Finite-Volume High-Fidelity Simulation Combined with Finite-Element-Based Reduced-Order Modeling of Incompressible Flow Problems

Abstract

We present a nonintrusive approach for combining high-fidelity simulations using Finite-Volume (FV) methods with Proper Orthogonal Decomposition (POD) and Galerkin Reduced-Order Modeling (ROM) methodology. By nonintrusive we here imply an approach that does not need specific knowledge about the high-fidelity Computational Fluid Dynamics (CFD) solver other than the velocity and pressure results given on an element mesh representing the related discrete interpolation spaces. The key step in the presented approach is the projection of the FV results onto suitable finite-element (FE) spaces and then use of classical POD Galerkin ROM framework. We do a numerical investigation of aerodynamic flow around an airfoil cross-section (NACA64) at low Reynolds number and compare the ROM results obtained with high-fidelity FV-generated snapshots against similar high-fidelity results obtained with FE using Taylor–Hood velocity and pressure spaces. Our results show that we achieve relative errors in the range of 1–10% in both H 1 -seminorm of the computed velocities and in the L 2 -norm of the computed pressure with reasonably few ROM modes. Similar accuracy was obtained for lift and drag.

Keywords

• NACA64 airfoil
• finite-volume method
• finite-element method
• proper orthogonal decomposition
• reduced-order model