Surrogate-based Analysis and Optimization

A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities

This paper addresses the solution of bound-constrained optimization problems using algorithms that require only the availability of objective function values but no derivative information. We refer to these algorithms as derivative-free algorithms. Fueled by a growing number of applications in science and engineering, the development of derivative-free optimization algorithms has long been studied, and it has found renewed interest in recent time. Along with many derivative-free algorithms, many software implementations have also appeared. The paper presents a review of derivative-free algorithms, followed by a systematic comparison of 22 related implementations using a test set of 502 problems. The test bed includes convex and nonconvex problems, smooth as well as nonsmooth problems. The algorithms were tested under the same conditions and ranked under several criteria, including their ability to find near-global solutions for nonconvex problems, improve a given starting point, and refine a near-optimal solution. A total of 112,448 problem instances were solved. We find that the ability of all these solvers to obtain good solutions diminishes with increasing problem size. For the problems used in this study, TOMLAB/MULTIMIN, TOMLAB/GLCCLUSTER, MCS and TOMLAB/LGO are better, on average, than other derivative-free solvers in terms of solution quality within 2,500 function evaluations. These global solvers outperform local solvers even for convex problems. Finally, TOMLAB/OQNLP, NEWUOA, and TOMLAB/MULTIMIN show superior performance in terms of refining a near-optimal solution.

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Derivative-free optimization: a review of algorithms and comparison of software implementations

The numerical simulation of high Reynolds number flows is hampered by model accuracy if the Reynolds-averaged Navier–Stokes (RANS) equations are used, and by computational cost if direct or large-eddy simulations (LES) that resolve the near-wall layer are employed. The cost of a calculation scales like the Reynolds number to the power 3 for direct numerical simulations, or 2.4 for LES, making the resolution of the wall layer at high Reynolds number infeasible even with the most advanced computers. In LES, an attractive alternative to compute high-Re flows is the use of wall-layer models, in which only the outer layer is resolved, while the near-wall region is modeled. Three broad classes of approaches are presently used: bypassing this region altogether using wall functions, solving a separate set of equations in the near-wall region, weakly coupled to the outer flow, or simulating the near-wall region in a global, Reynolds-averaged, sense. These approaches are discussed and their ranges of applicability are highlighted. Various unresolved issues in wall-layer modeling are presented.

Wall-layer models for large-eddy simulations

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

This article provides a critical review of computational techniques for flow-noise prediction and the underlying theories. Hybrid approaches, in which the turbulent noise source field is computed and/or modeled separately from the far-field calculation, are afforded particular attention. Numerical methods and modern flow simulation techniques are discussed in terms of their suitability and accuracy for flow-noise calculations. Other topics highlighted include some important formulation and computational issues in the application of aeroacoustic theories, generalized acoustic analogies with better accounts of flow-sound interaction, and recent computational investigations of noise-control strategies. The review ends with an analysis of major challenges and key areas for improvement in order to advance the state of the art of computational aeroacoustics.

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Computational prediction of flow-generated sound

The efficacy of large-eddy simulation (LES) with wall modeling for complex turbulent flows is assessed by considering turbulent boundary-layer flows past an asymmetric trailing-edge. Wall models based on turbulent boundary-layer equations and their simpler variants are employed to compute the instantaneous wall shear stress, which is used as approximate boundary conditions for the LES. It is demonstrated that, as first noted by Cabot and Moin [Flow Turb. Combust. 63, 269 (2000)], when a Reynolds-averaged Navier–Stokes type eddy viscosity is used in the wall-layer equations with nonlinear convective terms, its value must be reduced to account for only the unresolved part of the Reynolds stress. A dynamically adjusted mixing-length eddy viscosity is used in the turbulent boundary-layer equation model, which is shown to be considerably more accurate than the simpler wall models based on the instantaneous log law. This method predicts low-order velocity statistics in good agreement with those from the full LES with resolved wall-layers, at a small fraction of the original computational cost. In particular, the unsteady separation near the trailing-edge is captured correctly, and the prediction of surface pressure fluctuations also shows promise.

Dynamic wall modeling for large-eddy simulation of complex turbulent flows

Turbulent boundary layers near the trailing edge of a lifting surface are known to generate intense, broadband scattering noise as well as surface pressure e uctuations. Numerically predicting the trailing-edge noise requires that the noise-generating eddies over a wide range of length scales be adequately represented. The large-eddy simulation (LES) technique provides a promising tool for obtaining the unsteady wall-pressure e elds and the acousticsourcefunctions. An LES iscarried out forturbulent boundary-layere ow pastan asymmetrically beveled trailing edge ofa e at strut at a chord Reynolds number of 2 :15 £ 10 6 . The computed velocity and surface pressure statistics compare reasonably well with previous experimental measurements. The far-e eld acoustic calculation is facilitated by the integral solution to the Lighthill equation derived by Ffowcs-Williams and Hall. Computations havebeen carried outto determine thefar-e eld noisespectra,thesource-term characteristics, and therequirement for the integration domain size. It is found that the present LES domain is adequate for predicting noise radiation over a range of frequencies. At the low-frequency end, however, the spanwise source coherenceestimated based on surface pressure e uctuations does not decay sufe ciently, suggesting the need for a wider computational domain.

Computation of Trailing-Edge Flow and Noise Using Large-Eddy Simulation

Numerical simulation of the flow around a circular cylinder at high Reynolds numbers

This article provides a critical review of aero-optics with an emphasis on recent developments in computational predictions and the physical mechanisms of flow-induced optical distortions. Following a brief introduction of the fundamental theory and key concepts, computational techniques for aberrating flow fields and optical propagation are discussed along with a brief survey of wave-front sensors used in experimental measurements. New physical understanding generated through numerical and experimental investigations is highlighted for a number of important aero-optical flows, including turbulent boundary layers, separated shear layers, and flow over optical turrets. Approaches for mitigating aero-optical effects are briefly discussed.

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Meng Wang

Papers

Computational prediction of flow-generated sound

Dynamic wall modeling for large-eddy simulation of complex turbulent flows

Computation of Trailing-Edge Flow and Noise Using Large-Eddy Simulation

Numerical simulation of the flow around a circular cylinder at high Reynolds numbers

Physics and Computation of Aero-Optics