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Fluids
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Wavelets and Fluid Dynamics
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Wavelets and Fluid Dynamics

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 (31 May 2022) | Viewed by 13547

Special Issue Editor

Dr. Giuliano De Stefano

E-Mail Website
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
Special Issues, Collections and Topics in MDPI journals

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 being very useful in modelling 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 modelling 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 dynamics.

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 (hot-wire and particle image velocimetry);

- Wavelet analysis techniques in cavitating flows;

- 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 the solution of reaction–diffusion problems;

- 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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • wavelet multiresolution analysis
  • coherent vortex extraction
  • computational fluid dynamics
  • adaptive mesh refinement
  • turbulence modelling and simulation

Published Papers (6 papers)

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Research

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13 pages, 1956 KiB  
Article
A Comparative Analysis of In-Situ Optical Velocimetries for Oil Spill Flow Rate Estimation
by Osman Abu Bkar, Mark Ovinis and Abdalellah O. Mohmmed
Fluids 2022, 7(4), 126; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7040126 - 28 Mar 2022
Viewed by 1717
Abstract
In the Deepwater Horizon oil spill, optical plume velocimetry (OPV), a flow measurement technique for use in seafloor hydrothermal systems, was found to have the least uncertainty in estimating the rate at which oil was escaping from the well in the deep sea. [...] Read more.
In the Deepwater Horizon oil spill, optical plume velocimetry (OPV), a flow measurement technique for use in seafloor hydrothermal systems, was found to have the least uncertainty in estimating the rate at which oil was escaping from the well in the deep sea. However, OPV still had a high uncertainty of 21%, partly due to the limited accuracy of the temporal cross-correlation algorithm used. In this work, the accuracy of several in-situ optical velocimetries, namely wavelet-based optical velocimetry (WOV), OPV, and two classical correlation-based algorithms, namely fast Fourier transform (FFT) and normalized cross-correlation (NCC), for a plume flow with Reynolds numbers varying from 1847 to 11,656 was investigated. WOV, FFT, and NCC resulted in flow rates closer to the expected turbulent plume flow rate as compared to OPV. Moreover, a noisy velocity field was found using OPV. The accuracy of wavelet-based algorithm outperformed all cross-correlation based algorithms. The flow rate was measured with an error of 8.5% using WOV, whereas errors of 18.2%, 19.7%, to 21.1% were obtained when applying FFT, OPV, and NCC, respectively. There was a statistically significant difference between wavelet-based and correlation-based algorithms, but no statistically significant difference between the estimation of the three cross-correlation based velocimetries. WOV outperformed the other velocimetries and estimated flow rates with an error of 8.5%, whereas the OPV, FFT, and NCC were estimated with errors of 19.7%, 18.2%, and 50.8%, respectively. Full article
(This article belongs to the Special Issue Wavelets and Fluid Dynamics)
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17 pages, 3567 KiB  
Article
Galilean-Invariant Characteristic-Based Volume Penalization Method for Supersonic Flows with Moving Boundaries
by Nurlybek Kasimov, Eric Dymkoski, Giuliano De Stefano and Oleg V. Vasilyev
Fluids 2021, 6(8), 293; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6080293 - 20 Aug 2021
Cited by 11 | Viewed by 2507
Abstract
This work extends the characteristic-based volume penalization method, originally developed and demonstrated for compressible subsonic viscous flows in (J. Comput. Phys. 262, 2014), to a hyperbolic system of partial differential equations involving complex domains with moving boundaries. The proposed methodology is shown to [...] Read more.
This work extends the characteristic-based volume penalization method, originally developed and demonstrated for compressible subsonic viscous flows in (J. Comput. Phys. 262, 2014), to a hyperbolic system of partial differential equations involving complex domains with moving boundaries. The proposed methodology is shown to be Galilean-invariant and can be used to impose either homogeneous or inhomogeneous Dirichlet, Neumann, and Robin type boundary conditions on immersed boundaries. Both integrated and non-integrated variables can be treated in a systematic manner that parallels the prescription of exact boundary conditions with the approximation error rigorously controlled through an a priori penalization parameter. The proposed approach is well suited for use with adaptive mesh refinement, which allows adequate resolution of the geometry without over-resolving flow structures and minimizing the number of grid points inside the solid obstacle. The extended Galilean-invariant characteristic-based volume penalization method, while being generally applicable to both compressible Navier–Stokes and Euler equations across all speed regimes, is demonstrated for a number of supersonic benchmark flows around both stationary and moving obstacles of arbitrary shape. Full article
(This article belongs to the Special Issue Wavelets and Fluid Dynamics)
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Review

