arXiv subjects

Guangcai Zhang

Publications and source records attributed to Guangcai Zhang.

At least 19 recordsLinked to original sources

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↗

arXiv2019

Entropy production in thermal phase separation: a kinetic-theory approach

Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium.

cond-mat.stat-mech↗

arXiv2018

A One-Dimensional Discrete Boltzmann Model for Detonation and an Abnormal Detonation Phenomenon

A one-dimensional discrete Boltzmann model for detonation simulation is presented. Instead of numerical solving Navier-Stokes equations, this model obtains the information of flow field through numerical solving specially discretized Boltzmann equation. Several classical benchmarks including Sod shock wave tube, Colella explosion problem, and one-dimensional self-sustainable stable detonation are simulated to validate the new model. Based on the new model, the influence of negative temperature coefficient of reaction rate on detonation is further investigated. It is found that an abnormal detonation with two wave heads periodically appears under negative temperature coefficient condition. The causes of the abnormal detonation are analyzed. One typical cycle of the periodic abnormal detonation and its development process are discussed.

physics.flu-dyn↗

arXiv2018

Comparative Study on Several Criteria for Non-equilibrium Phase Separation

Several different kinds of criteria for non-equilibrium phase separation to discriminate the two stages, the spinnodal decompostion (SD) and domain growth (DG), are compared and further investigated. The characteristic domain size and morphological function present two geometric criteria. Both of them can only provide rough estimations for the crossover from SD to DG. The reason for domain size is that the crossover in this description covers a process, instead of a specific time. The reason for the morphological function is that the result may rely on chosen threshold value. However, both the non-equilibrium strength and the entropy production rate are physical criteria and are more convenient to provide critical times. In fact, not only the non-equilibrium strength defined in the moment space opened by all the independent components of the used non-equilibrium quantities but also those defined in its subspaces can be used as criteria. Each of those criteria characterizes the phase separation process from its own perspective. Consequently, the obtained critical times may show slight differences. It should be pointed out that these slight differences are not contradictive, but consistent with each other and complementary in describing the complex phenomena.

physics.flu-dyn↗

arXiv2018

Discrete Boltzmann trans-scale modeling of high-speed compressible flows

We present a general framework for constructing trans-scale \emph{discrete Boltzmann models} (DBMs) for high-speed compressible flows ranging from continuum to transition regime. This is achieved by designing a higher-order discrete equilibrium distribution function which satisfies additional nonhydrodynamic kinetic moments. In order to characterize the \emph{% thermodynamic non-equilibrium} (TNE) effects and estimate the condition under which the DBMs at various levels should be used, two novel measures are presented: (i) the relative TNE strength, describing the relative strength of the ($N+1$)-th order TNE effects to the $N$-th order one; (ii) the TNE discrepancy between DBM simulation and relevant theoretical analysis. Whether or not the higher-order TNE effects should be taken into account in the modeling and which level of DBM should be adopted, is best described by the relative TNE intensity and/or the discrepancy, rather than by the value of the Knudsen number. As a model example, a two-dimensional DBM with $26$ discrete velocities at Burnett level is formulated, verified, and validated.

physics.flu-dyn↗

arXiv2018

Comparative study of discrete Boltzmann model and Navier-Stokes

Discrete Boltzmann model (DBM) is a type of coarse-grained mesoscale kinetic model derived from the Boltzmann equation. Physically, it is roughly equivalent to a hydrodynamic model supplemented by a coarse-grained model for the relevant thermodynamic non-equilibrium (TNE) behaviours. The Navier-Stokes (NS) model is a traditional macroscopic hydrodynamic model based on continuity hypothesis and conservation laws. In this study, the two models are compared from two aspects, physical capability and computational cost, by simulating two kinds of flow problems including the thermal Couette flow and a Mach 3 step problem. In the cases where the TNE effects are weak, both the two models give accurate results for the hydrodynamic behaviour. Besides, DBM can provide more detailed non-equilibrium information, while the NS is more efficient if concern only the density, momentum, energy and their derived quantities. It is concluded that, if the TNE effects are strong or are to be investigated, the NS is insufficient while DBM is a good choice. While in the cases where the TNE effects are weak and only the macro flow fields are to be studied, the NS is more preferable.

