Spatial Filtering for Reduced Order Modeling

Abstract

Spatial filtering has been central in the development of large eddy simulation reduced order models (LES-ROMs) (Wang et al. in Comput. Meth. Appl. Mech. Eng. 237–240:10–26, 2012, [9], Xie et al. in Data-driven filtered reduced order modeling of fluid flows, 2018, [11], Xie et al. in Comput. Methods Appl. Mech. Eng. 313:512–534, 2017, [12]) and regularized reduced order models (Reg-ROMs) (Iliescu et al. in Int. J. Numer. Anal. Mod. 2017, [4], Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]) for efficient and relatively accurate numerical simulation of convection-dominated fluid flows. In this paper, we perform a numerical investigation of spatial filtering. To this end, we consider one of the simplest Reg-ROMs, the Leray ROM (L-ROM) (Iliescu et al. in Int. J. Numer. Anal. Mod. 2017, [4], Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]), which uses ROM spatial filtering to smooth the flow variables and decrease the amount of energy aliased to the lower index ROM basis functions. We also propose a new form of ROM differential filter (Sabetghadam and Jafarpour in Appl. Math. Comput. 218:6012–6026, 2012, [7], Wells et al. in Int. J. Numer. Meth. Fluids 84:598–615, 2017, [10]) and use it as a spatial filter for the L-ROM. We investigate the performance of this new form of ROM differential filter in the numerical simulation of a flow past a circular cylinder at a Reynolds number $Re=760$.