Two-dimensional MRT LB model for compressible and incompressible flows

Chen, Feng; Xu, Aiguo; Zhang, Guangcai; Wang, Yong-Long

doi:10.1007/s11467-013-0368-y

Cited by 17 publications

(26 citation statements)

References 31 publications

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“…Although from the mathematical point of view, the relaxation coefficient R k can be independently adjusted for each kinetic mode f k −f [75]. This modification is added so that the LBKM can recover the consistent Navier-Stokes equations in the hydrodynamic limit.…”

Section: Formulation Of the Lattice Boltzmann Kinetic Modelmentioning

confidence: 99%

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

et al. 2015

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To probe both the Hydrodynamic Non-Equilibrium (HNE) and Thermodynamic NonEquilibrium (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.

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Section: Formulation Of the Lattice Boltzmann Kinetic Modelmentioning

confidence: 99%

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

et al. 2015

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“…Besides recovering the hydrodynamic equations in the continuum limit, two key points for a DBM are as below: (i) in terms of the nonconserved moments, we can define two sets of measures for the deviation of the system from its thermodynamic equilibrium state, (ii) in the regimes where the system deviates from its thermodynamic equilibrium, the DBM may present more reasonable behaviors. Since the inverse of the transformation matrix C connecting the discrete equilibrium distribution function f eq and corresponding momentsf eq has been fixed, the extension to multiple-relaxation-time DBM [56] is straightforward. As for the DBM in spherical coordinates, if consider flow behaviors near the spherical center, the "force term" (the term for geometric effects) should consider the higher order nonequilibrium effects.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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

Zhang

et al. 2018

Front. Phys.

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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.

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“…In the recent two decades the lattice Boltzmann (LB) method has been becoming a promising simulation tool for various complex systems, 1,2 ranging from the low Mach number nearly incompressible°ows 3 to high speed compressible°ows under shocks, 4,5 from simple°uids to multiphase and/or multi-component°uids, [6][7][8][9][10][11][12][13][14] from phase transition kinetics 6,[8][9][10][11][12][13][14] to hydrodynamic instabilities, [15][16][17][18] etc. The LB methods in literature can be roughly classi¯ed into two categories, new solvers of various partial di®erential equations and kinetic models of various complex systems.…”

Section: Introductionmentioning

confidence: 99%

“…This idea was further speci¯ed in following works and considerable new physical insights for various systems were obtained from a more fundamental level. 2,5,[16][17][18] Most early LB models for multiphase°ows were for isothermal system and have been successfully applied to a wide variety of°ow problems, such as drop collisions, 19 wetting, 20 phase separation and phase ordering, 6-10 etc. In recent years, some thermal LB (TLB) multiphase models [11][12][13][14][21][22][23] have appeared.…”

Section: Introductionmentioning

confidence: 99%

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

Gan

Zhang

et al. 2014

Int. J. Mod. Phys. C

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We present a highly e±cient lattice Boltzmann (LB) kinetic model for thermal liquid-vapor system. Three key components are as below: (i) a discrete velocity model (DVM) by Kataoka et al. [Phys. Rev. E 69, 035701(R) (2004)]; (ii) a forcing term I i aiming to describe the interfacial stress and recover the van der Waals (VDW) equation of state (EOS) by Gonnella et al. [Phys. Rev. E 76, 036703 (2007)] and (iii) a Windowed Fast Fourier Transform (WFFT) scheme and its inverse by our group [Phys. Rev. E 84, 046715 (2011)] for solving the spatial derivatives, together with a second-order Runge-Kutta (RK)¯nite di®erence scheme for solving the temporal derivative in the LB equation. The model is veri¯ed and validated by well-known benchmark tests. The results recovered from the present model are well consistent with previous ones [Phys. Rev. E 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 e±cient by about 10 times and more accurate than the original one.

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Two-dimensional MRT LB model for compressible and incompressible flows

Cited by 17 publications

References 31 publications

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

Multiple-relaxation-time lattice Boltzmann kinetic model for combustion

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

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

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