A hybrid projection/data-driven reduced order model for the Navier-Stokes equations with nonlinear filtering stabilization. (English) Zbl 07788132
Summary: 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 computationally 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 hybrid 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 nonlinear 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 \(0 \leq Re \leq 100\). The accuracy 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.
MSC:
| 76Mxx | Basic methods in fluid mechanics |
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 76Dxx | Incompressible viscous fluids |
Keywords:
proper orthogonal decomposition; reduced order model; large eddy simulation; nonlinear filtering stabilization; projection-based methods; data-driven strategiesReferences:
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