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7,571 Results Found

  • Article
  • Open Access
4 Citations
3,917 Views
10 Pages

20 May 2021

Direct numerical simulations were performed to study the effects of the domain size of a minimal flow unit (MFU) and its inherent periodic boundary conditions on flow physics of a turbulent channel flow in a range of 200≤Reτ≤1000. This was accomplish...

(This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth)
  • Article
  • Open Access
15 Citations
7,065 Views
14 Pages

21 April 2023

Wind loads can endanger the safety and stability of bridges, especially long-span cable-supported bridges. Therefore, it is important to evaluate the potential wind loads during the bridge design stage. Traditionally, wind load evaluation is performe...

(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
  • Article
  • Open Access
100 Views
21 Pages

A Physics-Inspired Multi-Flow Graph Neural Network with Explicit Flow Allocation for Sustainable Rainfall-Driven Flood Simulation

  • Xinru Zhang,
  • Fuxin Chai,
  • Hongping Zhang,
  • Yuchen Xiao and ,
  • Huimin Xu,
  • Ying Ding and
  • Xi Yang
  • + 2 authors+ 0 author

12 November 2026

Graph-based surrogate models offer an efficient alternative to hydrodynamic simulations, but accurately representing multi-directional runoff propagation remains challenging. This study proposes a physics-inspired multi-flow graph neural network with...

(This article belongs to the Section Sustainable Water Management)
  • Article
  • Open Access
5 Citations
2,908 Views
22 Pages

In the area of synthetic sensors for flow angle estimation, the present work aims to describe the verification in a relevant environment of a physics-based approach using a dedicated technological demonstrator. The flow angle synthetic solution is ba...

(This article belongs to the Special Issue Unmanned Aircraft Systems with Autonomous Navigation)
  • Article
  • Open Access
4 Citations
1,956 Views
22 Pages

Research on Power Flow Prediction Based on Physics-Informed Graph Attention Network

  • Qiyue Huang,
  • Yapeng Wang,
  • Xu Yang,
  • Sio-Kei Im and
  • Jianxiu Cai

29 September 2025

As an emerging distributed energy system, microgrid power flow prediction plays a crucial role in optimizing energy dispatch and power grid operation. Traditional methods of power flow prediction mainly rely on statistics and time series models, negl...

  • Article
  • Open Access
863 Views
18 Pages

27 February 2026

As a mesh-free solving paradigm, Physics-Informed Neural Networks (PINNs) demonstrate potential in both forward and inverse problems by embedding physical equations into the loss function. However, they still face challenges in capturing the spatiote...

(This article belongs to the Section Computing and Artificial Intelligence)
  • Article
  • Open Access
11 Citations
6,910 Views
18 Pages

Investigation of Physics-Informed Neural Networks to Reconstruct a Flow Field with High Resolution

  • Zhou Yang,
  • Yuwang Xu,
  • Jionglin Jing,
  • Xuepeng Fu and ,
  • Bofu Wang,
  • Haojie Ren,
  • Mengmeng Zhang and
  • Tongxiao Sun
  • + 3 authors+ 0 author

25 October 2023

Particle image velocimetry (PIV) is a widely used experimental technique in ocean engineering, for instance, to study the vortex fields near marine risers and the wake fields behind wind turbines or ship propellers. However, the flow fields measured...

(This article belongs to the Section Ocean Engineering)
  • Article
  • Open Access

Transient Multiphase Flow Nested-Closure Extended Physics-Informed Neural Network (TM-NC-XPINN): Boundary-Supervised Reconstruction of Gas–Liquid Pipe Flow

  • Jun Chen,
  • Zhiyu Xu,
  • Jueqi Li,
  • Yukun Mao and ,
  • Junbo Zhang,
  • Jingwen Song,
  • Daqiang Feng,
  • Jianing Li,
  • Haoyu Wang and
  • Jianjun Zhu
  • + 5 authors+ 0 author
Processes2026, 14(22), 3673;https://doi.org/10.3390/pr14223673 
(registering DOI)

15 November 2026

We investigate a physics-constrained neural network for reconstructing transient gas–liquid pipe flow under prescribed initial and boundary conditions. The method combines phase mass and mixture momentum equations with a horizontal drift-flux c...

