Abstract
A short review of wavelet-based adaptive methods for modeling and simulation of incompressible turbulent flows is presented. Wavelet-based computational modeling approaches of different fidelities are recast into an integrated hierarchical adaptive eddy-capturing turbulence modeling framework. The wavelet threshold filtering procedure and the associated wavelet-filtered Navier–Stokes equations are briefly discussed, along with the adaptive wavelet collocation method that is used for numerical computations. Depending on the level of wavelet thresholding, the simulation is possibly supplemented with a localized closure model. The latest advancements in spatiotemporally varying wavelet thresholding procedures along with the adaptive-anisotropic wavelet-collocation method make the development of a fully adaptive approach feasible with potential applications for complex turbulent flows.
Highlights
The detailed comparisons of computational fluid dynamics (CFD) results against experimental findings have clearly shown the importance of capturing the dominant threedimensional flow structures when simulating fluid turbulence (e.g., [1])
The development of wavelet-based adaptive large-eddy simulation (LES) (WA-LES) addresses shortcomings of traditional LES approaches by using a dynamic grid adaptation strategy that resolves energetic coherent eddies regardless of their size. The centerpiece of this approach is the existence of energetic coherent structures that govern turbulent flow dynamics across the full spectral range [5]. This novel methodology, which is based on the application of a wavelet threshold filtering (WTF) procedure, demonstrated the ability to dynamically resolve and track the most energetic part of the coherent turbulent eddies while exploiting a field compression that allows for a significant reduction of the number of grid points used in the numerical computations
For the results reported in this work, derivative approximations are provided by multi-level central fourth-order finite difference (FD) schemes at the local adaptive resolution level
Summary
The detailed comparisons of computational fluid dynamics (CFD) results against experimental findings have clearly shown the importance of capturing the dominant threedimensional flow structures when simulating fluid turbulence (e.g., [1]). The centerpiece of this approach is the existence of energetic coherent structures that govern turbulent flow dynamics across the full spectral range [5] This novel methodology, which is based on the application of a wavelet threshold filtering (WTF) procedure, demonstrated the ability to dynamically resolve and track the most energetic part of the coherent turbulent eddies while exploiting a field compression that allows for a significant reduction of the number of grid points used in the numerical computations. The principal idea behind WA-LES was taken one step further by introducing the variable wavelet thresholding strategy to locally and temporally maintain the desired level of turbulence resolution This was achieved by ensuring that only the a priori specified fraction of turbulent kinetic energy, SGS dissipation, or other statistical quantities was resolved. The multi-resolution nature of WTF allows small dissipative scales to be partially resolved more effectively than for classical LES filters
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