arXiv subjects

Aiguo Xu

Publications and source records attributed to Aiguo Xu.

At least 19 recordsLinked to original sources

arXiv2025

Stability analysis of discrete Boltzmann simulation for supersonic flows: Influencing factors, coupling mechanisms and optimization strategies

Supersonic flow simulations face challenges in trans-scale modeling, numerical stability, and complex field analysis due to inherent nonlinear, nonequilibrium, and multiscale characteristics. The discrete Boltzmann method (DBM) provides a multiscale kinetic modeling framework and analysis tool to capture complex discrete/nonequilibrium effects. While the numerical scheme plays a fundamental role in DBM simulations, a comprehensive stability analysis remains lacking. Similar to LBM, complexity mainly lies in the intrinsic coupling between velocity and spatiotemporal discretizations, compared with CFD. This study conducts von Neumann stability analysis to investigate key factors influencing DBM simulation stability, including phase-space discretization, thermodynamic nonequilibrium (TNE) levels, spatiotemporal schemes, initial conditions, and model parameters. Key findings include: (i) the moment-matching approach outperforms the expansion- and weighting-based methods in the test simulations; (ii) increased TNE enhances system nonlinearity and the intrinsic nonlinearity embedded in the model equations, amplifying instabilities; (iii) additional viscous dissipation based on distribution functions improves stability but distorts flow fields and alters constitutive relations; (iv) larger CFL numbers and relative time steps degrade stability, necessitating appropriate time-stepping strategies. To assess the stability regulation capability of DBMs across TNE levels, stability-phase diagrams and probability curves are constructed via morphological analysis within the moment-matching framework. These diagrams identify common stable parameter regions across model orders. This study reveals key factors and coupling mechanisms affecting DBM stability and proposes strategies for optimizing equilibrium distribution discretization, velocity design, and parameter selection in supersonic regimes.

physics.flu-dyn↗

arXiv2025

Droplet coalescence kinetics: Coalescence mechanisms and thermodynamic non-equilibrium effects under isothermal and non-isothermal conditions

This study investigates the droplet coalescence mechanisms and the interplay between various thermodynamic non-equilibrium (TNE) effects under isothermal and non-isothermal conditions kinetically. The main findings include: (1) Coalescence initiation and cut-through mechanisms: In non-isothermal conditions, the temperature rise caused by the release of latent heat during phase transition slightly increases the surface tension gradient (driving force) near the contact point of the two droplets, while significantly enhancing the pressure gradient (resistance). This results in a significantly prolonged coalescence initiation time compared to the isothermal case. In both cases, pressure extends the liquid-vapor interface in opposite directions, promoting the growth of the liquid bridge. (2) TNE effects: Latent heat-induced temperature rise significantly refrains the TNE intensity in thermal case. Before and after droplet contact, non-equilibrium quantities driven by the temperature gradient and those driven by the velocity gradient, alternate in dominating the coalescence process. This competition and interplay result in a more complex spatial and spatiotemporal evolution of TNE effects compared to the isothermal case. (3) Entropy production mechanisms: In the non-isothermal case, entropy production is contributed not only by $\bm {\Delta}^{\ast}_2$ but also by $\bm {\Delta}^{\ast}_{3,1}$, with the former being the dominant contributor. The temperature field reduces the entropy production rate, while extends its duration, and increases the total entropy production. This research provides kinetic insights for dynamic, cross-scale regulation and multifunctional integration of coalescence processes in industrial applications.

physics.flu-dyn↗

arXiv2025

Effects of reflection distance on Richtmyer-Meshkov instability in the reshock process: A discrete Boltzmann study

The Richtmyer-Meshkov (RM) instability occurs when a perturbed interface between two fluids undergoes impulsive acceleration due to a shock wave. In this paper, a numerical investigation of the RM instability during the reshock process is conducted using the two-component discrete Boltzmann method. The influence of reflection distance on the RM instability, including both hydrodynamic and thermodynamic non-equilibrium effects, is explored in detail. The interaction time between the reflected shock wave and the material interface varies with different reflection distances. Larger reflection distances lead to a longer evolution time of the material interface before reshock, resulting in more complex effects on the interface deformation, the mixing extent of the fluid system, and non-equilibrium behaviors after reshock. Additionally, while the reflection distance has a minimal impact on mixing entropy before the secondary impact, a significant difference emerges after the secondary impact. This suggests that the secondary impact enhances the evolution of the RM instability. Furthermore, non-equilibrium behaviors or quantities exhibit complex dynamics due to the influence of the transmitted shock wave, transverse waves, rarefaction waves, material interfaces, and dissipation/diffusion processes.

