A. LaBryer

A framework for large eddy simulation of Burgers turbulence based upon spatial and temporal statistical information

We present a novel theoretical framework that has the potential not only to improve the reliability and computational efficiency of large-eddy simulation (LES) predictions for turbulent flows but also promises to address a major drawback of many existing constructs of LES, namely, inaccurate predictions for the underlying spatiotemporal structure. In our proposed framework, subgrid models are constructed based upon information that is consistent with the underlying spatiotemporal statistics of the flow. Unlike many pre-existing LES approaches, the proposed subgrid models include non-Markovian memory terms whose origins can be related to the optimal prediction formalism. These optimal subgrid models are studied within the context of the forced Burgers equation. Results indicate that the proposed models perform better than standard LES models by virtue of their ability to better preserve the underlying spatiotemporal statistical structure of the flow. Furthermore, the presence of coarse-grained temporal information in our subgrid models allows for faster simulations (resulting in about an order of magnitude reduction in computational time, in comparison to conventional LES) through the use of larger time steps.

Modeling the Nonlinear Structural Dynamics of a Plunging Membrane Airfoil using a High Dimensional Harmonic Balance Approach

High fidelity computational models are developed to study the nonlinear structural dynamics of a plunging membrane airfoil, which is based upon previous experimental work. Two airfoil structures are investigated: a one-dimensional string and a three-dimensional Feeler gauge. Time-periodic flapping is assumed for both cases. The nonlinear equations of motion are semi-discretized in space using the finite element method, and then discretized in time using both a high dimensional harmonic balance approach and a standard finite differencing scheme. Solutions for both time-discretization methods are compared. For weak to moderately nonlinear string problems, the harmonic balance solution compares favorably with the finite difference solution, and is two to three orders of magnitude faster to compute. When the string exhibits stronger nonlinear behavior, the harmonic balance method yields results that diverge from the true solution when multiple harmonics are used. This is likely due to the presence of multiple subharmonics in the frequency response curve. The Feeler gauge problem is investigated to explore the possibility of unstable planar motion and chaotic vibrations during plunging. While the spectral contents of the response contain multiple frequencies, neither unstable planar dynamics nor chaotic vibrations were encountered within the range of parameters tested. Further investigation is needed to determine whether such a response is possible for the current model.

Optimal Temporal Reduced Order Modeling for Nonlinear Dynamical Systems

Many physical phenomena governed by nonlinear dynamics possess motions that occur on a wide range of timescales. Numerical solutions for such problems often require a large number of variables to achieve acceptable accuracy. When an insucient resolution is used to evolve a solution, an irreversible loss of information occurs, which can lead to substantial errors. Presented here is a novel method for optimal temporal reduced order modeling (OPTROM), which can be used to enhance the fidelity of any time domain solution technique. Statistical information about the unresolved variables, in the form of conditional expectations, is used to more accurately predict the evolution of the resolved variables. To demonstrate the OPTROM technique, harmonic balance solutions for a Dung oscillator are investigated. The need for, and ecacy of, the technique is greatest when solutions are obtained with a low resolution.