Abstract
This article represents the second part of a review by De Stefano and Vasilyev (2021) on wavelet-based adaptive methods for modeling and simulation of turbulent flows. Unlike the hierarchical adaptive eddy-capturing approach, described in the first part and devoted to high-fidelity modeling of incompressible flows, this companion paper focuses on the adaptive eddy-resolving framework for compressible flows in complex geometries, which also includes model-form adaptation from low to high fidelity models. A hierarchy of wavelet-based eddy-resolving methods of different fidelity has been developed for different speed regimes, various boundary conditions, and Reynolds numbers. Solutions of various fidelity are achieved using a range of modeling approaches from unsteady Reynolds-averaged Navier–Stokes simulation to delayed detached eddy simulation, wall-modeled and wall-resolved large eddy simulations. These novel methodologies open the door to construct a hierarchical approach for simulation of compressible flows covering the whole range of possibilities, from only resolving the average or dominant frequency, to capturing the intermittency of turbulence eddies, and to directly simulating the full turbulence spectrum. The generalized hierarchical wavelet-based adaptive eddy-resolving approach, once fully integrated into a single inherently interconnected simulation, results in being a very competitive and predictive tool for complicated flows in industrial design and analysis with high efficiency and accuracy.
Highlights
Accurate modeling of compressible turbulent flows required in aerospace industry, including aeronautical and rotorcraft engineering, turbomachinery, automotive and railway transportation, energy and several technology-related industries, continues to be one of the major challenges in developing simulation-based predictive tools that can be used for design and analysis of fluid engineering systems and/or their components [1]
Along with WA-direct numerical simulation (DNS) and coherent vortex simulation (CVS), these methods serve as segregated steps towards the construction of a unified wavelet-based adaptive hierarchical eddyresolving framework for modeling complex wall-bounded compressible turbulent flows, capable of performing simulations with various fidelity, from no-modeling DNS to fullmodeling Reynolds-averaged Navier–Stokes (RANS), depending on the requirement and balance of accuracy and computational efficiency
The wavelet-based adaptive delayed detached eddy simulation (WA-DDES) approach for wall-bounded compressible turbulent flows was developed in Ref. [15], where its effectiveness was demonstrated for flow simulations using the SA model based formulation [35]
Summary
Accurate modeling of compressible turbulent flows required in aerospace industry, including aeronautical and rotorcraft engineering, turbomachinery, automotive and railway transportation, energy and several technology-related industries, continues to be one of the major challenges in developing simulation-based predictive tools that can be used for design and analysis of fluid engineering systems and/or their components [1]. Despite the use of highly stretched meshes with relatively large spacings in the wall-parallel directions to reduce the total number of active nodes, a relatively small wall-normal mesh spacings are employed in the region immediately adjacent to the wall, i.e., where y+ < 1 To overcome this restriction, the new wavelet-based adaptive wall-modeled LES (WA-WMLES) method has been introduced in Ref. Along with WA-DNS and CVS, these methods serve as segregated steps towards the construction of a unified wavelet-based adaptive hierarchical eddyresolving framework for modeling complex wall-bounded compressible turbulent flows, capable of performing simulations with various fidelity, from no-modeling DNS to fullmodeling RANS, depending on the requirement and balance of accuracy and computational efficiency. The family of eddy-resolving DES models is better described in terms of length scale formulations [49], where either Reynolds-averaged in the near-wall region (referred to as RANS region) or low-pass wavelet-filtered Navier–Stokes equations away from the wall (LES region) are solved. All the details about the governing equations and turbulence closure models can be found in the reference articles for the different approaches that are WA-LES [14], WA-URANS [16], WA-DDES [15], and WA-WMLES [17]
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