arXiv subjects

Chuandong Lin

Publications and source records attributed to Chuandong Lin.

At least 19 recordsLinked to original sources

arXiv2026

Discrete Boltzmann model at Burnett level for compressible multicomponent flows under external forces

This work extends the Burnett-level discrete Boltzmann model (DBM) from single-component to multicomponent compressible flows under external forces, building on the fundamental framework of the high-precision discrete kinetic method. A high-isotropy 25-discrete-velocity set is adopted to guarantee numerical stability and spatial symmetry, while a rigorous moment-matching strategy is developed to construct the equilibrium distribution function and external force term. Different from the single-component counterpart, the present model intrinsically incorporates interspecies mass diffusion effects and multi-component thermodynamic nonequilibrium behaviors, which are critical for complex compressible multicomponent systems. The Chapman--Enskog expansion verifies that the proposed model can exactly recover the Burnett-level governing equations for forced multicomponent compressible flows in the continuum limit. Five canonical benchmark cases, including multicomponent mass diffusion, compressible Sod shock tube, thermal Couette flow, Kelvin--Helmholtz instability, and Rayleigh--Taylor instability, are systematically performed. Numerical results demonstrate that the developed Burnett-level multicomponent DBM achieves high accuracy and robustness in capturing both hydrodynamic evolution and multicomponent nonequilibrium characteristics under external forces.

physics.flu-dyn↗

arXiv2026

A One-Dimensional Discrete Boltzmann Method for Multidimensional Compressible Flows

A simple and efficient one-dimensional discrete Boltzmann method is developed for compressible flows with tunable specific heat ratios by incorporating extra degrees of freedom. To guarantee Galilean invariance in numerical simulations, a discrete velocity set is constructed with high spatial symmetry. Furthermore, an operator-splitting scheme is proposed to extend the one-dimensional kinetic formulation to simulations of one-, two-, and three-dimensional flow systems within a unified framework. The proposed model and numerical method are verified and validated against several benchmark problems, including the Sod shock tube, Lax shock tube, 2D Riemann problem, uniform translational flow, and acoustic wave propagation. The results demonstrate the accuracy, robustness, and flexibility of the present approach for compressible flow simulations.

physics.flu-dyn↗

arXiv2025

Burnett-level multi-relaxation-time central-moment discrete Boltzmann modeling of reactive flows

A multi-relaxation-time central-moment discrete Boltzmann method (CDBM) is developed for compressible reactive flows, incorporating the effects of chemical reactions. The Chapman--Enskog multiscale analysis demonstrates that the model recovers the Burnett equations in the hydrodynamic limit, with tunable specific heat ratios and Prandtl numbers. Within the CDBM framework, a unified Boltzmann equation governs the evolution of hydrodynamic variables, thermodynamic quantities, and higher-order central moments. The collision and reaction term are consistently computed via matrix inversion method. A two-dimensional twenty-five discrete velocities, exhibiting favorable spatial symmetry, is constructed and employed. The model is validated through simulations of the thermal Couette flow, homogeneous chemical reaction, steady detonation wave, and collision of two detonation waves. This work presents a versatile numerical simulation tool capable of addressing complex reactive flows characterized by hydrodynamic and thermodynamic nonequilibrium effects, applicable to both scientific research and engineering practice.

physics.flu-dyn↗

arXiv2025

Kinetic study of compressible Rayleigh-Taylor instability with time-varying acceleration

Rayleigh-Taylor (RT) instability commonly arises in compressible systems with time-dependent acceleration in practical applications. To capture the complex dynamics of such systems, a two-component discrete Boltzmann method is developed to systematically investigate the compressible RT instability driven by variable acceleration. Specifically, the effects of different acceleration periods, amplitudes, and phases are systematically analyzed. The simulation results are interpreted from three key perspectives: the density gradient, which characterizes the spatial variation in density; the thermodynamic non-equilibrium strength, which quantifies the system's deviation from local thermodynamic equilibrium; and the fraction of non-equilibrium regions, which captures the spatial distribution of non-equilibrium behaviors. Notably, the fluid system exhibits rich and diverse dynamic patterns resulting from the interplay of multiple competing physical mechanisms, including time-dependent acceleration, RT instability, diffusion, and dissipation effects. These findings provide deeper insights into the evolution and regulation of compressible RT instability under complex driving conditions.

