Special Issue "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: 30 September 2023 | Viewed by 1955

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
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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

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 1600 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.

Published Papers (2 papers)

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Research

Article
Volumetric Rendering on Wavelet-Based Adaptive Grid
Fluids 2022, 7(7), 245; https://doi.org/10.3390/fluids7070245 - 16 Jul 2022
Viewed by 765
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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Article
A Wavelet-Based Adaptive Finite Element Method for the Stokes Problems
Fluids 2022, 7(7), 221; https://doi.org/10.3390/fluids7070221 - 30 Jun 2022
Viewed by 900
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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