physics.flu-dyn↗

arXiv2025

Supersonic flow kinetics: Mesoscale structures, thermodynamic nonequilibrium effects and entropy production mechanisms

Supersonic flow is a typical nonlinear, nonequilibrium, multiscale, and complex phenomenon. This paper applies discrete Boltzmann method/model (DBM) to simulate and analyze these characteristics. A Burnett-level DBM for supersonic flow is constructed based on the Shakhov-BGK model. Higher-order analytical expressions for thermodynamic nonequilibrium effects are derived, providing a constitutive basis for improving traditional macroscopic hydrodynamics modeling. Criteria for evaluating the validity of DBM are established by comparing numerical and analytical solutions of nonequilibrium measures. The multiscale DBM is used to investigate discrete/nonequilibrium characteristics and entropy production mechanisms in shock regular reflection. The findings include: (a) Compared to NS-level DBM, the Burnett-level DBM offers more accurate representations of viscous stress and heat flux, ensures non-negativity of entropy production in accordance with the second law of thermodynamics, and exhibits better numerical stability. (b) Near the interfaces of incident and reflected shock waves, strong nonequilibrium driving forces lead to prominent nonequilibrium effects. By monitoring the timing and location of peak nonequilibrium quantities, the evolution characteristics of incident and reflected shock waves can be accurately and dynamically tracked. (c) In the intermediate state, the bent reflected shock and incident shock interface are wider and exhibit lower nonequilibrium intensities compared to their final state. (d) The Mach number enhances various kinds of nonequilibrium intensities in a power-law manner $D_{mn} \sim \mathtt{Ma}^α$. The power exponent $α$ and kinetic modes of nonequilibrium effects $m$ follows a logarithmic relation $α\sim \ln (m - m_0)$. This research provides new perspectives and kinetic insights into supersonic flow studies.

physics.flu-dyn↗

arXiv2025

Hydrodynamic and thermodynamic non-equilibrium characteristics of shock waves: Insights from the discrete Boltzmann method

Shock waves are typical non-equilibrium phenomena in nature and engineering, driven by hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) effects. However, the mechanisms underlying these non-equilibrium effects are not fully understood. This study develops the discrete Boltzmann method (DBM) by directly discretizing velocity space, allowing for the adequate capture of higher-order HNE and TNE effects. To reveal these mechanisms, we derive analytical solutions for distribution functions and TNE quantities at various orders using CE analysis, although DBM simulations do not rely on these theoretical derivations. Using argon shock structures as a case study, DBM simulations of interface profiles and thickness at the macroscopic level agree well with experimental data and direct simulation Monte Carlo results. At the mesoscopic level, DBM-derived distribution functions and TNE measures closely match their corresponding analytical solutions. The effect of Mach number on HNE is analyzed by examining the shape and thickness of density, temperature, and velocity interfaces. Key findings include: (i) Mach number induces a two-stage effect on macroscopic quantities, influencing both interface smoothness and thickness, and (ii) as Mach number increases, the region of strong compressibility shifts from the outflow region to the inflow region. As for TNE characteristics, increasing Mach number significantly amplifies TNE intensity and expands the non-equilibrium region. This research provides kinetic insights into the multiscale nature and effects of non-equilibrium characteristics in shock waves, offering theoretical references for constructing kinetic models that describe different types and orders of non-equilibrium effects.

physics.flu-dyn↗

arXiv2025

Multiscale thermodynamic nonequilibrium effects in Kelvin-Helmholtz instability and their relative importance

This study investigates the complex kinetics of thermodynamic nonequilibrium effects (TNEs) and their relative importance during the development of Kelvin-Helmholtz instability (KHI) using high-order discrete Boltzmann models (DBMs). First, the capabilities and differences among various discrete velocity sets in capturing TNEs and distribution functions are assessed. Practical guidelines for constructing discrete velocity stencils are proposed to enhance phase-space discretization and improve the robustness of high-order DBM simulation. At different stages of KHI and under varying initial conditions, multiscale TNEs, such as viscous stresses of different orders, emerge with distinct dominant roles. Specifically, three scenarios are identified: (i) regimes dominated by first-order TNEs,(ii) alternation between first- and second-order TNEs, and (iii) states where second-order TNEs govern the system's behavior. To quantitatively capture these transitions, criteria for TNE dominance at different orders in KHI evolution are established based on the relative thermodynamic nonequilibrium intensity ($R_{\text{TNE}}$). In scenarios dominated by second-order TNEs, differences between first-order and second-order models are compared in terms of macroscopic quantities, nonequilibrium effects, and kinetic moments, revealing the physical limitations of low-order models in capturing TNEs. Furthermore, the effectiveness, extensibility, and limitations of a representative high-order model are examined under second-order TNE-dominated conditions. To encapsulate these findings, a nonequilibrium phase diagram that visually maps the multiscale characteristics of KHI is constructed. This diagram not only provides intuitive insights into the dynamic interplay of different nonequilibrium effects but also serves as a kinetic roadmap for selecting suitable models under diverse nonequilibrium conditions.