(This article belongs to the Special Issue Subsurface Flow and AI: Advanced Modeling, Simulation, and Applications)
  • Article
  • Open Access
5 Citations
3,408 Views
21 Pages

7 February 2024

Flow through complex thermodynamic machinery is intricate, incorporating turbulence, compressibility effects, combustion, and solid–fluid interactions, posing a challenge to classical physics. For example, it is not currently possible to simula...

(This article belongs to the Section Aeronautics)
  • Article
  • Open Access
455 Views
18 Pages

Axial flow fans play a critical role in the safety and efficiency of industrial processes. This paper proposes an operation monitoring approach for axial flow fans based on physics-guided support vector regression and alarm delay timer. The physical...

(This article belongs to the Section Automation and Control Systems)
  • Article
  • Open Access
462 Views
47 Pages

Hybrid Convolutional, Transformer and Physics-Encoding Networks for Multiphase Flow Pattern Identification in Vertical Pipelines

  • Eric Thompson Brantson,
  • Mukhtar Abdulkadir,
  • Ransford Yeboah,
  • Ebenezer Kobina Abakah and ,
  • Edzie William Otubuah and
  • Martin Luther Afirim
  • + 1 author+ 0 author

24 August 2026

Accurate identification of multiphase flow patterns in vertical pipelines is critical for operational safety and efficiency in the oil and gas industry. Yet, conventional methods struggle with subjectivity and transitional regimes. This study develop...

(This article belongs to the Special Issue Advances in Multiphase Flow Measurement and Simulation)
  • Article
  • Open Access
10 Citations
3,045 Views
16 Pages

30 April 2024

This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flows in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural n...

(This article belongs to the Topic Artificial Intelligence (AI) Applied in Civil Engineering, 2nd Volume)
  • Article
  • Open Access
2 Citations
650 Views
26 Pages

24 June 2026

The increasing integration of renewable generation introduces highly stochastic operating conditions, substantially enlarging the operating space and posing severe computational challenges for traditional iterative power flow solvers. To address this...

(This article belongs to the Special Issue Application of Swarm Intelligence for Multi-Energy Virtual Power Plants)
  • Article
  • Open Access
93 Views
26 Pages

Cross-Geometry Flow-Field Prediction in Irregular Wellbores Using Parameterized Physics-Informed Neural Networks

  • Zhichao Xie,
  • Jian Yang,
  • Chi Zhao,
  • Long Chen and ,
  • Jiali Wang and
  • Yunhai Zhao
  • + 1 author+ 0 author

3 November 2026

Irregular borehole enlargement alters annular flow structures and can create low-velocity regions that impair hole cleaning. However, conventional computational fluid dynamics (CFD) requires repeated geometric reconstruction and numerical simulations...

(This article belongs to the Special Issue Advanced Process Modeling, Fluid Dynamics, and Optimization in Complex Well Engineering)
  • Article
  • Open Access
14 Citations
5,649 Views
18 Pages

19 January 2024

With the rapid development of artificial intelligence technology, the physics-informed neural network (PINN) has gradually emerged as an effective and potential method for solving N-S equations. The treatment of constraints is vital to the PINN predi...

(This article belongs to the Special Issue Recent Advances in Engineering Applications of Computational Fluid Dynamics)
  • Review
  • Open Access
6 Citations
1,250 Views
32 Pages

17 June 2026

In characterizing unconventional reservoirs, conventional Digital Rock Physics (DRP) has long been constrained by three fundamental bottlenecks: the trade-off between imaging resolution and field of view, challenges in reconstructing multiscale pore...

(This article belongs to the Special Issue Rock Mechanics in Underground Engineering)
  • Article
  • Open Access
83 Citations
15,884 Views
17 Pages

Turbulence Modeling for Physics-Informed Neural Networks: Comparison of Different RANS Models for the Backward-Facing Step Flow

  • Fabian Pioch,
  • Jan Hauke Harmening,
  • Andreas Maximilian Müller,
  • Franz-Josef Peitzmann and ,
  • Dieter Schramm and
  • Ould el Moctar
  • + 1 author+ 0 author

26 January 2023

Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorpo...

