Multiple-relaxation-time lattice Boltzmann model for compressible fluids

Chen, Feng; Xu, Aiguo; Zhang, Guangcai; Li, Yingjun

doi:10.1016/j.physleta.2011.04.013

Cited by 34 publications

(32 citation statements)

References 76 publications

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“…5(a) and (d), which is also accompanied by a small increase in the bulk velocity. The latter has been observed by other kinetic approaches and was linked to the particle mean free path [81,89,90]. Fluctuations are present in all quantities but are expected to decrease for larger N .…”

Section: B Sod Testsupporting

confidence: 52%

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

Sagert

Bauer

Colbry

et al. 2014

Journal of Computational Physics

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We introduce a massively parallelized test-particle based kinetic Monte Carlo code that is capable of modeling the phase space evolution of an arbitrarily sized system that is free to move in and out of the continuum limit. Our code combines advantages of the DSMC and the Point of Closest Approach techniques for solving the collision integral. With that, it achieves high spatial accuracy in simulations of large particle systems while maintaining computational feasibility. Using particle mean free paths which are small with respect to the characteristic length scale of the simulated system, we reproduce hydrodynamic behavior. To demonstrate that our code can retrieve continuum solutions, we perform a test-suite of classic hydrodynamic shock problems consisting of the Sod, the Noh, and the Sedov tests. We find that the results of our simulations which apply millions of test-particles match the analytic solutions well. In addition, we take advantage of the ability of kinetic codes to describe matter out of the continuum regime when applying large particle mean free paths. With that, we study and compare the evolution of shock waves in the hydrodynamic limit and in a regime which is not reachable by hydrodynamic codes.

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Section: B Sod Testsupporting

confidence: 52%

Hydrodynamic shock wave studies within a kinetic Monte Carlo approach

Sagert

Bauer

Colbry

et al. 2014

Journal of Computational Physics

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“…In fact, given the great importance of high speed compressible flows in the aforementioned fields, constructing LB models for this area has been attempted since the early days of LB research, which yields the following five approaches, i.e., the adaptive approach by Sun et al [10], the circular function approach by Qu, et al [11], the doubledistribution-function (DDF) approach by Li, et al [12], the additional viscosity single-relaxation-time (AD SRT) approach [13,14] and the multiple-relaxation-time (MRT) approach [15,16] by our group. In the adaptive approach, particle velocities can vary with the Mach number and internal energy, and the Maxwellian distribution function (MDF) is replaced by the Kronecker function.…”

mentioning

confidence: 99%

“…Compared to the SRT approach [9,13,14,17] where f eq is conveniently expanded in terms of macroscopic quantities by only keeping the first relevant orders, this way is more simple and convenient, since it needs not to solve the complex kinetic moments to give the specific formulations of f eq . Compared to the MRT approach [15,16], the physical modeling process is more natural and straightforward, since the constructions of the transformation matrix and corresponding distribution function in the kinetic moment space are direct. Furthermore, this scheme has better generalization, since it works for all the one-, two-and three-dimensional model constructions and the choosing of DVM has a high degree of flexibility which results in higher efficiency and better stability of this approach.…”

mentioning

confidence: 99%

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

Gan¹,

Xu²,

Zhang³

et al. 2013

EPL

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PACS 47.11.-j -Computational methods in fluid dynamics. PACS 51.10.+y -Kinetic and transport theory of gases. PACS 05.20.Dd -Kinetic theory.Abstract. -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) f eq and a discrete velocity model with flexible velocity size. The DEDF is obtained by f eq = C −1 M, where M is a set of moment of the Maxwellian distribution function, and C is the matrix connecting the DEDF and the moments. The numerical components of C are determined by the discrete velocity model. The calculation of 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.

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“…This scheme does not change the framework of the original LB model. The second is to develop Multiple Relaxation Time(MRT) LB models [41][42][43][44][45]. The framework is changed in the second scheme.…”

Section: Introductionmentioning

confidence: 99%