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Entropy
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Kinetic Theory-Based Methods in Fluid Dynamics, 2nd Edition
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Kinetic Theory-Based Methods in Fluid Dynamics, 2nd Edition

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 8807

Special Issue Editors

Prof. Dr. Chengwen Zhong

E-Mail Website
Guest Editor
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
Interests: computational fluid dynamics; nonequilibrium flows; lattice boltzmann method; gas kinetic theory; discrete velocity methods; multi-scale numerical methods
Prof. Dr. Liming Yang

E-Mail Website
Guest Editor
Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Interests: computational fluid dynamics; gas kinetic scheme; discrete velocity method; lattice boltzmann method; fluid-structure interaction
Special Issues, Collections and Topics in MDPI journals
Dr. Congshan Zhuo

E-Mail Website
Guest Editor
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
Interests: computational fluid dynamics; aerodynamics; nonequilibrium flows; gas kinetic theory; lattice boltzmann method
Dr. Sha Liu

E-Mail Website
Guest Editor
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China.
Interests: complex science; gas kinetic theory; multi-scale physics; rarefied gas dynamics; computational fluid dynamics; non-equilibrium flows; multi-scale numerical methods and predictions
Dr. Liangqi Zhang

E-Mail Website
Guest Editor
College of Aerospace Engineering, Chongqing University, Chongqing 400044, China
Interests: computational fluid dynamics; gas kinetic scheme, discrete velocity method, lattice boltzmann method; fluid-structure interaction
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The kinetic theory is derived from statistical mechanics at the mesoscopic scale. The kinetic theory exceeds the macroscopic interpretations (expressed by the Navier–Stokes equations) in theoretical generality: no limits from the continuum assumption. Within the framework of kinetic theory, several approaches have been developed, including the lattice Boltzmann method (LBM), the discrete velocity method (DVM), the gas kinetic scheme (GKS), the unified gas-kinetic scheme (UGKS), the discrete unified gas kinetic scheme (DUGKS), the gas-kinetic unified algorithm (GKUA), the unified gas-kinetic wave-particle method (UGKWP), the simplified unified wave-particle method (SUWP), the unified stochastic particle method (USP), the nonlinear coupled constitutive relation method (NCCR), the 13/26-moment equations method (G13/26), and many more. These approaches serve distinct and essential roles in nearly all fields of fluid dynamics research.

The inherent limitations of kinetic theory-based solutions in engineering issues sometimes restrict their wider use. In most cases, kinetic theory-based approaches utilize far more computer memory than macroscopic methods. Furthermore, high-fidelity simulations of physical issues outside of the continuum regime are typically time-consuming. As a result, the research community urgently needs to develop and use strong and efficient kinetic theory-based solutions for broad fluid dynamics challenges.

This Special Issue aims to be a forum for presenting recent progress in the very active area of kinetic theory-based methods in fluid dynamics. Papers dealing with the development of kinetic theory-related numerical schemes and their applications to fluid dynamics problems are particularly welcome.

Prof. Dr. Chengwen Zhong
Prof. Dr. Liming Yang
Dr. Congshan Zhuo
Dr. Sha Liu
Dr. Liangqi Zhang
Guest Editors

Manuscript Submission Information

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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. Entropy 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 2600 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

  • lattice Boltzmann method
  • discrete velocity method
  • unified gas-kinetic scheme
  • discrete unified gas kinetic scheme
  • gas-kinetic unified algorithm
  • unified gas-kinetic wave-particle method
  • simplified unified wave-particle method
  • unified stochastic particle
  • gas-kinetic scheme and others
  • kinetic theory-based flux solvers
  • general synthetic iterative scheme
  • nonlinear coupled constitutive relation
  • 13/26-moment equations
  • high-order methods
  • multiphase/multiphysics flows
  • microflows
  • rarefied flows
  • flows in porous media
  • particle-laden flows

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Related Special Issue

Published Papers (6 papers)

