A hybrid projection/data-driven reduced order model for the Navier-Stokes equations with nonlinear filtering stabilization

We develop a Reduced Order Model (ROM) for the Navier-Stokes equations with nonlinear filtering stabilization. Our approach, that can be interpreted as a Large Eddy Simulation model, combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computa-tionally efficient finite volume method. The main novelty of our ROM lies in the use within the EFR algorithm of a nonlinear, deconvolution-based indicator function that identifies the regions of the domain where the flow needs regularization. The ROM we propose is a hy-brid projection/data-driven strategy: a classical Proper Orthogonal Decomposition Galerkin projection approach for the reconstruction of the velocity and the pressure fields and a data-driven reduction method to approximate the indicator function used by the nonlin-ear differential filter. This data-driven technique is based on interpolation with Radial Basis Functions. We test the performance of our ROM approach on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0 < Re < 100. The accu-racy of the ROM is assessed against results obtained with the full order model for velocity, pressure, indicator function and time evolution of the aerodynamics coefficients. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

We propose a Reduced Order Model (ROM) for the Navier-Stokes equations with nonlinear filtering stabilization, which combines a three-step algorithm called Evolve-Filter-Relax (EFR) with an efficient finite volume method. The novelty lies in the use of a nonlinear indicator function within the EFR algorithm to identify regions needing regularization. The ROM combines a projection approach for velocity and pressure fields with a data-driven reduction method for the indicator function.