physics.flu-dyn↗

arXiv2025

Investigating the Effect of Relaxation Time on Richtmyer-Meshkov Instability under Reshock Impact: A Two-Component Discrete Boltzmann Method Study

The Richtmyer-Meshkov (RM) instability plays an important role in various natural and engineering fields, such as inertial confinement fusion. In this work, the effect of relaxation time on the RM instability under reshock impact is investigated by using a two-component discrete Boltzmann method. The hydrodynamic and thermodynamic characteristics of the fluid system are comprehensively analyzed from the perspectives of the density gradient, vorticity, kinetic energy, mixing degree, mixing width, and non-equilibrium intensity. Simulation results indicate that for larger relaxation time, the diffusion and dissipation are enhanced, the physical gradients decrease, and the growth of the interface is suppressed. Furthermore, the non-equilibrium manifestations show complex patterns, driven by the competitive physical mechanisms of the diffusion, dissipation, shock wave, rarefaction wave, transverse wave, and fluid instabilities. These findings provide valuable insights into the fundamental mechanism of compressible fluid flows.

physics.flu-dyn↗

arXiv2025

Central-moment-based discrete Boltzmann modeling of compressible flows

In this work, a central-moment-based discrete Boltzmann method (CDBM) is constructed for fluid flows with variable specific heat ratios. The central kinetic moments are employed to calculate the equilibrium discrete velocity distribution function in the CDBM. In comparison to previous incompressible central-moment-based lattice Boltzmann method, the CDBM possesses the capability of investigating compressible flows with thermodynamic nonequilibrium effects beyond conventional hydrodynamic models. Unlike all existing DBMs which are constructed in raw-moment space, the CDBM stands out by directly providing the nonequilibrium effects related to the thermal fluctuation. The proposed method has been rigorously validated using benchmarks of the Sod shock tube, Lax shock tube, shock wave phenomena, two-dimensional sound wave, and the Taylor-Green vortex flow. The numerical results exhibit an exceptional agreement with theoretical predictions.

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

Kinetic modelling of economic markets with individual and collective transactions

Two kinetic exchange models are proposed to explore the dynamics of closed economic markets characterized by random exchanges, saving propensities, and collective transactions. Model I simulates a system where individual transactions occur among agents with saving tendencies, along with collective transactions between groups. Model II restricts individual transactions to agents within the same group, but allows for collective transactions between groups. A three-step trading process--comprising intergroup transactions, intragroup redistribution, and individual exchanges--is developed to capture the dual-layered market dynamics. The saving propensity is incorporated using the Chakraborti-Chakrabarti model, applied to both individual and collective transactions. Results reveal that collective transactions increase wealth inequality by concentrating wealth within groups, as indicated by higher Gini coefficients and Kolkata indices. In contrast, individual transactions across groups mitigate inequality through more uniform wealth redistribution. The interplay between saving propensities and collective transactions governs deviation degree and entropy, which display inverse trends. Higher saving propensities lead to deviations from the Boltzmann-Gibbs equilibrium, whereas specific thresholds result in collective transaction dominance, producing notable peaks or troughs in these metrics. These findings underscore the critical influence of dual-layered market interactions on wealth distribution and economic dynamics.

nlin.CG↗

arXiv2025

Burnett-level discrete Boltzmann modeling of compressible flows under force

In this paper, a Burnett-level discrete Boltzmann model (DBM) is proposed for the compressible flow in a force field, and a discrete velocity set with 25 velocities is constructed for the DBM, featuring good spatial symmetry. In the discrete Boltzmann equation, both the discrete equilibrium distribution function and the force term satisfy 25 independent moment relations and are computed with the matrix inversion method. This approach ensures high physical accuracy, computational efficiency, and ease of implementation. Through the Chapman-Enskog expansion analysis, it is demonstrated that the current DBM can recover the Burnett equations for the compressible system under force in the continuum limit. Moreover, the DBM has the capability of capturing essential thermodynamic nonequilibrium behaviors. Finally, the model is validated through five typical benchmarks, including the free falling, Sod shock tube, sound wave, thermal Couette flow, and Rayleigh-Taylor instability.