physics.flu-dyn↗

arXiv2025

Thermodynamic nonequilibrium effects in three-dimensional high-speed compressible flows: Multiscale modeling and simulation via the discrete Boltzmann method

Three-dimensional (3D) high-speed compressible flow is a typical nonlinear, nonequilibrium, and multiscale complex flow. Traditional fluid mechanics models, based on the quasi-continuum assumption and near-equilibrium approximation, are insufficient to capture significant discrete effects and thermodynamic nonequilibrium effects (TNEs) as the Knudsen number increases. To overcome these limitations, a discrete Boltzmann modeling and simulation method, rooted in kinetic and mean-field theories, has been developed. By applying Chapman-Enskog multiscale analysis, the essential kinetic moment relations $\bm{\Phi}$ for characterizing second-order TNEs are determined. These relations are invariants in coarse-grained physical modeling, providing a unique mesoscopic perspective for analyzing TNE behaviors. A discrete Boltzmann model, accurate to the second-order in the Knudsen number, is developed to enable multiscale simulations of 3D supersonic flows. As key TNE measures, nonlinear constitutive relations (NCRs), are theoretically derived for the 3D case, offering a constitutive foundation for improving macroscopic fluid modeling. The NCRs in three dimensions exhibit greater complexity than their two-dimensional counterparts. This complexity arises from increased degrees of freedom, which introduce additional kinds of nonequilibrium driving forces, stronger coupling between these forces, and a significant increase in nonequilibrium components. At the macroscopic level, the model is validated through several classical test cases, ranging from 1D to 3D scenarios, from subsonic to supersonic regimes. At the mesoscopic level, the model accurately captures typical TNEs, such as viscous stress and heat flux, around mesoscale structures, across various scales and orders. This work provides kinetic insights that advance multiscale simulation techniques for 3D high-speed compressible flows.

physics.flu-dyn↗

arXiv2024

Kinetics of Rayleigh-Taylor instability in van der Waals fluid: the influence of compressibility

Early studies on Rayleigh-Taylor instability (RTI) primarily relied on the Navier-Stokes (NS) model. As research progresses, it becomes increasingly evident that the kinetic information that the NS model failed to capture is of great value for identifying and even controlling the RTI process; simultaneously, the lack of analysis techniques for complex physical fields results in a significant waste of data information. In addition, early RTI studies mainly focused on the incompressible case and the weakly compressible case. In the case of strong compressibility, the density of the fluid from the upper layer (originally heavy fluid) may become smaller than that of the surrounding (originally light) fluid, thus invalidating the early method of distinguishing light and heavy fluids based on density. In this paper, tracer particles are incorporated into a single-fluid discrete Boltzmann method (DBM) model that considers the van der Waals potential. By using tracer particles to label the matter-particle sources, a careful study of the matter-mixing and energy-mixing processes of the RTI evolution is realized in the single-fluid framework. The effects of compressibility on the evolution of RTI are examined mainly through the analysis of bubble and spike velocities, the ratio of area occupied by heavy fluid, and various entropy generation rates of the system. It is demonstrated that: (1) compressibility has a suppressive effect on the spike velocity, and this suppressive impact diminishes as the Atwood number ($At$) increases. The influence of compressibility on bubble velocity shows a staged behavior with increasing $At$. (2) The impact of compressibility on the entropy production rate associated with the heat flow (${\dot{S}_{NOEF}}$) is related to the stages of RTI evolution.

