arXiv subjects

Aiguo Xu

Publications and source records attributed to Aiguo Xu.

At least 55 records · Page 3Linked to original sources

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↗

arXiv2015

Double-distribution-function discrete Boltzmann model for combustion

A 2-dimensional discrete Boltzmann model for combustion is presented. Mathematically, the model is composed of two coupled discrete Boltzmann equations for two species and a phenomenological equation for chemical reaction process. Physically, the model is equivalent to a reactive Navier-Stokes model supplemented by a coarse-grained model for the thermodynamic nonequilibrium behaviours. This model adopts 16 discrete velocities. It works for both subsonic and supersonic combustion phenomena with flexible specific heat ratio. To discuss the physical accuracy of the coarse-grained model for nonequilibrium behaviours, three other discrete velocity models are used for comparisons. Numerical results are compared with analytical solutions based on both the first-order and second-order truncations of the distribution function. It is confirmed that the physical accuracy increases with the increasing moment relations needed by nonequlibrium manifestations. Furthermore, compared with the single distribution function model, this model can simulate more details of combustion.

cond-mat.soft↗

arXiv2015

Discrete Boltzmann modeling of multiphase flows: hydrodynamic and thermodynamic non-equilibrium effects

A discrete Boltzmann model (DBM) is developed to investigate the hydrodynamic and thermodynamic non-equilibrium (TNE) effects in phase separation processes. The interparticle force drives changes and the gradient force, induced by gradients of macroscopic quantities, opposes them. In this paper, we investigate the interplay between them by providing detailed inspection of various non-equilibrium observables. Based on the TNE features, we define a TNE strength which roughly estimates the deviation amplitude from the thermodynamic equilibrium. The time evolution of the TNE intensity provides a convenient and efficient physical criterion to discriminate the stages of the spinodal decomposition and domain growth. Via the DBM simulation and this criterion, we quantitatively study the effects of latent heat and surface tension on phase separation. It is found that, the TNE strength attains its maximum at the end of the spinodal decomposition stage, and it decreases when the latent heat increases from zero. The surface tension effects are threefold, to prolong the duration of the spinodal decomposition stage, decrease the maximum TNE intensity, and accelerate the speed of the domain growth stage.

cond-mat.soft↗

arXiv2015

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

To probe both the Hydrodynamic Non-Equilibrium (HNE) and Thermodynamic Non-Equilibrium (TNE) in the combustion process, a two-dimensional Multiple-Relaxation-Time (MRT) version of Lattice Boltzmann Kinetic Model(LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Beside describing the evolutions of the conserved quantities, the density, momentum and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some non-conserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various non-equilibrium behaviours, including the complex interplays between various HNEs, between various TNEs and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increase the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.

cond-mat.soft↗

arXiv2014

Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into in the modified lattice Boltzmann equation, which could recovery the Navier-Stokes equations, including contribution of chemical reaction, via the Chapman-Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium. The internal kinetic energies in different degrees freedoms around the detonation front do not coincide due to the fluid viscosity. They show the maximum difference at the inflexion point where the pressure has the largest spatial derivative. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.

cond-mat.soft↗

arXiv2014

Discrete Boltzmann model of compressible flows with spherical or cylindrical symmetry

To study simultaneously the hydrodynamic and thermodynamic behaviors in compressible flow systems with spherical or cylindrical symmetry, we present a theoretical framework for constructing Discrete Boltzmann Model(DBM) with spherical or cylindrical symmetry in spherical or cylindrical 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 . Even though the hydrodynamic models are one- or two-dimensional, the DBM needs a Discrete Velocity Model(DVM) with 3 dimensions. We use a DVM with 26 velocities to formulate the DBM which recovers the Navier-Stokes equations with spherical or cylindrical symmetry in the hydrodynamic limit. For the system with \emph{global} cylindrical symmetry, we formulated also a DBM based on a DVM with 2 dimensions and 16 velocities. In terms of the nonconserved moments, we define two sets of measures for the deviations of the system from its thermodynamic equilibrium state. The extension of current model to the multiple-relaxation-time version is straightforward.

cond-mat.stat-mech↗

arXiv2014

Discrete Boltzmann modeling of liquid-vapor system

We further probe the Discrete Boltzmann Modeling(DBM) of the single-component two phase flows or the liquid-vapor system. There are two kinds of nonequilibrium effects in the system. The first is the Mechanical NonEquilibrium(MNE). The second is the Thermodynamic NonEquilibrium(TNE). The MNE is well described in the traditional fluid dynamic theory. The description of TNE resorts to the gas kinetic theory. Since based on the Boltzmann equation, the DBM makes possible to analyze both the MNE and TNE. The TNE is the main discussion of this work. A major purpose of this work is to show that the DBM results can be used to confirm and/or improve the macroscopic modeling of complex system.

cond-mat.soft↗

arXiv2014

Lattice Boltzmann kinetic modeling and simulation of thermal liquid-vapor system

We present a highly efficient lattice Boltzmann (LB) kinetic model for thermal liquid-vapor system. Three key components are as beow: (i) a discrete velocity model by Kataoka \emph{et al.} [Phys. Rev. E \textbf{69}, 035701(R)(2004)]; (ii) a forcing term $I_{i}$ aiming to describe the interfacial stress and recover the van der Waals equation of state by Gonnella \emph{et al.} [Phys. Rev. E \textbf{76}, 036703 (2007)]; and (iii) a Windowed Fast Fourier Transform (WFFT) scheme and its inverse by our group [Phys. Rev. E \textbf{84}, 046715 (2011)] for solving the spatial derivatives, together with a second-order Runge-Kutta (RK) finite difference scheme for solving the temporal derivative in the LB equation. The model is verified and validated by well-known benchmark tests. The results recovered from the present model are well consistent with previous ones[Phys. Rev. E \textbf{84}, 046715 (2011)] or theoretical analysis. The usage of less discrete velocities, high-order RK algorithm and WFFT scheme with 16th-order in precision makes the model more efficient by about $10$ times and more accurate than the original one.

cond-mat.soft↗

arXiv2014

Polar coordinate lattice Boltzmann modeling of compressible flows

We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modifiedWarming-Beam (MWB) scheme.Within theMWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RMinstability occurs. It is found that themacroscopic effects due to deviating from thermodynamic equilibrium around thematerial interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function.

cond-mat.soft↗

arXiv2013

Simulation study on cavity growth in ductile metal materials under dynamic loading

Cavity growth in ductile metal materials under dynamic loading is investigated via the material point method. Two typical cavity effects in the region subjected to rarefaction wave are identified: (i) part of material particles flow away from the cavity in comparison to the initial loading velocity, (ii) local regions show weaker negative or even positive pressures. Neighboring cavities interact via coalescence of isobaric contours. The growth of cavity under tension shows staged behaviors. After the initial slow stage, the volume and the dimensions in both the tensile and transverse directions show linear growth rate with time until the global tensile wave arrives at the upper free surface. It is interesting that the growth rate in the transverse direction is faster than that in the tensile direction. The volume growth rate linearly increases with the initial tensile velocity. After the global tensile wave passed the cavity, both the maximum particle velocity in the tensile direction and the maximum particle velocity in the opposite direction increase logarithmically with the initial tensile speed. The shock wave reflected back from the cavity and compression wave from the free surface induce the initial behavior of interfacial instabilities such as the Richtmyer-Meshkov instability, which is mainly responsible for the irregularity in the morphology of deformed cavity. The local temperatures and distribution of hot spots are determined by the plastic work. Compared with the dynamical process, the heat conduction is much slower.

cond-mat.mtrl-sci↗