(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
  • Article
  • Open Access
10 Citations
7,885 Views
23 Pages

Physics-Informed Neural Networks (PINNs) are a new class of machine learning algorithms that are capable of accurately solving complex partial differential equations (PDEs) without training data. By introducing a new methodology for fluid simulation,...

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)
  • Article
  • Open Access
6 Citations
1,838 Views
20 Pages

Model-Data Hybrid-Driven Real-Time Optimal Power Flow: A Physics-Informed Reinforcement Learning Approach

  • Ximing Zhang,
  • Xiyuan Ma,
  • Yun Yu,
  • Duotong Yang and ,
  • Zhida Lin,
  • Changcheng Zhou,
  • Huan Xu and
  • Zhuohuan Li
  • + 3 authors+ 0 author

1 July 2025

With the rapid development of artificial intelligence technology, DRL has shown great potential in solving complex real-time optimal power flow problems of modern power systems. Nevertheless, traditional DRL methodologies confront dual bottlenecks: (...

(This article belongs to the Topic Game Theory and Artificial Intelligence Methods in Sustainable and Renewable Energy Power Systems)
  • Article
  • Open Access
6 Citations
2,166 Views
32 Pages

A Systematic Analysis of Physics-Informed Neural Networks for Two-Phase Flow with Capillarity: The Muskat–Leverett Problem

  • Timur Imankulov,
  • Alibek Kuljabekov,
  • Samson Dawit Bekele,
  • Zhumabek Zhantayev and ,
  • Bakytzhan Assilbekov and
  • Yerzhan Kenzhebek
  • + 1 author+ 0 author

10 December 2025

This work develops and systematically evaluates a physics-informed neural network (PINN) solver for the fully coupled, time-dependent Muskat–Leverett system with capillarity modeled in the pressure equation. A single shallow–wide multilay...

(This article belongs to the Section Fluid Science and Technology)
  • Article
  • Open Access
612 Views
22 Pages

21 July 2026

In Virtual Power Plants (VPPs), computing the Optimal Energy Flow (OEF) for integrated electricity–heat systems is essential but challenged by highly asymmetric topologies and multi-timescale characteristics. Traditional data-driven models ofte...

(This article belongs to the Special Issue Application of Swarm Intelligence for Multi-Energy Virtual Power Plants—2nd Edition)
  • Article
  • Open Access
187 Views
37 Pages

Pulsating flow offers a practical means of modifying convective heat transfer in microchannels, but thermal enhancement may be accompanied by increased thermodynamic irreversibility. This study develops a physics-informed neural network (PINN) framew...

  • Article
  • Open Access
468 Views
27 Pages

Physics-Informed Neural Network for Reconstructing Free-Surface Transient Flow Fields in Long-Distance Water-Conveyance Tunnels from Sparse Observations

  • Xiulian Li,
  • Zhiyuan Chen,
  • Donghui Qi,
  • Yize Zhang and ,
  • Zhaoyang Deng and
  • Ling Zhou
  • + 1 author+ 0 author

7 September 2026

Long-distance free-surface water-conveyance tunnels require a spatially continuous representation of transient water depth, yet in practice flow is monitored at only a few sections. This study develops a physics-informed neural network (PINN) that re...

(This article belongs to the Section Hydraulics and Hydrodynamics)
  • Article
  • Open Access
9 Citations
4,175 Views
20 Pages

19 October 2024

A physics-informed convolutional neural network (PICNN) is proposed to simulate two-phase flow in porous media with time-varying well controls. While most PICNNs in the existing literature worked on parameter-to-state mapping, our proposed network pa...

(This article belongs to the Special Issue Modeling of Multiphase Flow Phenomena)
  • Article
  • Open Access
1 Citations
1,137 Views
18 Pages

A Hybrid Physics-Informed Neural Network (PINN) for the Electro-Oxidation of 2-Chlorophenol on BDD Electrodes in a Flow-By Reactor Under Batch Recirculation

  • Alejandro Regalado-Méndez,
  • Damayrí M. Salinas-Camacho,
  • Reyna Natividad,
  • Mario E. Cordero and ,
  • Luis G. Zárate,
  • Hugo Pérez-Pastenes,
  • César Pérez-Alonso and
  • Ever Peralta-Reyes
  • + 3 authors+ 0 author

9 June 2026

The electro-oxidation of persistent organic pollutants such as 2-chlorophenol (2-CPh) using boron-doped diamond (BDD) electrodes offers a promising wastewater treatment route, yet conventional mechanistic models (e.g., CFD) suffer from prohibitive co...

