Discrete Boltzmann trans-scale modeling of high-speed compressible flows

Gan, Yanbiao; Xu, Aiguo; Zhang, Guangcai; Zhang, Yudong; Succi, Sauro

doi:10.1103/physreve.97.053312

Cited by 75 publications

(49 citation statements)

References 108 publications

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“…The discrete Boltzmann equation, particle velocity, and hydrodynamic quantities have been nondimensionalized by suitable reference variables as listed in Ref. [56].…”

Section: Verification and Validationmentioning

confidence: 99%

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

Gan

Zhang

et al. 2019

Front. Phys.

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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.

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“…The discrete Boltzmann equation, particle velocity, and hydrodynamic quantities have been nondimensionalized by suitable reference variables as listed in Ref. [56].…”

Section: Verification and Validationmentioning

confidence: 99%

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

Gan

Zhang

et al. 2019

Front. Phys.

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“…From a computational resource perspective, the remarkable merits are brevity of programming, numerical potency, inherent parallelism, and ease treatment of intricate boundary conditions. This kind of method has comprehensive capacities in quite several fields, from phonon transport [13] to approximate incompressible flows [14][15][16][17][18][19][20][21][22][23][24][25], full compressible flows [26][27][28][29][30][31][32][33][34][35][36][37], dendrite growth [38,39] and thermal multiphase flows [40]. Recently, the mesoscopic kinetics method is also becoming increasingly popular in computational mathematics and engineering science for solving certain NPDEs, including Burgers' equations [41,42], Korteweg-de Vries equation [43], Gross-Pitaevskii equation [44], convection-diffusion equation [45][46][47][48][49][50][51], Kuramoto-Sivashinsky equation [52], wave equation [53,54], Dirac equation [55], Poisson equation…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model

Lai

Shi

2019

Entropy

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In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon.

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“…The other type of kinetic models is to capture both hydrodynamic and thermodynamic nonequilibrium behaviours beyond the macroscopic models. The successful physical models include the unified gas kinetic scheme [24][25][26], the discrete unified gas kinetic scheme [27,28], the discrete Boltzmann method (DBM) [29][30][31][32][33][34][35][36][37][38][39], etc. These powerful models are suitable for continuum and rarefied systems with a wide range of Knudsen numbers, and capable to subsonic and supersonic flows with essential nonequilibrium effects.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method

Lin

Su²,

Zhang

2020

Entropy

Self Cite

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A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.

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Discrete Boltzmann trans-scale modeling of high-speed compressible flows

Cited by 75 publications

References 108 publications

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method

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