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

Siddiqui, M. Salman; Fonn, Eivind; Kvamsdal, Trond; Rasheed, Adil

doi:10.3390/en12071271

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

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Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway

CSE Group, Mathematics and Cybernetics, Sintef Digital, NO-7034 Trondheim, Norway

Author to whom correspondence should be addressed.

Energies 2019, 12(7), 1271; https://doi.org/10.3390/en12071271

Received: 13 February 2019 / Revised: 19 March 2019 / Accepted: 1 April 2019 / Published: 2 April 2019

(This article belongs to the Special Issue Recent Advances in Aerodynamics of Wind Turbines)

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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. View Full-Text

Keywords: NACA64 airfoil; finite-volume method; finite-element method; proper orthogonal decomposition; reduced-order model

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Siddiqui, M.S.; Fonn, E.; Kvamsdal, T.; Rasheed, A. Finite-Volume High-Fidelity Simulation Combined with Finite-Element-Based Reduced-Order Modeling of Incompressible Flow Problems. Energies 2019, 12, 1271. https://doi.org/10.3390/en12071271

AMA Style

Siddiqui MS, Fonn E, Kvamsdal T, Rasheed A. Finite-Volume High-Fidelity Simulation Combined with Finite-Element-Based Reduced-Order Modeling of Incompressible Flow Problems. Energies. 2019; 12(7):1271. https://doi.org/10.3390/en12071271

Chicago/Turabian Style

Siddiqui, M. S., Eivind Fonn, Trond Kvamsdal, and Adil Rasheed. 2019. "Finite-Volume High-Fidelity Simulation Combined with Finite-Element-Based Reduced-Order Modeling of Incompressible Flow Problems" Energies 12, no. 7: 1271. https://doi.org/10.3390/en12071271

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

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