Abstract
This article reviews state-of-the-art adaptive, multiresolution wavelet methodologies for modeling and simulation of turbulent flows with various examples. Different numerical methods for solving the Navier-Stokes equations in adaptive wavelet bases are described. We summarize coherent vortex extraction methodologies, which utilize the efficient wavelet decomposition of turbulent flows into space-scale contributions, and present a hierarchy of wavelet-based turbulence models. Perspectives for modeling and computing industrially relevant flows are also given.
Highlights
Wavelets, introduced by Grossmann & Morlet (1984), have significantly impacted many areas of science and engineering
This article provides a review on the subject of wavelet methods in computational fluid dynamics (CFD) and discusses different wavelet-based approaches, emphasizing turbulence modeling and simulations using wavelets
Wavelet multiresolution analysis offers a unique framework for modeling and simulating turbulent flows, namely the tight integration of the numerics and physics-based modeling that enables the development of a unified hierarchy of turbulence models of different fidelity
Summary
Wavelets, introduced by Grossmann & Morlet (1984), have significantly impacted many areas of science and engineering (e.g., signal and image processing, speech recognition, and computer graphics). Many attractive mathematical properties of wavelets [namely, efficient multiscale decompositions, localization properties in physical and wave-number spaces, and the existence of recursive O(N ) fast wavelet transform], together with techniques for preconditioning and compression of operators and matrices, motivated their use for the numerical solution of partial differential equations (PDEs) on adaptive grids. The ability of wavelets to identify and isolate localized structures such as shock waves and vortices, combined with the mathematical rigor of multiresolution analysis, made them attractive candidates for adaptive computational approaches and turbulence modeling. The use of wavelets for modeling and simulations of turbulent flows is a relatively new area of research, with a limited number of people working in the field, and the need for a systematic introduction to the subject is rather pressing. This review aims to provide an overview of wavelet methodologies in CFD, summarizes existing wavelet-based numerical algorithms, and discusses state-of-the-art turbulence modeling and simulations using wavelets, and their future potential for CFD
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