Wavelets and Fluids

A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Mathematical and Computational Fluid Mechanics".

Deadline for manuscript submissions: closed (20 December 2023) | Viewed by 10622

Special Issue Editor


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Guest Editor
Department of Engineering, University of Campania Luigi Vanvitelli, 81031 Aversa, Italy
Interests: computational fluid dynamics; turbulence modelling and simulation; large-eddy simulation; wavelets and fluids
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Special Issue Information

Dear Colleagues,

Wavelets have been gaining more and more popularity in a number of research areas in science and engineering. This Special Issue is aimed at collecting both research and review articles to provide a state-of-the-art overview of the current investigations and topics on wavelet-based methods in fluid dynamics research. The attractive mathematical properties of wavelets (efficient multiscale decomposition, space–wavenumber/time–frequency localization), along with the existence of fast wavelet transforms, result in them being very useful in the modeling and simulation of fluid flows.

Wavelet analysis has been applied to fluid dynamics numerical and experimental data. Wavelet-related functions have been chosen as basis or test functions for the numerical solutions of the fluid dynamics equations, where many successful efforts have been put forth in wavelet-based dynamic adaptation strategies and multiresolution representation approaches. Wavelet-based adaptive methods have been developed for turbulent flow modeling and simulation.

This Special Issue welcomes a whole range of contributions, in which wavelet methods and related techniques are developed and/or applied to different research areas in fluid mechanics.

Topics of interest include but are not limited to:

  • Wavelet transforms and multiresolution analysis;
  • Wavelet multiscale filtering and de-noising;
  • Wavelet analysis techniques for numerical data;
  • Wavelet analysis techniques for experimental data;
  • Wavelet analysis in physics of fluids;
  • Wavelet analysis in fluids engineering;
  • Wavelet methods in mathematical and computational fluid dynamics;
  • Wavelet collocation methods;
  • Wavelet methods for the Navier–Stokes equations;
  • Wavelet methods for flow and heat transfer problems;
  • Wavelet methods for reactive flows;
  • Wavelet methods for cavitating flows;
  • Wavelets and turbulence modelling;
  • Wavelet-based coherent vortex extraction;
  • Wavelets and turbulence simulation;
  • Coherent vortex simulation;
  • Wavelet-based adaptive direct numerical simulation;
  • Wavelet-based adaptive large-eddy simulation;
  • Wavelet-based adaptive Reynolds-averaged Navier–Stokes modelling.

Dr. Giuliano De Stefano
Guest Editor

Manuscript Submission Information

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Published Papers (6 papers)

