2D Burgers Equations with Large Reynolds Number Using POD/DEIM and Calibration Yuepeng Wanga), I.Michael Navonb)

Abstract: Model order reduction (MOR) of the 2D Burgers equation is investigated. The mathematical formulation of POD/DEIM reduced order model (ROM) is derived based on the Galerkin projection and discrete empirical interpolation method (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 Re = 100 and Re = 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 Re = 1000 has an accuracy with error O(103) versus O(10 4) in the case of Re = 100 when compared to 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 discarded POD modes. It is shown that the computational results of this calibrated low-order model (LOM) exhibit considerable agreement with the real high-fidelity model, which implies the efficiency of the closure model used