physics.flu-dyn↗

arXiv2025

Lattice Boltzmann simulation reveals supercritical bifurcation in flow mode transitions of power-law fluids in the four-roll mill

The four-roll mill has been traditionally viewed as a device generating simple extensional flow with a central stagnation point. Our systematic investigation using a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model reveals unexpected richness in the flow physics, identifying two previously unreported supercritical bifurcation modes: a quadrifoliate vortex mode featuring four symmetrical counter-rotating vortices, and a dumbbell-shaped quad-vortex mode where vortices detach from but remain symmetric about the stagnation point. The numerical framework, representing the first successful extension of TRT-RLB method to power-law fluid dynamics, enables comprehensive mapping of flow characteristics across Reynolds numbers ($1 \leq Re \leq 50$), power-law indices ($0.7 \leq n \leq 1.3$), and geometric configurations. The transition from quadrifoliate vortex mode exhibits distinct pathways depending on the power-law index: at relatively small $n$, the flow undergoes a direct supercritical bifurcation to simple extensional flow, while at relatively large $n$, it evolves through an intermediate dumbbell-shaped state. Among geometric parameters, the roller radius $r$ emerges as the dominant factor controlling bifurcation points and vortex dimensions, whereas the roller-container gap $\delta$ exerts minimal influence on flow regimes. The transitions between flow modes can be precisely characterized through the evolution of vortex dimensions and velocity gradients at the stagnation point, providing quantitative criteria for flow regime identification. These findings enrich our fundamental understanding of bifurcation phenomena in extensional devices and provide quantitative guidelines for achieving desired flow patterns in four-roll mill applications.

physics.flu-dyn↗

arXiv2024

Discrete Boltzmann model with split collision for nonequilibrium reactive flows

A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based on a unified set of discrete Boltzmann equations that describes the evolution of each chemical species with adjustable acceleration, specific heat ratio, and Prandtl number. On the righ-hand side of discrete Boltzmann equations, the collision, force, and reaction terms denote the change rates of distribution functions due to self- and cross-collisions, external forces, and chemical reactions, respectively. The source terms can be calculated in three ways, among which the matrix inversion method possesses the highest physical accuracy and computational efficiency. Through Chapman-Enskog analysis, it is proved that the DBM is consistent with the reactive Navier-Stokes equations, Fick's law and Stefan-Maxwell diffusion equation in the hydrodynamic limit. Compared with the one-step-relaxation model, the split collision model offers a detailed and precise measurement of hydrodynamic, thermodynamic, and chemical nonequilibrium effects. Finally, the model is validated by six benchmarks, including multicomponent diffusion, mixture in the force field, Kelvin-Helmholtz instability, flame at constant pressure, opposing chemical reaction, and steady detonation.

cond-mat.stat-mech↗

arXiv2022

Kinetic modeling of economic markets with heterogeneous saving propensities

The lattice gas automaton (LGA) is proposed for a closed economic market of agents with heterogeneous saving interests. There are two procedures in the standard LGA, i.e., "propagation" + "transaction". If the propagation step is removed and the transaction is conducted among all agents, the LGA reduces to a more simplified kinetic model. In addition, two dealing rules are imposed on the transaction phase. Under Rule I, the trading volume depends on the average saving propensities of an arbitrary pair of agents in trade. Under Rule II, the exchange is governed by a stochastic parameter between the saving propensities of two traders. Besides, two sampling methods are introduced for the random selection of two agents in the iterative process. Specifically, Sampling I is the sampling with replacement and is easier to program. Sampling II is the sampling without replacement and owns a higher computing efficiency. There are slight differences between the stationary wealth distributions simulated by using the two transaction rules and sampling approaches. In addition, the accuracy, robustness and efficiency of the econophysics models are validated by typical numerical tests. The reduced LGA without the propagation step owns a higher computational efficiency than the standard LGA. Moreover, the impact of saving propensities of agents in two groups on the wealth distributions is studied, and the influence of proportions of agents is investigated as well. To quantitatively measure the wealth inequality, the Gini coefficients, Kolkata indices, and deviation degrees of all agents and two groups are simulated and analyzed in detail. This work is helpful to further analyze and predict the dynamic process of wealth distribution in the realistic economic market.