physics.flu-dyn↗

arXiv2018

Discrete Boltzmann method for non-equilibrium flows: based on Shakhov model

A general framework for constructing discrete Boltzmann model for non-equilibrium flows based on the Shakhov model is presented. The Hermite polynomial expansion and a set of discrete velocity with isotropy are adopted to solve the kinetic moments of discrete equilibrium distribution function. Such a model possesses both an adjustable specific heat ratio and Prandtl number, and can be applied to a wide range of flow regimes including continuous, slip, and transition flows. To recover results for actual situations, the nondimensionalization process is demonstrated. To verify and validate the new model, several typical non-equilibrium flows including the Couette flow, Fourier flow, unsteady boundary heating problem, cavity flow, and Kelvin-Helmholtz instability are simulated. Comparisons are made between the results of discrete Boltzmann model and those of previous models including analytic solution in slip flow, Lattice ES-BGK, and DSMC based on both BGK and hard-sphere models. The results show that the new model can accurately capture the velocity slip and temperature jump near the wall, and show excellent performance in predicting the non-equilibrium flow even in transition flow regime. In addition, the measurement of non-equilibrium effects is further developed and the non-equilibrium strength $D^*_n$ in the n-th order moment space is defined. The nonequilibrium characteristics and the advantage of using $D^*_n$ in Kelvin-Helmholtz instability are discussed. It concludes that the non-equilibrium strength $D^*_n$ is more appropriate to describe the interfaces than the individual components of $Delta^*_n$. Besides, the $D^*_3$ and $D^*_{3,1}$ can provide higher resolution interfaces in the simulation of Kelvin-Helmholtz instability.

physics.flu-dyn↗

arXiv2018

Collaboration and Competition Between Richtmyer-Meshkov instability and Rayleigh-Taylor instability

The two-dimensional Richtmyer-Meshkov Instability(RMI) system and the coexisting system combined with Rayleigh-Taylor Instability(RTI) are simulated with a multiple-relaxation time discrete Boltzmann model. It is found that, for the RMI system, the correlation between globally averaged non-organized energy flux and nonuniformity of temperature is nearly 1; the correlation between globally averaged non-organized momentum flux and nonuniformity of velocity and that between globally averaged thermodynamic non-equilibrium strength and nonuniformity of density are also high. In the coexisting system combined with RTI, the collaboration and competition mechanisms of the two instabilities are investigated. In the case where RMI dominates, an interesting interface inversion process is observed. The parameter regions for RMI dominates and RTI dominates are given. The effects of gravity acceleration and Mach number on nonequilibrium are carefully studied, via which the effects of RTI and RMI strengths on the extent of material mixing are better probed.

cond-mat.soft↗

arXiv2018

Discrete ellipsoidal statistical BGK model and Burnett equations

To simulate non-equilibrium compressible flows, a new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in Burnett level, two kinds of discrete velocity model are introduced; the relations between non-equilibrium quantities and the viscous stress and heat flux in Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, based on the Navier-Stokes, the Burnett equations, etc.

physics.flu-dyn↗

arXiv2018

Discrete Boltzmann model for implosion and explosion related compressible flow with spherical symmetry

To kinetically model implosion and explosion related phenomena, we present a theoretical framework for constructing Discrete Boltzmann Model(DBM) with spherical symmetry in spherical coordinates. To this aim, a key technique is to use \emph{local} Cartesian coordinates to describe the particle velocity in the kinetic model. Thus, the geometric effects, like the divergence and convergence, are described as a \textquotedblleft force term\textquotedblright. To better access the nonequilibrium behavior, even though the corresponding hydrodynamic model is one-dimensional, the DBM uses a Discrete Velocity Model(DVM) with 3 dimensions. A new scheme is introduced so that the DBM can use the same DVM no matter considering the extra degree of freedom or not. As an example, a DVM with 26 velocities is formulated to construct the DBM in the Navier-Stokes level. Via the DBM, one can study simultaneously the hydrodynamic and thermodynamic nonequilibrium behaviors in the implosion and explosion process which are not very close to the spherical center. The extension of current model to the multiple-relaxation-time version is straightforward.

physics.comp-ph↗

arXiv2017

Discrete Boltzmann modeling of Rayleigh-Taylor instability in two-component compressible flows

A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor instability (RTI) in two-component compressible flows. Each species has a flexible specific heat ratio and is described by one discrete Boltzmann equation (DBE). Independent discrete velocities are adopted for the two DBEs. The collision and force terms in the DBE account for the molecular collision and external force, respectively. Two types of force terms are exploited. In addition to recovering the modified Navier-Stokes equations in the hydrodynamic limit, the DBM has the capability of capturing detailed nonequilibrium effects. Furthermore, we use the DBM to investigate the dynamic process of the RTI. The invariants of tensors for nonequilibrium effects are presented and studied. For low Reynolds numbers, both global nonequilibrium manifestations and the growth rate of the entropy of mixing show three stages (i.e., the reducing, increasing, and then decreasing trends) in the evolution of the RTI. On the other hand, the early reducing tendency is suppressed and even eliminated for high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.

cond-mat.soft↗

arXiv2017

Three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium

We present a series of three-dimensional discrete Boltzmann (DB) models for compressible flows in and out of equilibrium. The key formulating technique is the construction of discrete equilibrium distribution function through inversely solving the kinetic moment relations that it satisfies. The crucial physical requirement is that all the used kinetic moment relations must be consistent with the non-equilibrium statistical mechanics. The necessity of such a kinetic model is that, with increasing the complexity of flows, the dynamical characterization of non-equilibrium state and the understanding of the constitutive relations need higher order kinetic moments and their evolution. The DB models at the Euler and Navier-Stokes levels proposed by this scheme are validated by several well-known benchmarks, ranging from one-dimension to three-dimension. Particularly, when the local Mach number, temperature ratio, and pressure ratio are as large as $10^2$, $10^4$, and $10^5$, respectively, the simulation results are still in excellent agreement with the Riemann solutions. How to model deeper thermodynamic non-equilibrium flows by DB is indicated. Via the DB method, it convenient to simulate nonequilibrium flows without knowing exact form of the hydrodynamic equations.