(This article belongs to the Special Issue Fundamentals and Practical Applications of Artificial Intelligence, Machine Learning, and Deep Learning in Photo- and Electrochemical-Based Wastewater Treatment)
  • Article
  • Open Access
12 Citations
4,145 Views
15 Pages

Observational and Critical State Physics Descriptions of Long-Range Flow Structures

  • Peter E. Malin,
  • Peter C. Leary,
  • Lawrence M. Cathles and
  • Christopher C. Barton

Using Fracture Seismic methods to map fluid-conducting fracture zones makes it important to understand fracture connectivity over distances greater 10–20 m in the Earth’s upper crust. The principles required for this understanding are dev...

(This article belongs to the Special Issue Future Advances in Basin Modeling: Suggestions from Current Observations, Analyses, and Simulations)
  • Article
  • Open Access
3 Citations
2,196 Views
20 Pages

Response of Arabidopsis thaliana to Flooding with Physical Flow

  • Momoko Kaji,
  • Kazuma Katano,
  • Taufika Islam Anee,
  • Hiroshi Nitta and ,
  • Ryotaro Yamaji,
  • Rio Shimizu,
  • Shunsuke Shigaki,
  • Hiroyuki Suzuki and
  • Nobuhiro Suzuki
  • + 4 authors+ 0 author

16 December 2024

Flooding causes severe yield losses worldwide, making it urgent to enhance crop tolerance to this stress. Since natural flooding often involves physical flow, we hypothesized that the effects of submergence on plants could change when combined with p...

(This article belongs to the Special Issue Deciphering Plant Molecular Data Using Computational Methods)
  • Review
  • Open Access
18 Citations
11,035 Views
29 Pages

A Review of Flotation Physical Froth Flow Modifiers

  • Tawona M. Jera and
  • Clayton Bhondayi

10 August 2021

Over the past few decades, the need to process more minerals while lowering capital costs has led to an increase in the size of flotation cells, e.g., 0.03 m3 to 1000 m3. However, this increase has created new challenges in the operation and design o...

(This article belongs to the Section Mineral Processing and Extractive Metallurgy)
  • Article
  • Open Access
14 Citations
6,221 Views
24 Pages

Physics-Based Deep Learning for Flow Problems

  • Yubiao Sun,
  • Qiankun Sun and
  • Kan Qin

19 November 2021

It is the tradition for the fluid community to study fluid dynamics problems via numerical simulations such as finite-element, finite-difference and finite-volume methods. These approaches use various mesh techniques to discretize a complicated geome...

(This article belongs to the Section A: Sustainable Energy)
  • Article
  • Open Access
2 Citations
2,313 Views
16 Pages

Shared flow in collective physical and sports activities and subjective well-being

  • Larraitz N. Zumeta,
  • Nekane Basabe,
  • Saioa Telletxea,
  • Alberto Amutio and
  • Magdalena Bobowik

This study examines physical and sport activities as a source of shared flow or optimal shared experiences and their relationship with subjective well-being (SWB). Two studies are presented with university students (N=88 and N=285) participating in g...

  • Article
  • Open Access
4 Citations
1,998 Views
19 Pages

The volume of flow demand in cyber-physical power systems (CPPSs) fluctuates unevenly across coupled networks and is susceptible to congestion or overload due to consumers’ energy demand or extreme disasters. Therefore, considering the elastici...

  • Article
  • Open Access
3 Citations
3,337 Views
15 Pages

Contributions of Physical Activity and Positive Psychological Functioning to Flow and Well-Being

  • Nuno Rodrigues,
  • Luís Sérgio Vieira,
  • Cátia Sofia Martins,
  • Catarina Moreira and
  • Saúl Neves de Jesus

2 September 2025

Studies highlight the importance of physical activity (PA) in relation to positive psychological functioning (PPF) among adults. Physical inactivity is strongly associated with lower levels of PPF, supporting the idea that lifestyle choices can be id...

