Recent progresses on numerical investigations of microscopic structure of strong shock waves in fluid

et al. 2017

Phys. Rev. E

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.

Section: Introductionmentioning

confidence: 95%

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

Lin

et al. 2017

Phys. Rev. E

“…For example, the TNE intensity has been used to discriminate the spinodal decomposition stage and the domain growth stage in phase separation [28]; the abundant TNE characteristics have been used to distinguish and capture various interfaces [26,29] in numerical experiments, to investigate the fundamental mechanisms for entropy increase [31] in complex flows. Some of the new observations brought by DBM, for example, the nonequilibrium fine structures of shock waves, have been confirmed and supplemented by the results of molecular dynamics [53][54][55].…”

Section: Introductionmentioning

confidence: 73%

Discrete Boltzmann model for implosion- and explosionrelated compressible flow with spherical symmetry

et al. 2018

Front. Phys.

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 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 "force term". 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 multiplerelaxation-time version is straightforward.

“…The latter is helpful for understanding the constitutive relations for the former. Some of the new observations brought by DBM, for example, the non-equilibrium fine structures of shock waves [27], have been confirmed and supplemented by the results of molecular dynamics [28][29][30]. It should be pointed out that the molecular dynamics simulations can also give microscopic view of points to the origin of the slip near boundary, such as the non-isotropic strong molecular evaporation flux from the liquid [31], which might help to develop more physically reasonable mesoscopic models for slip-flow regime.Generally, there are two steps to simplify the full Boltzmann equation.…”

mentioning

confidence: 73%

“…So the discrete velocities model is chosen as Fig.1(a) and the special value of each discrete velocity is given in Eq. (30). The other DVM contains 36 discrete velocities and is denoted by D2V36 which is shown in Fig.1(b).…”

Section: Es Esmentioning

confidence: 99%

Discrete ellipsoidal statistical BGK model and Burnett equations

et al. 2018

Front. Phys.

A new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed to simulate non-equilibrium compressible flows. 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.Key words: discrete Boltzmann model, ellipsoidal statistical BGK, Burnett equations, non-equilibrium quantities, actual distribution function. boundary conditions), but it fails to provide the correct viscous stress and heat flux in transitional regime. The reason for the inapplicability of NS equations in transitional flow is that the constitutive equations, i.e. Newton's viscosity law and the Fourier heat conduction law, are assumed to be linear which is inapposite when the non-equilibrium (or rarefaction) effect is significant. The Burnett equations [3,6], which are obtained from the Boltzmann equation through Chapman-Enskog (CE) expansion, have a modified constitutive equations and can work in part of the transition flow zones. However, the Burnett equations often encounter numerical instabilities because of the high order derivatives in the viscosity and heat flux terms [6].It has been known that Boltzmann equation is applicable for all of the four flow regimes mentioned above. Unfortunately, the original Boltzmann equation is too complicated to be solved directly [7]. The multidimensional nature of distribution function and collision operator pose a great challenge for its numerical solution. Realistic numerical computations of the Boltzmann equation are based on probabilistic methods, such as direct simulation Monte Carlo (DSMC) method[8], or deterministic fast numerical methods, such as fast spectral method (FSM) [7]. In general, however, the computation cost is still too expensive for the direct solution of the Boltzmann equation. So, a variety of simplified methods have been developed to approximate the solution of the Boltzmann equation, such as the unified gas-kinetic scheme(UGKS)[9,10], the discrete velocity method (DVM) [11], the discrete unified gas-kinetic scheme (DUGKS) [12,13], the lattice Boltzmann method (LBM) [14][15][16][17][18], and the discrete Boltzmann method(DBM) [19][20][21].Recently, DBM has been developed as a non-equilibrium flow simulation tool and has been widely used in various flow conditions including high speed compressible flow, multiphase flow [22], flow instability [23][24], combustion and detonation [25][26], etc. Besides the values and evolutions of conserved kineti...