discrete empirical interpolation method‐reduced order model and provided detailed solution. A flow calibration with Tikhonov regularization serving as closure model is also carried out in order to recover the turbulent closure. The computational results exhibit considerable agreement with the real high‐fidelity model.