physics.flu-dyn↗

arXiv2017

Discrete Boltzmann method with Maxwell-type boundary condition for slip flow

The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been know that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model. Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model. To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.

physics.flu-dyn↗

arXiv2017

Discrete Boltzmann Modeling of Compressible Flows

Mathematically, the typical difference of Discrete Boltzmann Model (DBM) from the traditional hydrodynamic one is that the Navier-Stokes (NS) equations are replaced by a discrete Boltzmann equation. But physically, this replacement has a significant gain: a DBM is roughly equivalent to a hydrodynamic model supplemented by a coarse-grained model of the Thermodynamic Non-Equilibrium (TNE) effects, where the hydrodynamic model can be and can also beyond the NS. Via the DBM, it is convenient to perform simulations on systems with flexible Knudsen number. The observations on TNE are being obtaining more applications with time.

physics.flu-dyn↗

arXiv2016

Viscosity, heat conductivity and Prandtl number effects in Rayleigh-Taylor Instability

Two-dimensional Rayleigh-Taylor(RT) instability problem is simulated with a multiple-relaxation-time discrete Boltzmann model with gravity term. The viscosity, heat conductivity and Prandtl number effects are probed from the macroscopic and the non-equilibrium views. In macro sense, both viscosity and heat conduction show significant inhibitory effect in the reacceleration stage, and the inhibition effect is mainly achieved by inhibiting the development of Kelvin-Helmholtz instability. Before this, the Prandtl number effect is not sensitive. Based on the view of non-equilibrium, the viscosity, heat conductivity, and Prandtl number effects on non-equilibrium manifestations, and the correlation degrees between the non-uniformity and the non-equilibrium strength in the complex flow are systematic investigated.

cond-mat.soft↗

arXiv2016

Kinetic modeling of detonation and effects of negative temperature coefficient

The kinetic modeling and simulation of reactive flows, especially for those with detonation, are further investigated. From the theoretical side, a new set of hydrodynamic equations are deduced, where the viscous stress tensor and heat flux are replaced by two non-equilibrium quantities that have been defined in our previous work. The two non-equilibrium quantities are referred to as NonOrganized Momentum Flux (NOMF) and Non-Organized Energy Flux (NOEF), respectively, here. The numerical results of viscous stress (heat flux) have a good agreement with those of NOMF (NOEF) near equilibrium state. Around sharp interfaces, the values of NOMF (NOEF) deviate reasonably from those of viscous stress (heat flux). Based on this hydrodynamic model, the relations between the two non-equilibrium quantities and entropy productions are established. Based on the discrete Boltzmann model, four kinds of detonation phenomena with different reaction rates, including Negative Temperature Coefficient (NTC) regime, are simulated and investigated. The differences of the four kinds of detonations are studied from three aspects: hydrodynamic quantities, non-equilibrium quantities and entropy productions.

cond-mat.soft↗

arXiv2016

Thermo-hydrodynamic non-equilibrium effects on compressible Rayleigh-Taylor instability

The effects of compressibility on Rayleigh-Taylor instability (RTI) are investigated by inspecting the interplay between thermodynamic and hydrodynamic non-equilibrium phenomena (TNE, HNE, respectively) via a discrete Boltzmann model (DBM). Two effective approaches are presented, one tracking the evolution of the \emph{local} TNE effects and the other focussing on the evolution of the mean temperature of the fluid, to track the complex interfaces separating the bubble and the spike regions of the flow. It is found that, both the compressibility effects and the \emph{global} TNE intensity show opposite trends in the initial and the later stages of the RTI. Compressibility delays the initial stage of RTI and accelerates the later stage. Meanwhile, the TNE characteristics are generally enhanced by the compressibility, especially in the later stage. The global or mean thermodynamic non-equilibrium indicators provide physical criteria to discriminate between the two stages of the RTI.

cond-mat.soft↗

arXiv2016

Complex fields in heterogeneous materials under shock: modeling, simulation and analysis

In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different scales. Construct/Choose a model according to the scale and main mechanisms working at that scale. Perform numerical simulations using the relatively mature schemes. The physical information is transferred between neighboring scales in such a way: The statistical information of results in smaller scale contributes to establishing the constitutive equation in larger one. Except for the microscopic Molecular Dynamics (MD) model, both the mesoscopic and macroscopic models can be further classified into two categories, solidic and fluidic models, respectively. The basic ideas and key techniques of the MD, material point method and discrete Boltzmann method are briefly reviewed. Among various schemes used in analyzing the complex fields and structures, the morphological analysis and the home-built software, GISO, are briefly introduced. New observations are summarized for scales from the larger to the smaller.

cond-mat.soft↗