physics.flu-dyn↗

arXiv2024

Plasma kinetics: Discrete Boltzmann modelling and Richtmyer-Meshkov instability

A discrete Boltzmann model (DBM) for plasma kinetics is proposed. The constructing of DBM mainly considers two aspects. The first is to build a physical model with sufficient physical functions before simulation. The second is to present schemes for extracting more valuable information from massive data after simulation. For the first aspect, the model is equivalent to a magnetohydrodynamic model plus a coarse-grained model for the most relevant TNE behaviors including the entropy production rate. A number of typical benchmark problems including Orszag-Tang (OT) vortex problem are used to verify the physical functions of DBM. For the second aspect, the DBM use non-conserved kinetic moments of (f-feq) to describe non-equilibrium state and behaviours of complex system. The OT vortex problem and the Richtmyer-Meshkov instability (RMI) are practical applications of the second aspect. For RMI with interface inverse and re-shock process, it is found that, in the case without magnetic field, the non-organized momentum flux shows the most pronounced effects near shock front, while the non-organized energy flux shows the most pronounced behaviors near perturbed interface. The influence of magnetic field on TNE effects shows stages: before the interface inverse, the TNE strength is enhanced by reducing the interface inverse speed; while after the interface inverse, the TNE strength is significantly reduced. Both the global average TNE strength and entropy production rate contributed by non-organized energy flux can be used as physical criteria to identify whether or not the magnetic field is sufficient to prevent the interface inverse.

physics.plasm-ph↗

arXiv2024

Advances in the kinetics of heat and mass transfer in near-continuous complex flows

The study of macro continuous flow has a long history. Simultaneously, the exploration of heat and mass transfer in small systems with a particle number of several hundred or less has gained significant interest in the fields of statistical physics and nonlinear science. However, due to absence of suitable methods, the understanding of mesoscale behavior situated between the aforementioned two scenarios, which challenges the physical function of traditional continuous fluid theory and exceeds the simulation capability of microscopic molecular dynamics method, remains considerably deficient. This greatly restricts the evaluation of effects of mesoscale behavior and impedes the development of corresponding regulation techniques. To access the mesoscale behaviors, there are two ways: from large to small and from small to large. Given the necessity to interface with the prevailing macroscopic continuous modeling currently used in the mechanical engineering community, our study of mesoscale behavior begins from the side closer to the macroscopic continuum, that is from large to small. Focusing on some fundamental challenges encountered in modeling and analysis of near-continuous flows, we review the research progress of discrete Boltzmann method (DBM). The ideas and schemes of DBM in coarse-grained modeling and complex physical field analysis are introduced. The relationships, particularly the differences, between DBM and traditional fluid modeling as well as other kinetic methods are discussed. After verification and validation of the method, some applied researches including the development of various physical functions associated with discrete and non-equilibrium effects are illustrated. Future directions of DBM related studies are indicated.

physics.flu-dyn↗

arXiv2023

Droplet coalescence kinetics: thermodynamic non-equilibrium effects and entropy production mechanism

The thermodynamic non-equilibrium (TNE) effects and the relationships between various TNE effects and entropy production rate, morphology, kinematics, and dynamics during two initially static droplet coalescence are studied in detail via the discrete Boltzmann method. The temporal evolutions of the total TNE strength ($D^*$) and the total entropy production rate ($\dot S$) can both provide concise, effective and consistent physical criteria to distinguish the stages of droplet coalescence. Specifically, when $\bar D^*$ and $\dot S$ reach their maxima, it corresponds to the time when the liquid-vapor interface length changes the fastest; when $D^*$ and $\dot S$ reach their valleys, it corresponds to the moment of the droplet being the longest elliptical shape. During the merging process, the force contributed by surface tension in the coalescence direction acts as the primary promoting force for droplet coalescence and reaches its maximum concurrently with coalescent acceleration. In contrast, the force contributed by non-organized momentum fluxes (NOMFs) in the coalescing direction inhibits the merging process and reaches its maximum at the same time as $D^*$. For the coalescence of two unequal size droplets, the smaller droplet exhibits larger values for TNE intensity, merging velocity, driving force contributed by surface tension, and resistance contributed by NOMFs. Moreover, these values gradually increase with the initial radius ratio of the large and small droplets due to larger curvature. However, non-equilibrium components and forces related to shear velocity in the small droplet, are all smaller than those in the larger droplet and gradually decrease with the radius ratio.

physics.flu-dyn↗

arXiv2023

Viscous effects on morphological and thermodynamic non-equilibrium characterizations of shock-bubble interaction