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Research

28 pages, 6126 KiB  
Article
Gas Kinetic Scheme Coupled with High-Speed Modifications for Hypersonic Transition Flow Simulations
by Chengrui Li, Wenwen Zhao, Hualin Liu, Youtao Xue, Yuxin Yang and Weifang Chen
Entropy 2024, 26(2), 173; https://doi.org/10.3390/e26020173 - 18 Feb 2024
Cited by 1 | Viewed by 1168
Abstract
The issue of hypersonic boundary layer transition prediction is a critical aerodynamic concern that must be addressed during the aerodynamic design process of high-speed vehicles. In this context, we propose an advanced mesoscopic method that couples the gas kinetic scheme (GKS) with the [...] Read more.
The issue of hypersonic boundary layer transition prediction is a critical aerodynamic concern that must be addressed during the aerodynamic design process of high-speed vehicles. In this context, we propose an advanced mesoscopic method that couples the gas kinetic scheme (GKS) with the Langtry–Menter transition model, including its three high-speed modification methods, tailored for accurate predictions of high-speed transition flows. The new method incorporates the turbulent kinetic energy term into the Maxwellian velocity distribution function, and it couples the effects of high-speed modifications on turbulent kinetic energy within the computational framework of the GKS solver. This integration elevates both the transition model and its high-speed enhancements to the mesoscopic level, enhancing the method’s predictive capability. The GKS-coupled mesoscopic method is validated through a series of test cases, including supersonic flat plate simulation, multiple hypersonic cone cases, the Hypersonic International Flight Research Experimentation (HIFiRE)-1 flight test, and the HIFiRE-5 case. The computational results obtained from these cases exhibit favorable agreement with experimental data. In comparison with the conventional Godunov method, the new approach encompasses a broader range of physical mechanisms, yielding computational results that closely align with the true physical phenomena and marking a notable elevation in computational fidelity and accuracy. This innovative method potentially satisfies the compelling demand for developing a precise and rapid method for predicting hypersonic boundary layer transition, which can be readily used in engineering applications. Full article
(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics, 2nd Edition)
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29 pages, 7999 KiB  
Article
Wetting and Spreading Behavior of Axisymmetric Compound Droplets on Curved Solid Walls Using Conservative Phase Field Lattice Boltzmann Method
by Yue Wang and Jun-Jie Huang
Entropy 2024, 26(2), 172; https://doi.org/10.3390/e26020172 - 17 Feb 2024
Viewed by 1264
Abstract
Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this [...] Read more.
Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this paper, the influence of the properties of curved solid wall (including the shape, curvature, and contact angle) on the wetting behavior of compound droplets is explored. The axisymmetric lattice Boltzmann method, based on the conservative phase field formulation for ternary fluids, was used to numerically study the wetting and spreading of a compound droplet of the Janus type on various curved solid walls at large density ratios, focusing on whether the separation of compound droplets occurs. Several types of wall geometries were considered, including a planar wall, a concave wall with constant curvature, and a convex wall with fixed or variable curvature (specifically, a prolate or oblate spheroid). The effects of surface wettability, interfacial angles, and the density ratio (of droplet to ambient fluid) on the wetting process were also explored. In general, it was found that, under otherwise identical conditions, droplet separation tends to happen more likely on more hydrophilic walls, under larger interfacial angles (measured inside the droplet), and at larger density ratios. On convex walls, a larger radius of curvature of the surface near the droplet was found to be helpful to split the Janus droplet. On concave walls, as the radius of curvature increases from a small value, the possibility to observe droplet separation first increases and then decreases. Several phase diagrams on whether droplet separation occurs during the spreading process were produced for different kinds of walls to illustrate the influences of various factors. Full article
(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics, 2nd Edition)
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26 pages, 1096 KiB  
Article
A Unified Gas-Kinetic Particle Method for Radiation Transport in an Anisotropic Scattering Medium