physics.soc-ph↗

arXiv2021

Nonequilibrium effects of reactive flow based on gas kinetic theory

How to accurately probe chemically reactive flows with essential thermodynamic nonequilibrium effects is an open issue. Via the Chapman-Enskog analysis, the local nonequilibrium particle velocity distribution function is derived from the gas kinetic theory. It is demonstrated theoretically and numerically that the distribution function depends on the physical quantities and derivatives, and is independent of the chemical reactions directly. Based on the simulation results of the discrete Boltzmann model, the departure between equilibrium and nonequilibrium distribution functions is obtained and analyzed around the detonation wave. Besides, it has been verified for the first time that the kinetic moments calculated by summations of the discrete distribution functions are close to those calculated by integrals of their original forms.

physics.flu-dyn↗

arXiv2021

Specific heat ratio effects of compressible Rayleigh-Taylor instability studied by discrete Boltzmann method

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.

physics.flu-dyn↗

arXiv2020

A simple and efficient kinetic model for wealth distribution with saving propensity effect: based on lattice gas automaton

The dynamics of wealth distribution plays a critical role in the economic market, hence an understanding of its nonequilibrium statistical mechanics is of great importance to human society. For this aim, a simple and efficient one-dimensional (1D) lattice gas automaton (LGA) is presented for wealth distribution of agents with or without saving propensity. The LGA comprises two stages, i.e., random propagation and economic transaction. During the former phase, an agent either remains motionless or travels to one of its neighboring empty sites with a certain probability. In the subsequent procedure, an economic transaction takes place between a pair of neighboring agents randomly. It requires at least 4 neighbors to present correct simulation results. The LGA reduces to the simplest model with only random economic transaction if all agents are neighbors and no empty sites exist. The 1D-LGA has a higher computational efficiency than the 2D-LGA and the famous Chakraborti-Chakrabarti economic model. Finally, the LGA is validated with two benchmarks, i.e., the wealth distributions of individual agents and dual-earner families. With the increasing saving fraction, both the Gini coefficient and Kolkata index (for individual agents or two-earner families) reduce, while the deviation degree (defined to measure the difference between the probability distributions with and without saving propensities) increases. It is demonstrated that the wealth distribution is changed significantly by the saving propensity which alleviates wealth inequality.

physics.soc-ph↗

arXiv2020

A multi-component discrete Boltzmann model for nonequilibrium reactive flows

We propose a multi-component discrete Boltzmann model (DBM) for premixed, nonpremixed, or partially premixed nonequilibrium reactive flows. This model is suitable for both subsonic and supersonic flows with or without chemical reaction and/or external force. A two-dimensional sixteen-velocity model is constructed for the DBM. In the hydrodynamic limit, the DBM recovers the modified Navier-Stokes equations for reacting species in a force field. Compared to standard lattice Boltzmann models, the DBM presents not only more accurate hydrodynamic quantities, but also detailed nonequilibrium effects that are essential yet long-neglected by traditional fluid dynamics. Apart from nonequilibrium terms (viscous stress and heat flux) in conventional models, specific hydrodynamic and thermodynamic nonequilibrium quantities (high order kinetic moments and their departure from equilibrium) are dynamically obtained from the DBM in a straightforward way. Due to its generality, the developed methodology is applicable to a wide range of phenomena across many energy technologies, emissions reduction, environmental protection, mining accident prevention, chemical and process industry.

physics.comp-ph↗

arXiv2020

Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects

A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate nonequilibrium behaviors of the compressible Kelvin-Helmholtz instability (KHI). It is found that, in the dynamic KHI process, the mixing degree and fluid flow are similar for cases with various thermal conductivity and initial temperature configurations. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI.

physics.flu-dyn↗

arXiv2019

Nonequilibrium and morphological characterizations of Kelvin-Helmholtz instability in compressible flows

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.

cond-mat.soft↗