  • Review
  • Open Access
1 Citations
647 Views
33 Pages

Recent Advances in Characterization Techniques for the Physical Properties of Multiphase Flows and Seepage Mechanisms

  • Shu Tang,
  • Rui Shen,
  • Wei Xiong,
  • Shengchun Xiong and ,
  • Jiale Shi,
  • Weimin Chen,
  • Guo Wang and
  • Zhengyong Luo
  • + 3 authors+ 0 author

5 June 2026

The transport behavior of multiphase flow in porous media is governed by the cross-scale coupling between fluid properties and pore structure, and serves as the theoretical foundation for core processes in fields such as energy development, undergrou...

(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
  • Article
  • Open Access
51 Citations
12,965 Views
15 Pages

Modeling of 3D Blood Flows with Physics-Informed Neural Networks: Comparison of Network Architectures

  • Philipp Moser,
  • Wolfgang Fenz,
  • Stefan Thumfart,
  • Isabell Ganitzer and
  • Michael Giretzlehner

27 January 2023

Machine learning-based modeling of physical systems has attracted significant interest in recent years. Based solely on the underlying physical equations and initial and boundary conditions, these new approaches allow to approximate, for example, the...

  • Article
  • Open Access
10 Citations
4,576 Views
14 Pages

15 April 2020

Irrigation return flow (RF) is a critical component of the water cycle in an agricultural watershed, influencing the flow regime of downstream river. As such, it should be accurately quantified when developing water resources management plans and pra...

(This article belongs to the Special Issue Study for Ungauged Catchments—Data, Models and Uncertainties)
  • Article
  • Open Access
29 Citations
7,459 Views
32 Pages

Groundwater Flow Modeling in Karst Aquifers: Coupling 3D Matrix and 1D Conduit Flow via Control Volume Isogeometric Analysis—Experimental Verification with a 3D Physical Model

  • Luka Malenica,
  • Hrvoje Gotovac,
  • Grgo Kamber,
  • Srdjan Simunovic and ,
  • Srikanth Allu and
  • Vladimir Divic
  • + 1 author+ 0 author

5 December 2018

A novel numerical model for groundwater flow in karst aquifers is presented. A discrete-continuum (hybrid) approach, in which a three-dimensional matrix flow is coupled with a one-dimensional conduit flow, was used. The laminar flow in the karst matr...

(This article belongs to the Section Hydraulics and Hydrodynamics)
  • Article
  • Open Access
6 Citations
3,737 Views
11 Pages

31 March 2022

Flow pattern and inclusion removal in a novel-designed crucible in the planar flow casting process were studied in the present paper. A color dye water experiment was used to show the flow field and validate the mathematical modeling. It was shown th...

(This article belongs to the Special Issue Numerical Modeling of Metallurgical Processes: Continuous Casting and Electroslag Remelting)
  • Article
  • Open Access
2 Citations
1,957 Views
18 Pages

19 May 2025

In a modern flexible interconnected distribution network, the dynamic coupling effect between the traditional AC network model and the power electronic converter significantly enhances the nonlinearity and non-convexity of power flow calculations. In...

(This article belongs to the Special Issue Applications of Smart Microgrids in Renewable Energy Development)
  • Article
  • Open Access
1 Citations
4,125 Views
22 Pages

Modeling flow field evolution accurately is important for numerous natural and engineering applications, such as pollutant dispersion in the ocean and atmosphere, yet remains challenging because of the highly nonlinear, multi-physics, and high-dimens...

(This article belongs to the Special Issue Artificial Intelligence and Its Application in Ocean Engineering)
  • Article
  • Open Access
1 Citations
1,660 Views
13 Pages

Measurement Method of Physical Parameters of Two-Phase Flow Based on Dual-Frequency Demodulation

  • Chunhui Song,
  • Chengzhi Yao,
  • Qinghong Liu,
  • Wenyu Sun and
  • Hui Zhang

23 November 2023

Oil-water two-phase flow commonly occurs in the process of crude oil electric dehydration. Here, through dynamic changes in the water content and conductivity of oil-water two-phase flow in the process of electric dehydration, the influence of water...