A two-fluid discrete Boltzmann model with a flexible Prandtl number is formulated to study the shock-bubble interaction (SBI). This paper mainly focuses on the viscous effects on morphological and thermodynamic non-equilibrium (TNE) characterizations during the SBI process. Due to the rapid and brief nature of the SBI process, viscosity has a relatively limited influence on macroscopic parameters but significantly affects the TNE features of the fluid system. Morphologically, viscosity affects the configuration of the vortex pair, increases both the amplitudes of gradients of average density and average temperature of the fluid field, and reduces circulation of the bubble. As a higher viscosity fluid absorbs more energy from the shock wave, it leads to an increase in both the proportion of the high-density region and the corresponding boundary length for a fixed density threshold. The spatiotemporal features of TNE quantities are analyzed from multiple perspectives. The spatial configuration of these TNE quantities exhibits interesting symmetry, which aids in understanding the way and extent to which fluid unit deviates from the equilibrium state. Theoretically, viscosity influences these TNE quantities by affecting the transport coefficients and gradients of macroscopic quantity. Meanwhile, the viscosity increases the entropy production rate originating from the non-organized momentum flux mainly through amplifying the transport coefficient and enhances the entropy production rate contributed by the non-organized energy flux by raising the temperature gradient. These multi-perspective results collectively provide a relatively comprehensive depiction of the SBI.

physics.flu-dyn↗

arXiv2023

Brief introduction to discrete Boltzmann modeling and analysis method

We briefly introduce several fundamental problems that cause the creation of Discrete Boltzmann modeling and analysis Method(DBM), corresponding solutions, the relationship and difference between DBM and traditional fluid modeling and other kinetic methods, and some applications of DBM and discrete/non-equilibrium effects.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium kinetics effects in Richtmyer-Meshkov instability and reshock processes

Nonequilibrium kinetic effects are widespread in fluid systems and might have a significant impact on the inertial confinement fusion ignition process, and the entropy production rate is a key factor in accessing the compression process. In this work, we study the Richtmyer-Meshkov instability (RMI) and the reshock process by a two-fluid discrete Boltzmann method (DBM). Firstly, the DBM result for the perturbation amplitude evolution is in good agreement with that of experiment. Greatly different from the case of normal shocking on unperturbed plane interface between two uniform media, in the RMI case, the Thermodynamic Non-Equilibrium (TNE) quantities show complex but inspiring kinetic effects in the shocking process and behind the shock front. The kinetic effects are detected by two sets of TNE quantities. The first set are $\left |Δ_{2}^{ {\rm{*}}}\right |$,$\left |Δ_{3,1}^{ {\rm{*}}}\right |$, $\left | Δ_{3}^{ {\rm{*}}}\right |$, and $\left |Δ_{4,2}^{ {\rm{*}}}\right |$. All the four TNE measures abruptly increase in the shocking process. $\left |Δ_{3,1}^{ {\rm{*}}}\right |$ and $\left |Δ_{3}^{ {\rm{*}}}\right |$ show similar behaviors. They continue to increase in a much lower rate behind the shock front. $\left |Δ_{2}^{ {\rm{*}}}\right |$ and $\left |Δ_{4,2}^{ {\rm{*}}}\right |$ have different dimensions, but show similar behaviors. They quickly decrease to be very small behind the shock front. The second set of TNE quantities are ${\dot{S} _{NOMF}}$, ${\dot{S} _{NOEF}}$ and ${\dot{S} _{sum}}$. It is found that the mixing zone is the primary contribution region to the ${\dot{S} _{NOEF}}$, while the flow field region excluding mixing zone is the primary contribution region to the ${\dot{S} _{NOMF}}$. The light fluid has a higher entropy production rate than the heavy fluid.

physics.flu-dyn↗

arXiv2023

Specific-heat ratio effects on the interaction between shock wave and heavy-cylindrical bubble: based on discrete Boltzmann method

Specific-heat ratio effects on the interaction between a planar shock wave and a two-dimensional heavy-cylindrical bubble are studied by the discrete Boltzmann method. Snapshots of schlieren images and evolutions of characteristic scales, being consistent with experiments, are obtained. The specific-heat ratio effects on some relevant dynamic behaviors such as the bubble shape, deformation process, average motion, vortex motion, mixing degree of the fluid system are carefully studied, as well as the related Thermodynamic Non-Equilibriums (TNE) behaviors including the TNE strength, entropy production rate of the system. Specifically, it is found that the influence of specific-heat ratio on the entropy production contributed by non-organized energy flux (NOEF) is more significant than that caused by non-organized momentum flux (NOMF). Effects of specific-heat ratio on entropy production caused by NOMF and NOEF are contrary. The effects of specific-heat ratio on various TNE quantities show interesting differences. These differences consistently show the complexity of TNE flows which is still far from clear understanding.

