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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.

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: (i) compressibility has a suppressive effect on the spike velocity, and this suppressive impact diminishes as the Atwood number ( A t ) increases. The influence of compressibility on bubble velocity shows a staged behavior with increasing A t . (ii) The impact of compressibility on the entropy production rate associated with the heat flow ( S ˙ N O E F ) is related to the stages of RTI evolution. Moreover, this staged impact of compressibility on S ˙ N O E F varies with A t . Compressibility exhibits an inhibitory effect on the entropy production rate associated with viscous stresses ( S ˙ N O M F ). (iii) By incorporating the morphological parameter of the proportion of area occupied by heavy fluid ( A h ), it is observed that the first minimum point of d A h / d t can serve as a criterion for identifying the point at which bubble velocity reaches its first maximum value. The series of physical cognition provides a more accurate understanding of the RTI kinetics and a helpful reference for the development of corresponding regulation techniques.

We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann model. Technically, two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes. One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures; the other is to evaluate the growth rate of KHI from the slopes of morphological functionals. Physically, it is found that the time histories of width of mixing layer, TNE intensity, and boundary length show high correlation and attain their maxima simultaneously. The viscosity effects are twofold, stabilize the KHI, and enhance both the local and global TNE intensities. Contrary to the monotonically inhibiting effects of viscosity, the heat conduction effects firstly refrain then enhance the evolution afterwards. The physical reasons are analyzed and presented.

A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.

Based on the framework of our previous work [H.L. Lai et al., Phys. Rev. E, 94, 023106 (2016)], we continue to study the effects of Knudsen number on two-dimensional Rayleigh–Taylor (RT) instability in compressible fluid via the discrete Boltzmann method. It is found that the Knudsen number effects strongly inhibit the RT instability but always enormously strengthen both the global hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) effects. Moreover, when Knudsen number increases, the Kelvin–Helmholtz instability induced by the development of the RT instability is difficult to sufficiently develop in the later stage. Different from the traditional computational fluid dynamics, the discrete Boltzmann method further presents a wealth of non-equilibrium information. Specifically, the two-dimensional TNE quantities demonstrate that, far from the disturbance interface, the value of TNE strength is basically zero; the TNE effects are mainly concentrated on both sides of the interface, which is closely related to the gradient of macroscopic quantities. The global TNE first decreases then increases with evolution. The relevant physical mechanisms are analyzed and discussed.

Rayleigh-Taylor (RT) instability widely exists in nature and engineering fields. How to better understand the physical mechanism of RT instability is of great theoretical significance and practical value. At present, abundant results of RT instability have been obtained by traditional macroscopic methods. However, research on the thermodynamic non-equilibrium (TNE) effects in the process of system evolution is relatively scarce. In this paper, the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT instability. The evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium region. Firstly, as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region, the average TNE intensity first increases and then reduces, and it increases with the specific heat ratio decreasing; the specific heat ratio has the same effect on the global strength of the viscous stress tensor. Secondly, the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex structure. Thirdly, under the competition between the temperature gradients and the contact area of the two fluids, the average intensity of the non-equilibrium quantity related to the heat flux shows diversity, and the influence of the specific heat ratio is also quite remarkable.

Based on the Hermite expansion approach, a type of discrete Boltzmann model is devised to simulate the open channel flows governed by the Saint‐Venant equations. In this model, a four‐discrete‐velocity set is adopted, and a local equilibrium distribution with the fourth‐order polynomials is kept to simulate the supercritical flows. To numerically solve the kinetic equation, the finite difference method is employed. The model is numerically validated by using four benchmark problems, i.e., dam‐break flows, hydraulic jump, steady flow over a bump, and the flume dam‐break flows with rectangular and triangular cross‐sections. Then, the thin film method is incorporated into the proposed model to deal with the wet‐dry boundaries, and this ability has been validated by two cases, i.e., the dam‐break flows in a converging–diverging channel and over a triangular obstacle. It is found that the present discrete Boltzmann model can accurately predict the subcritical, transcritical, and supercritical flows with source terms and wet‐dry boundaries.

A new kinetic model for multiphase flow was presented under the framework of the discrete Boltzmann method (DBM). Significantly different from the previous DBM, a bottom-up approach was adopted in this model. The effects of molecular size and repulsion potential were described by the Enskog collision model; the attraction potential was obtained through the mean-field approximation method. The molecular interactions, which result in the non-ideal equation of state and surface tension, were directly introduced as an external force term. Several typical benchmark problems, including Couette flow, two-phase coexistence curve, the Laplace law, phase separation, and the collision of two droplets, were simulated to verify the model. Especially, for two types of droplet collisions, the strengths of two non-equilibrium effects, D ¯ 2 * and D ¯ 3 * , defined through the second and third order non-conserved kinetic moments of ( f − f e q ) , are comparatively investigated, where f ( f e q ) is the (equilibrium) distribution function. It is interesting to find that during the collision process, D ¯ 2 * is always significantly larger than D ¯ 3 * , D ¯ 2 * can be used to identify the different stages of the collision process and to distinguish different types of collisions. The modeling method can be directly extended to a higher-order model for the case where the non-equilibrium effect is strong, and the linear constitutive law of viscous stress is no longer valid.

The effects of initial perturbations on the Rayleigh-Taylor instability (RTI), Kelvin-Helmholtz instability (KHI), and the coupled Rayleigh-Taylor-Kelvin-Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. It is found that the initial perturbation has a significant influence on the evolution of RTI. The sharper the interface, the faster the growth of bubble or spike. While the influence of initial interface shape on KHI evolution can be ignored. Based on the mean heat flux strength D 3,1, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism in the early stage of the RTKHI, (ii) the transition point from KHI-like to RTI-like for the case where the KHI dominates at earlier time and the RTI dominates at later time. It is found that the early main mechanism is related to the shape of the initial interface, which is represented by both the bilateral contact angle θ 1 and the middle contact angle θ 2. The increase of θ 1 and the decrease of θ 2 have opposite effects on the critical velocity. When θ 2 remains roughly unchanged at 90 degrees, if θ 1 is greater than 90 degrees (such as the parabolic interface), the critical shear velocity increases with the increase of θ 1, and the ellipse perturbation is its limiting case; If θ 1 is less than 90 degrees (such as the inverted parabolic and the inverted ellipse disturbances), the critical shear velocities are basically the same, which is less than that of the sinusoidal and sawtooth disturbances. The influence of inverted parabolic and inverted ellipse perturbations on the transition point of the RTKHI system is greater than that of other interfaces: (i) For the same amplitude, the smaller the contact angle θ 1, the later the transition point appears; (ii) For the same interface morphology, the disturbance amplitude increases, resulting in a shorter duration of the linear growth stage, so the transition point is greatly advanced.

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.