arXiv subjects

Yanbiao Gan

Publications and source records attributed to Yanbiao Gan.

34 records · Page 2Linked to original sources

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↗

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

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↗

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↗

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↗

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↗

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↗

arXiv2013

Lattice BGK kinetic model for high speed compressible flows: hydrodynamic and nonequilibrium behaviors

We present a simple and general approach to formulate the lattice BGK model for high speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) $\mathbf{f}^{eq}$ and a discrete velocity model with flexible velocity size. The DEDF is obtained by $\mathbf{f}^{eq}=\mathbf{C}^{-1}\mathbf{M}$, where $\mathbf{M}$ is a set of moment of the Maxwellian distribution function, and $\mathbf{C}$ is the matrix connecting the DEDF and the moments. The numerical components of $\mathbf{C}$ are determined by the discrete velocity model. The calculation of $\mathbf{C}^{-1}$ is based on the analytic solution which is a function of the parameter controlling the sizes of discrete velocity. The choosing of discrete velocity model has a high flexibility. The specific heat ratio of the system can be flexible. The approach works for the one-, two- and three-dimensional model constructions. As an example, we compose a new lattice BGK kinetic model which works not only for recovering the Navier-Stokes equations in the continuum limit but also for measuring the departure of system from its thermodynamic equilibrium. Via adjusting the sizes of the discrete velocities the stably simulated Mach number can be significantly increased up to 30 or even higher. The model is verified and validated by well-known benchmark tests. Some macroscopic behaviors of the system due to deviating from thermodynamic equilibrium around the shock wave interfaces are shown.

cond-mat.soft↗

arXiv2012

Cellular automata model for elastic solid material

The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem. In this paper we present a new two-dimensional CA model for solid dynamics. In this model the solid body is represented by a set of white and black particles alternatively positioned in the $x$- and $y$- directions. The force acting on each particle is represented by the linear summation of relative displacements of the nearest-neighboring particles. The key technique in this new model is the construction of eight coefficient matrices. Theoretical and numerical analyses show that the present model can be mathematically described by a conservative system. So, it works for elastic material. In the continuum limit the CA model recovers the well-known Navier equations. The coefficient matrices are related to the shear module and Poisson ratio of the material body. Compared with previous CA model for solid body, this model realizes the natural coupling of deformations in the $x$- and $y$- directions. Consequently, the wave phenomena related to the Poisson ratio effects are successfully recovered. This work advances significantly the CA modeling and simulation in the field of computational solid dynamics.

nlin.CG↗

arXiv2012

Lattice Boltzmann modeling and simulation of compressible flows

In this mini-review we summarize the progress of Lattice Boltzmann(LB) modeling and simulating compressible flows in our group in recent years. Main contents include (i) Single-Relaxation-Time(SRT) LB model supplemented by additional viscosity, (ii) Multiple-Relaxation-Time(MRT) LB model, and (iii) LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model supplemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross-Krook (LBGK). So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a completely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.

cond-mat.soft↗

arXiv2011

Phase separation in thermal systems: LB study and morphological characterization

We investigate thermal and isothermal symmetric liquid-vapor separations via a FFT-Thermal Lattice Boltzmann (FFT-TLB) model. Structure factor, domain size and Minkowski functionals are employed to characterize the density and velocity fields as well as to understand the configurations and the kinetic processes. Compared with the isothermal phase separation, the freedom in temperature prolongs the Spinodal Decomposition (SD) stage and induces different rheological and morphological behaviors in the thermal system. After the transient procedure, both the thermal and isothermal separations show power-law scalings in domain growth; while the exponent for thermal system is lower than that for isothermal system. With respect to the density of field, the isothermal system presents more likely bicontinuous configurations with narrower interfaces, while the thermal system presents more likely configurations with scattered bubbles. Heat creation, conduction and lower interfacial stresses are main reasons for the differences in thermal system. Different from the case with isothermal phase separation, the release of latent heat causes the changing of local temperature which results in new local mechanical balance. When the Prandtl number becomes smaller, the system approaches thermodynamical equilibrium more quickly. The increasing of mean temperature makes lower the interfacial stress in the following way: $σ=σ_{0}[(T_{c}-T)/(T_{c}-T_{0})]^{3/2}$, where $T_{c}$ is the critical temperature and $σ_{0}$ is the interfacial stress at a reference temperature $T_{0}$, which is the main reason for lower growth exponent in thermal case.

cond-mat.soft↗

arXiv2011

FFT-LB modeling of thermal liquid-vapor systems

We further develop a thermal LB model for multiphase flows. In the improved model, we propose to use the FFT scheme to calculate both the convection term and external force term. The usage of FFT scheme is detailed and analyzed. By using the FFT algorithm spatiotemporal discretization errors are decreased dramatically and the conservation of total energy is much better preserved. A direct consequence of the improvement is that the unphysical spurious velocities at the interfacial regions can be damped to neglectable scale. Together with the better conservation of total energy, the more accurate flow velocities lead to the more accurate temperature field which determines the dynamical and final states of the system. With the new model, the phase diagram of the liquid-vapor system obtained from simulation is more consistent with that from theoretical calculation. Very sharp interfaces can be achieved. The accuracy of simulation results are also verified by the Laplace law. The FFT scheme can be easily applied to other models for multiphase flows.

cond-mat.soft↗

arXiv2011

Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients

A two-dimensional lattice Boltzmann model with 19 discrete velocities for compressible Euler equations is proposed (D2V19-LBM). The fifth-order Weighted Essentially Non-Oscillatory (5th-WENO) finite difference scheme is employed to calculate the convection term of the lattice Boltzmann equation. The validity of the model is verified by comparing simulation results of the Sod shock tube with its corresponding analytical solutions. The velocity and density gradient effects on the Kelvin-Helmholtz instability (KHI) are investigated using the proposed model. Sharp density contours are obtained in our simulations. It is found that, the linear growth rate $γ$ for the KHI decreases with increasing the width of velocity transition layer ${D_{v}}$ but increases with increasing the width of density transition layer ${D_ρ}$. After the initial transient period and before the vortex has been well formed, the linear growth rates, $γ_v$ and $γ_ρ$, vary with ${D_{v}}$ and ${D_ρ}$ approximately in the following way, $\lnγ_{v}=a-bD_{v}$ and $γ_ρ=c+e\ln D_ρ ({D_ρ}<{D_ρ^{E}})$, where $a$, $b$, $c$ and $e$ are fitting parameters and ${D_ρ^{E}}$ is the effective interaction width of density transition layer. When ${D_ρ}>{D_ρ^{E}}$ the linear growth rate $γ_ρ$ does not vary significantly any more. One can use the hybrid effects of velocity and density transition layers to stabilize the KHI. Our numerical simulation results are in general agreement with the analytical results [L. F. Wang, \emph{et al.}, Phys. Plasma \textbf{17}, 042103 (2010)].

cond-mat.soft↗

arXiv2008

Two-Dimensional Lattice Boltzmann Model For Compressible Flows With High Mach Number

In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by Watari and Tsutahara [Phys Rev E \textbf{67},036306(2003)], (ii) a modified Lax-Wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included, (iii) artificial viscosity. The improved model is convenient to compromise the high accuracy and stability. The included dispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the scheme to satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In our numerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems.

cond-mat.soft↗