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Fluids
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Advanced Numerical Methods for Turbulence Simulation
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Advanced Numerical Methods for Turbulence Simulation

A Special Issue of Fluids (ISSN 2311-5521) belonging to the section "Turbulence".

Deadline for manuscript submissions: 28 February 2027 | Viewed by 359

Editors

Dr. Zelong Yuan

E-Mail Website
Guest Editor
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Interests: turbulence modeling; computational fluid mechanics; physics-informed learning
Prof. Dr. Chao Wang

E-Mail Website
Guest Editor
College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China
Interests: propeller hydrodynamics; fluid mechanics; wake dynamics
Special Issues, Collections and Topics in MDPI journals
Dr. Yunpeng Wang

E-Mail Website
Guest Editor
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
Interests: machine learning; subgrid-scale modeling; large-eddy simulation

Special Issue Information

Dear Colleagues,

Turbulent flows are characterized by complex nonlinear dynamics, multiscale interactions, and strong unsteadiness, making their accurate numerical prediction a continuing challenge in fluid mechanics. This Special Issue, “Advanced Numerical Methods for Turbulence Simulation”, aims to collect recent developments in computational approaches for the simulation and modeling of turbulent flows. Topics of interest include high-order numerical schemes, direct numerical simulation, large-eddy simulation, turbulence closure modeling, and related methods for improving accuracy, stability, and computational efficiency. Contributions involving machine learning and data-driven approaches for turbulence modeling, model correction, flow prediction, and reduced-order simulation are also welcome. This Special Issue seeks to provide a platform for new algorithms, models, and applications that advance the reliability and capability of numerical turbulence simulations. 

Dr. Zelong Yuan
Prof. Dr. Chao Wang
Dr. Yunpeng Wang
Guest Editors

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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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

  • turbulence modeling
  • large-eddy simulation
  • direct numerical simulation
  • high-order numerical schemes
  • machine learning

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Published Papers (1 paper)

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Review

26 pages, 27434 KB  
Review
The Partially Averaged Navier–Stokes Paradigm: Recent Advances Toward Predictive Scale-Resolving Turbulence Simulation
by Jiachen Zhu, Zelong Yuan, Yunpeng Wang and Haojun Yang
Fluids 2026, 11(9), 233; https://doi.org/10.3390/fluids11090233 - 15 Sep 2026
Viewed by 159
Abstract
Partially averaged Navier–Stokes (PANS) has evolved over the past two decades from a conventional RANS–DNS bridging model into a scale-resolving simulation framework with controllable turbulence resolution. By introducing the unresolved fractions of turbulent kinetic energy and dissipation, fk and fε, [...] Read more.
Partially averaged Navier–Stokes (PANS) has evolved over the past two decades from a conventional RANS–DNS bridging model into a scale-resolving simulation framework with controllable turbulence resolution. By introducing the unresolved fractions of turbulent kinetic energy and dissipation, fk and fε, PANS regulates the partition between modeled and resolved turbulence. However, the turbulence resolution achieved in practical simulations is not solely determined by the prescribed parameters, but also depends on the interaction among turbulence closure, grid resolution, numerical dissipation, and physical modeling. This review summarizes the theoretical foundations, resolution-control strategies, and engineering applications of PANS, with particular emphasis on the consistency between prescribed and realized turbulence resolution. The formulation of partially averaged governing equations, closure transformations, scale relationships, and the limiting behaviors toward RANS and DNS are first discussed. Recent developments in variable-resolution formulations, commutation-error treatment, scale-supplying variables, near-wall resolution approaches, dissipation-resolution control, and variable-density extensions are subsequently reviewed. Applications to canonical turbulence, separated flows, rotating machinery, marine hydrodynamics, cavitation, heat transfer, combustion, and compressible flows are assessed in terms of turbulence statistics, coherent structures, spectral characteristics, and engineering prediction capability. Existing studies demonstrate that PANS can recover energetic unsteadiness suppressed by RANS and improve predictions of complex flows when sufficient numerical resolution and appropriate physical closures are provided. Nevertheless, reducing fk does not necessarily guarantee improved accuracy, as the prescribed resolution must be consistent with grid resolution, time-step selection, numerical schemes, boundary treatments, and multiphysics models. Future developments of PANS will focus on reliable resolution estimation, conservative variable-resolution strategies, consistent multiphysics scale closures, and systematic verification and validation procedures to establish quantitative relationships among prescribed resolution, numerical realization, and predictive accuracy. In PANS, fk and fε define a scale-dependent closure rather than a scale separation set directly to the grid or filter. Full article
(This article belongs to the Special Issue Advanced Numerical Methods for Turbulence Simulation)
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