(This article belongs to the Section Electronic Sensors)
  • Article
  • Open Access
1 Citations
4,572 Views
11 Pages

A Self-Consistent Physical Model of the Bubbles in a Gas Solid Two-Phase Flow

  • Haiming Dong,
  • Jingfeng He,
  • Chenlong Duan and
  • Yuemin Zhao

2 March 2018

We develop a self-consistent physical model of bubbles in a gas solid two-phase flow. Using the Peng-Robonson state equation and a detailed specific heat ratio equation of bubbles, we obtain the kinetic equations of the bubbles on the basis of the Er...

(This article belongs to the Special Issue Modeling and Simulations for Membrane Processes of Industrial Interest)
  • Article
  • Open Access
6 Citations
4,892 Views
17 Pages

17 November 2023

To depict the pump power characteristics of radial centrifugal pumps, a physical model was developed. The model relies on established empirical equations. To parameterize the model for specific pumps, physically interpretable tuning factors were inte...

(This article belongs to the Section Industrial and Manufacturing Engineering)
  • Article
  • Open Access
8 Citations
3,894 Views
10 Pages

21 May 2020

This study examines the relationships between the flow in physical education (P.E.) class, school life stress, and aggression in adolescents. A total of 470 surveys collected from five different high schools in Daejeon, South Korea, were analyzed usi...

(This article belongs to the Section Sustainable Education and Approaches)
  • Feature Paper
  • Review
  • Open Access
21 Citations
12,633 Views
27 Pages

30 October 2020

Turbulent flows featuring additional scalar fields, such as chemical species or temperature, are common in environmental and industrial applications. Their physics is complex because of a broad range of scales involved; hence, efficient computational...

(This article belongs to the Special Issue Advances in the Chemical Mixing Process)
  • Article
  • Open Access
5 Citations
2,646 Views
33 Pages

17 August 2025

River flow forecasting remains a critical yet challenging task in hydrological science, owing to the inherent trade-offs between physics-based models and data-driven methods. While physics-based models offer interpretability and process-based insight...

  • Article
  • Open Access
41 Citations
9,849 Views
19 Pages

Data-Driven Pulsatile Blood Flow Physics with Dynamic Mode Decomposition

  • Milad Habibi,
  • Scott T. M. Dawson and
  • Amirhossein Arzani

14 July 2020

Dynamic mode decomposition (DMD) is a purely data-driven and equation-free technique for reduced-order modeling of dynamical systems and fluid flow. DMD finds a best fit linear reduced-order model that represents any given spatiotemporal data. In DMD...

(This article belongs to the Special Issue Classical and Modern Topics in Fluid Dynamics and Transport Phenomena)
  • Article
  • Open Access
651 Views
38 Pages

Physics-informed neural networks (PINNs) are difficult to train on strongly coupled, multi-objective systems: with fixed loss weights an otherwise identical run succeeds or diverges with the random seed, and a leading explanation attributes the failu...

  • Article
  • Open Access
2 Citations
1,864 Views
22 Pages

6 November 2025

Enhancing RAW images acquired under low-light conditions remains a fundamental yet challenging problem in computational photography and image signal processing. Recent deep learning-based approaches have shifted from real paired datasets toward synth...

(This article belongs to the Section Image and Video Processing)
  • Article
  • Open Access
3 Citations
4,046 Views
30 Pages

13 February 2021

Traditional vibration isolation systems, using natural rubber vibration isolators, display large peaks for the energy flow from the machine source and into the receiving foundation, at the unavoidable rigid body resonance frequencies. However, tough,...

(This article belongs to the Section Manufacturing Processes and Systems)
  • Article
  • Open Access
2 Citations
1,352 Views
22 Pages

3 April 2026

This paper employs Physics-Informed Neural Networks (PINNs) for the reconstruction and modelling of mean velocity profiles in fully developed turbulent channel flow over a high friction Reynolds number (Reτ). The network is trained with a high-fi...

(This article belongs to the Special Issue Advances in Computational and Experimental Fluid Dynamics, 2nd Edition)

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