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23 pages, 23552 KiB  
Review
Computational Fluid Dynamics Using the Adaptive Wavelet-Collocation Method
by Yash Mehta, Ari Nejadmalayeri and Jonathan David Regele
Fluids 2021, 6(11), 377; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6110377 - 22 Oct 2021
Cited by 1 | Viewed by 1700
Abstract
Advancements to the adaptive wavelet-collocation method over the last decade have opened up a number of new possible areas for active research. Volume penalization techniques allow complex immersed boundary conditions to be used with high efficiency for both internal and external flows. Anisotropic [...] Read more.
Advancements to the adaptive wavelet-collocation method over the last decade have opened up a number of new possible areas for active research. Volume penalization techniques allow complex immersed boundary conditions to be used with high efficiency for both internal and external flows. Anisotropic methods make it possible to use body-fitted meshes while still taking advantage of the dynamic adaptability properties wavelet-based methods provide. The parallelization of the approach has made it possible to perform large high-resolution simulations of detonation initiation and fluid instabilities to uncover new physical insights that would otherwise be difficult to discover. Other developments include space-time adaptive methods and nonreflecting boundary conditions. This article summarizes the work performed using the adaptive wavelet-collocation method developed by Vasilyev and coworkers over the past decade. Full article
(This article belongs to the Special Issue Wavelets and Fluid Dynamics)
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12 pages, 2052 KiB  
Review
On the Application of Wavelet Transform in Jet Aeroacoustics
by Roberto Camussi and Stefano Meloni
Fluids 2021, 6(8), 299; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6080299 - 23 Aug 2021
Cited by 14 | Viewed by 2173
Abstract
Wavelet transform has become a common tool for processing non-stationary signals in many different fields. The present paper reports a review of some applications of wavelet in aeroacoustics with a special emphasis on the analysis of experimental data taken in compressible jets. The [...] Read more.
Wavelet transform has become a common tool for processing non-stationary signals in many different fields. The present paper reports a review of some applications of wavelet in aeroacoustics with a special emphasis on the analysis of experimental data taken in compressible jets. The focus is on three classes of wavelet-based signal processing procedures: (i) conditional statistics; (ii) acoustic and hydrodynamic pressure separation; (iii) stochastic modeling. The three approaches are applied to an experimental database consisting of pressure time series measured in the near field of a turbulent jet. Future developments and possible generalization to other applications, e.g., airframe or propeller noise, are also discussed. Full article
(This article belongs to the Special Issue Wavelets and Fluid Dynamics)
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19 pages, 4826 KiB  
Review
Adaptive Wavelet Methods for Earth Systems Modelling
by Nicholas K.-R. Kevlahan
Fluids 2021, 6(7), 236; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6070236 - 29 Jun 2021
Cited by 3 | Viewed by 1627
Abstract
This paper reviews how dynamically adaptive wavelet methods can be designed to simulate atmosphere and ocean dynamics in both flat and spherical geometries. We highlight the special features that these models must have in order to be valid for climate modelling applications. These [...] Read more.
This paper reviews how dynamically adaptive wavelet methods can be designed to simulate atmosphere and ocean dynamics in both flat and spherical geometries. We highlight the special features that these models must have in order to be valid for climate modelling applications. These include exact mass conservation and various mimetic properties that ensure the solutions remain physically realistic, even in the under-resolved conditions typical of climate models. Particular attention is paid to the implementation of complex topography in adaptive models. Using wavetrisk as an example, we explain in detail how to build a semi-realistic global atmosphere or ocean model of interest to the geophysical community. We end with a discussion of the challenges that remain to developing a realistic dynamically adaptive atmosphere or ocean climate models. These include scale-aware subgrid scale parameterizations of physical processes, such as clouds. Although we focus on adaptive wavelet methods, many of the topics we discuss are relevant for adaptive mesh refinement (AMR). Full article
(This article belongs to the Special Issue Wavelets and Fluid Dynamics)
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14 pages, 10626 KiB  
Review
Hierarchical Adaptive Eddy-Capturing Approach for Modeling and Simulation of Turbulent Flows
by Giuliano De Stefano and Oleg V. Vasilyev
Fluids 2021, 6(2), 83; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6020083 - 13 Feb 2021
Cited by 12 | Viewed by 1965
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Wavelets and Fluid Dynamics)
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