Proper Orthogonal Decomposition Applied to the Reynolds-Averaged Navier--Stokes Equations
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abstract
Despite continuous advances in computational power, the scope of high-fidelity computational fluid dynamic results remains limited for applications requiring numerous repetitions. Examples of such applications include parametric studies and design iterations. This limited scope is particularly evident in computational aeroelasticity, for which the costs associated with unsteadiness of the flow and temporal variation of the mesh for higher-fidelity fluid models can be a burden computationally. Through reduced-order modeling, the governing partial differential equations of motion are reduced to ordinary differential equations through temporal-spatial separation. Reduced-order models have become an increasingly popular method in fluid and solid mechanics. For fluid mechanics, proper orthogonal decomposition can be used to develop a reduced-order model wherein the optimal set of spatial basis functions is computed from the flow snapshots collected from a full-order model, permitting subsequent simulations to determine the time-dependent coefficients that weight the basis functions. In this paper, proper orthogonal decomposition is discussed and applied to the Reynolds-averaged Navier-Stokes equations, and results are shown for flow through a channel. The results from subsonic and transonic flow regimes are presented and the full-order model is compared with reduced-order models using basis functions generated through proper orthogonal decomposition of the full-order model and through interpolation. Copyright 2012 American Institute of Aeronautics and Astronautics, Inc.
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50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