physics.flu-dyn↗

arXiv2022

Discrete Boltzmann modeling of detonation: based on the Shakhov model

A Discrete Boltzmann Model(DBM) based on the Shakhov model for detonation is proposed. Compared with the DBM based on the Bhatnagar-Gross-Krook (BGK) model, the current model has a flexible Prandtl numbers and consequently can be applied to a much wider range of detonation phenomena. Besides the Hydrodynamic Non-Equilibrium (HNE) behaviors usually investigated by the Navier-Stokes model, the most relevant Thermodynamic Non-Equilibrium (TNE) effects can be probed by the current model. The model is validated by some well-known benchmarks,and some steady and unsteady detonation processes are investigated. As for the von Neumann peak relative to the wave front, it is found that (i) (within the range of numerical experiments) the peak heights of pressure, density and flow velocity increase exponentially with the Prandtl number, the maximum stress increases parabolically with the Prandtl number, and the maximum heat flux decreases exponentially with the Prandtl number; (ii) the peak heights of pressure, density, temperature and flow velocity and the maximum stress within the peak are parabolically increase with the Mach number, the maximum heat flux decreases exponentially with the Mach number.

physics.flu-dyn↗

arXiv2022

Discrete Boltzmann multi-scale modeling of non-equilibrium multiphase flows

The aim of this paper is twofold: the first is to formulate and validate a multi-scale discrete Boltzmann method (DBM) based on density functional kinetic theory for thermal multiphase flow systems, ranging from continuum to transition flow regime; the second is to present some new insights into the thermo-hydrodynamic non-equilibrium (THNE) effects in the phase separation process. Methodologically, DBM includes three main pillars: (i) the determination of the fewest kinetic moment relations, which are required by the description of significant THNE effects beyond the realm of continuum fluid mechanics, (ii) the construction of appropriate discrete equilibrium distribution function recovering all the desired kinetic moments, (iii) the detection, description, presentation and analysis of THNE based on the moments of the non-equilibrium distribution ($f-f^{(eq)}$). The incorporation of appropriate additional higher-order thermodynamic kinetic moments considerably extends the DBM's capability of handling larger values of the liquid-vapor density ratio, curbing spurious currents, and ensuring mass-momentum-energy conservation. Compared with the DBM with only first-order THNE (Gan et al. Soft Matter 11,5336), the model retrieves kinetic moments beyond the third-order super-Burnett level, and is accurate for weak, moderate, and strong THNE cases even when the local Knudsen number exceeds $1/3$. Physically, the ending point of the linear relation between THNE and the concerned physical parameter provides a distinct criterion to identify whether the system is near or far from equilibrium. Besides, the surface tension refrains the local THNE around the interface, but expands the THNE range and strengthens the THNE intensity away from the interface through interface smoothing and widening.

physics.flu-dyn↗

arXiv2022

Discrete Boltzmann modeling of high-speed compressible flows with various depths of non-equilibrium

The non-equilibrium high-speed compressible flows present wealthy applications in engineering and science. With the deepening of Thermodynamic Non-Equilibrium (TNE), higher-order non-conserved kinetic moments of the distribution function are needed to capture the main feature of the flow state and evolution process. Based on the ellipsoidal statistical Bhatnagar-Gross-Krook model, Discrete Boltzmann Models (DBMs) that consider various orders (from the first up to the sixth order) of TNE effects are developed to study flows in various depths of TNE. Specifically, at first, two types of one-dimensional Riemann problems and a Couette flow are used to show the model's capability to capture large flow structures with zero-order and first-order TNE effects, respectively. Then, a shock wave structure given by Direct simulation Monte Carlo is used to verify the model's capability to capture fine structures at the level of mean free path of molecules. Further, we focus on the TNE degree of two colliding fluids. A five-component vector $\mathbf{S}_{TNE} = (τ, Δ\mathbf{u}, ΔT, \bm{Δ_{2}^{*}},\bm{Δ_{3,1}^{*}})$ is introduced to roughly characterize the TNE degree. It is found that the TNE strengths obtained from various perspectives are different. These findings demonstrate that the inadequacy of focusing only on the few kinetic moments appearing in Navier-Stokes increases with the degree of discreteness and deviation from thermodynamic equilibrium. Finally, a two-dimensional free jet is simulated to indicate that, to obtain satisfying hydrodynamic quantities, the DBM should include at least up to the third-order TNE effects.

physics.flu-dyn↗