by Yuan Hu, Chang Liu, Huayun Shen, Gang Xiao and Jinghong Li
Entropy 2024, 26(1), 52; https://doi.org/10.3390/e26010052 - 6 Jan 2024
Cited by 1 | Viewed by 1301
Abstract
In this paper, a unified gas kinetic particle (UGKP) method is developed for radiative transfer in both absorbing and anisotropic scattering media. This numerical method is constructed based on our theoretical work on the model reduction for an anisotropic scattering system. The macroscopic [...] Read more.
In this paper, a unified gas kinetic particle (UGKP) method is developed for radiative transfer in both absorbing and anisotropic scattering media. This numerical method is constructed based on our theoretical work on the model reduction for an anisotropic scattering system. The macroscopic solver of this method directly solves the macroscopic anisotropic diffusion equations, eliminating the need to solve higher-order moment equations. The reconstruction of macroscopic scattering source in the microscopic solver, based on the multiscale equivalent phase function we proposed in this work, has also been simplified as one single scattering process, significantly reducing the computational costs. The proposed method has also the property of asymptotic preserving. In the optically thick regime, the proposed method solves the diffusion limit equations for an anisotropic system. In the optically thin regime, the kinetic processes of photon transport are simulated. The consistency and efficiency of the proposed method have been validated by numerical tests in a wide range of flow regimes. The novel equivalent scattering source reconstruction can be used for various transport processes, and the proposed numerical scheme is widely applicable in high-energy density engineering applications. Full article
(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics, 2nd Edition)
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21 pages, 2211 KiB  
Article
Effects of Inclined Interface Angle on Compressible Rayleigh–Taylor Instability: A Numerical Study Based on the Discrete Boltzmann Method
by Bailing Chen, Huilin Lai, Chuandong Lin and Demei Li
Entropy 2023, 25(12), 1623; https://doi.org/10.3390/e25121623 - 5 Dec 2023
Viewed by 1257
Abstract
Rayleigh–Taylor (RT) instability is a basic fluid interface instability that widely exists in nature and in the engineering field. To investigate the impact of the initial inclined interface on compressible RT instability, the two-component discrete Boltzmann method is employed. Both the thermodynamic non-equilibrium [...] Read more.
Rayleigh–Taylor (RT) instability is a basic fluid interface instability that widely exists in nature and in the engineering field. To investigate the impact of the initial inclined interface on compressible RT instability, the two-component discrete Boltzmann method is employed. Both the thermodynamic non-equilibrium (TNE) and hydrodynamic non-equilibrium (HNE) effects are studied. It can be found that the global average density gradient in the horizontal direction, the non-organized energy fluxes, the global average non-equilibrium intensity and the proportion of the non-equilibrium region first increase and then reduce with time. However, the global average density gradient in the vertical direction and the non-organized moment fluxes first descend, then rise, and finally descend. Furthermore, the global average density gradient, the typical TNE intensity and the proportion of non-equilibrium region increase with increasing angle of the initial inclined interface. Physically, there are three competitive mechanisms: (1) As the perturbed interface elongates, the contact area between the two fluids expands, which results in an increasing gradient of macroscopic physical quantities and leads to a strengthening of the TNE effects. (2) Under the influence of viscosity, the perturbation pressure waves on both sides of the material interface decrease with time, which makes the gradient of the macroscopic physical quantity decrease, resulting in a weakening of the TNE strength. (3) Due to dissipation and/or mutual penetration of the two fluids, the gradient of macroscopic physical quantities gradually diminishes, resulting in a decrease in the intensity of the TNE. Full article
(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics, 2nd Edition)
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28 pages, 6694 KiB  
Article
Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes
by Linchang Han, Liming Yang, Zhihui Li, Jie Wu, Yinjie Du and Xiang Shen
Entropy 2023, 25(12), 1609; https://doi.org/10.3390/e25121609 - 30 Nov 2023
Viewed by 1128
Abstract