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Research

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19 pages, 43140 KiB  
Article
Experimental Analysis of a Cracked Cardan Shaft System under the Influence of Viscous Hydrodynamic Forces
by Bernard Xavier Tchomeni Kouejou and Alfayo Anyika Alugongo
Fluids 2023, 8(7), 211; https://doi.org/10.3390/fluids8070211 - 18 Jul 2023
Viewed by 1049
Abstract
Accurate prediction of the dynamic behavior of coupled shafts in a fluid medium is crucial to accurately estimate equipment life and enable safe operation. However, this task is far from trivial due to the vibrations induced by the highly nonlinear nature of the [...] Read more.
Accurate prediction of the dynamic behavior of coupled shafts in a fluid medium is crucial to accurately estimate equipment life and enable safe operation. However, this task is far from trivial due to the vibrations induced by the highly nonlinear nature of the machine system. This paper presents an experimental analysis of a cardan shaft under the influence of viscous hydrodynamic forces. An experimental setup was created using a cardan shaft rig installed in a plexiglas tank, with a self-aligned crack simulator supporting the driveshaft for crack extraction. Adequate instrumentation was used to measure the rotor’s fluctuation under industrial viscous fluid at various motor speeds. By analyzing the changes of unwanted high vibration, the obtained results demonstrated that the characteristics of the cracks in the fluid medium can be efficiently extracted from multiple tests using the wavelet synchrosqueezing transform and energy spectrum. This latter aspect, in particular, implies that the responses that can be observed in practice are highly sensitive to the values of the system parameters: average flow velocity, mass eccentricity, and shaft stiffness, among others. Finally, the study provides conclusions on practical applications for the reliable identification of cracks in a viscous fluid to validate the recently published theoretical study. Full article
(This article belongs to the Special Issue Wavelets and Fluids)
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17 pages, 3268 KiB  
Article
Stability and Resolution Analysis of the Wavelet Collocation Upwind Schemes for Hyperbolic Conservation Laws
by Bing Yang, Jizeng Wang, Xiaojing Liu and Youhe Zhou
Fluids 2023, 8(2), 65; https://doi.org/10.3390/fluids8020065 - 13 Feb 2023
Cited by 1 | Viewed by 1191
Abstract
The numerical solution of hyperbolic conservation laws requires algorithms with upwind characteristics. Conventional methods such as the numerical difference method can realize this characteristic by constructing special distributions of nodes. However, there are still no reports on how to construct algorithms with upwind [...] Read more.
The numerical solution of hyperbolic conservation laws requires algorithms with upwind characteristics. Conventional methods such as the numerical difference method can realize this characteristic by constructing special distributions of nodes. However, there are still no reports on how to construct algorithms with upwind characteristics through wavelet theory. To solve this problem, a system of high-order and stable wavelet collocation upwind schemes was successfully proposed by constructing interpolation wavelets with specific symmetry and smoothness. The effects of the characteristics of the scaling functions on the schemes were explored based on numerical tests and Fourier analysis. The numerical results revealed that the stability of the constructed scheme is affected by the smoothness order, N, and the asymmetry of the scaling function. The dissipation analysis suggested that schemes with N ∈ even have negative dissipation coefficients, leading to unstable behaviors. Only scaling functions with N ∈ odd and a bias magnitude of 1 can be used to construct stable upwind schemes due to the non-negative dissipation coefficients. Typical numerical examples verified the effectiveness of the proposed method, which is proved to have high accuracy and efficiency in solving high-speed flow problems with multi-scale smooth structures and discontinuities. Full article
(This article belongs to the Special Issue Wavelets and Fluids)
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12 pages, 1179 KiB  
Article
Volumetric Rendering on Wavelet-Based Adaptive Grid
by Alexei V. Vezolainen, Gordon Erlebacher, Oleg V. Vasilyev and David A. Yuen
Fluids 2022, 7(7), 245; https://doi.org/10.3390/fluids7070245 - 16 Jul 2022
Viewed by 1785
Abstract
Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve [...] Read more.
Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes. Full article
(This article belongs to the Special Issue Wavelets and Fluids)
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35 pages, 3727 KiB  
Article
A Wavelet-Based Adaptive Finite Element Method for the Stokes Problems
by Yury A. Mishin, Oleg V. Vasilyev and Taras V. Gerya
Fluids 2022, 7(7), 221; https://doi.org/10.3390/fluids7070221 - 30 Jun 2022
Viewed by 1618
Abstract
In this work, we present the mathematical formulation of the new adaptive multiresolution method for the Stokes problems of highly viscous materials arising in computational geodynamics. The method is based on particle-in-cell approach—the Stokes system is solved on a static Eulerian finite element [...] Read more.
In this work, we present the mathematical formulation of the new adaptive multiresolution method for the Stokes problems of highly viscous materials arising in computational geodynamics. The method is based on particle-in-cell approach—the Stokes system is solved on a static Eulerian finite element grid and material properties are carried in space by Lagrangian material points. The Eulerian grid is adapted using the wavelet-based adaptation algorithm. Both bilinear (Q1P0, Q1Q1) and biquadratic (Q2P-1) mixed approximations for the Stokes system are supported. The proposed method is illustrated for a number of linear and nonlinear two-dimensional benchmark problems of geophysical relevance. The results of the adaptive numerical simulations using the proposed method are in an excellent agreement with those obtained on non-adaptive grids and with analytical solutions, while computational requirements are few orders of magnitude less compared to the non-adaptive simulations in terms of both time and memory usage. Full article
(This article belongs to the Special Issue Wavelets and Fluids)
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Review

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20 pages, 2356 KiB  
Review
Wavelet Transforms and Machine Learning Methods for the Study of Turbulence
by Jahrul M Alam
Fluids 2023, 8(8), 224; https://doi.org/10.3390/fluids8080224 - 03 Aug 2023
Cited by 1 | Viewed by 2259
Abstract
This article investigates the applications of wavelet transforms and machine learning methods in studying turbulent flows. The wavelet-based hierarchical eddy-capturing framework is built upon first principle physical models. Specifically, the coherent vortex simulation method is based on the Taylor hypothesis, which suggests that [...] Read more.
This article investigates the applications of wavelet transforms and machine learning methods in studying turbulent flows. The wavelet-based hierarchical eddy-capturing framework is built upon first principle physical models. Specifically, the coherent vortex simulation method is based on the Taylor hypothesis, which suggests that the energy cascade occurs through vortex stretching. In contrast, the adaptive wavelet collocation method relies on the Richardson hypothesis, where the self-amplification of the strain field and a hierarchical breakdown of large eddies drive the energy cascade. Wavelet transforms are computational learning architectures that propagate the input data across a sequence of linear operators to learn the underlying nonlinearity and coherent structure. Machine learning offers a wealth of data-driven algorithms that can heavily use statistical concepts to extract valuable insights into turbulent flows. Supervised machine learning needs “perfect” turbulent flow data to train data-driven turbulence models. The current advancement of artificial intelligence in turbulence modeling primarily focuses on accelerating turbulent flow simulations by learning the underlying coherence over a low-dimensional manifold. Physics-informed neural networks offer a fertile ground for augmenting first principle physics to automate specific learning tasks, e.g., via wavelet transforms. Besides machine learning, there is room for developing a common computational framework to provide a rich cross-fertilization between learning the data coherence and the first principles of multiscale physics. Full article
(This article belongs to the Special Issue Wavelets and Fluids)
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24 pages, 2232 KiB  
Review
Wavelet-Based Adaptive Eddy-Resolving Methods for Modeling and Simulation of Complex Wall-Bounded Compressible Turbulent Flows
by Xuan Ge, Giuliano De Stefano, M. Yousuff Hussaini and Oleg V. Vasilyev
Fluids 2021, 6(9), 331; https://doi.org/10.3390/fluids6090331 - 15 Sep 2021
Cited by 8 | Viewed by 1900
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Wavelets and Fluids)
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