How to improve the computational efficiency of flow field simulations around irregular objects in near-continuum and continuum flow regimes has always been a challenge in the aerospace re-entry process. The discrete velocity method (DVM) is a commonly used algorithm for the discretized solutions [...] Read more.
How to improve the computational efficiency of flow field simulations around irregular objects in near-continuum and continuum flow regimes has always been a challenge in the aerospace re-entry process. The discrete velocity method (DVM) is a commonly used algorithm for the discretized solutions of the Boltzmann-BGK model equation. However, the discretization of both physical and molecular velocity spaces in DVM can result in significant computational costs. This paper focuses on unlocking the key to accelerate the convergence in DVM calculations, thereby reducing the computational burden. Three versions of DVM are investigated: the semi-implicit DVM (DVM-I), fully implicit DVM (DVM-II), and fully implicit DVM with an inner iteration of the macroscopic governing equation (DVM-III). In order to achieve full implicit discretization of the collision term in the Boltzmann-BGK equation, it is necessary to solve the corresponding macroscopic governing equation in DVM-II and DVM-III. In DVM-III, an inner iterative process of the macroscopic governing equation is employed between two adjacent DVM steps, enabling a more accurate prediction of the equilibrium state for the full implicit discretization of the collision term. Fortunately, the computational cost of solving the macroscopic governing equation is significantly lower than that of the Boltzmann-BGK equation. This is primarily due to the smaller number of conservative variables in the macroscopic governing equation compared to the discrete velocity distribution functions in the Boltzmann-BGK equation. Our findings demonstrate that the fully implicit discretization of the collision term in the Boltzmann-BGK equation can accelerate DVM calculations by one order of magnitude in continuum and near-continuum flow regimes. Furthermore, the introduction of the inner iteration of the macroscopic governing equation provides an additional 1–2 orders of magnitude acceleration. Such advancements hold promise in providing a computational approach for simulating flows around irregular objects in near-space environments. Full article
(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics, 2nd Edition)
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43 pages, 6932 KiB  
Article
Novel Schemes of No-Slip Boundary Conditions for the Discrete Unified Gas Kinetic Scheme Based on the Moment Constraints
by Wenqiang Guo and Guoxiang Hou
Entropy 2023, 25(5), 780; https://doi.org/10.3390/e25050780 - 10 May 2023
Viewed by 1994
Abstract
The boundary conditions are crucial for numerical methods. This study aims to contribute to this growing area of research by exploring boundary conditions for the discrete unified gas kinetic scheme (DUGKS). The importance and originality of this study are that it assesses and [...] Read more.
The boundary conditions are crucial for numerical methods. This study aims to contribute to this growing area of research by exploring boundary conditions for the discrete unified gas kinetic scheme (DUGKS). The importance and originality of this study are that it assesses and validates the novel schemes of the bounce back (BB), non-equilibrium bounce back (NEBB), and Moment-based boundary conditions for the DUGKS, which translate boundary conditions into constraints on the transformed distribution functions at a half time step based on the moment constraints. A theoretical assessment shows that both present NEBB and Moment-based schemes for the DUGKS can implement a no-slip condition at the wall boundary without slip error. The present schemes are validated by numerical simulations of Couette flow, Poiseuille flow, Lid-driven cavity flow, dipole–wall collision, and Rayleigh–Taylor instability. The present schemes of second-order accuracy are more accurate than the original schemes. Both present NEBB and Moment-based schemes are more accurate than the present BB scheme in most cases and have higher computational efficiency than the present BB scheme in the simulation of Couette flow at high Re. The present Moment-based scheme is more accurate than the present BB, NEBB schemes, and reference schemes in the simulation of Poiseuille flow and dipole–wall collision, compared to the analytical solution and reference data. Good agreement with reference data in the numerical simulation of Rayleigh–Taylor instability shows that they are also of use to the multiphase flow. The present Moment-based scheme is more competitive in boundary conditions for the DUGKS. Full article
(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics, 2nd Edition)
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