Velocity slip and temperature jump simulations by the three-dimensional thermal finite-difference lattice Boltzmann method

Watari, Minoru

doi:10.1103/physreve.79.066706

Cited by 34 publications

(27 citation statements)

References 31 publications

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“…al. 2007;Watari 2009). Lattice Boltzmann methods are particularly adapted to attack non-homogeneous boundary conditions, thanks to their fully local stream-and-collide nature.…”

Section: Introductionmentioning

confidence: 99%

Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes

et al. 2014

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We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh-Bénard (RB) cell, where the horizontal top boundary contains a periodic sequence of alternating thermal insulating and conducting patches, and we study the effects of the heterogeneous pattern on the global heat exchange, both at low and high Rayleigh numbers. At low Rayleigh numbers, we determine numerically the transition from a regime characterized by the presence of small convective cells localized at the inhomogeneous boundary to the onset of bulk convective rolls spanning the entire domain. Such a transition is also controlled analytically in the limit when the boundary pattern length is small compared with the cell vertical size. At higher Rayleigh number, we use numerical simulations based on a lattice Boltzmann method to assess the impact of boundary inhomogeneities on the fully turbulent regime up to Ra ∼ 10 10 .

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“…al. 2007;Watari 2009). Lattice Boltzmann methods are particularly adapted to attack non-homogeneous boundary conditions, thanks to their fully local stream-and-collide nature.…”

Section: Introductionmentioning

confidence: 99%

Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes

et al. 2014

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“…Each moving particle has four speeds and can be obtained from the unit vectors in Table I multiplied by difference c k . The speeds c k of moving particle is determined according to the method presented by Watari in Ref [16]. The F k in Eq.…”

Section: A Definition Of Knudsen Numbermentioning

confidence: 99%

“…Using the zero-mass flow normal to the wall [16], the density ρ R w and ρ L w can be respectively calculated by the following two equations:…”

Section: Diffuse Reflection Boundarymentioning

confidence: 99%

Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

Zhang¹,

Xu²,

Zhang³

et al. 2018

Commun. Theor. Phys.

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The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been know that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model. Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model. To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.

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“…The hypersonic rarefied gas flows with strong nonequilibrium characteristics are often encountered when spacecraft reentry into the atmosphere because of the low density of (Huang et al 2012;Liu et al 2016a), the discrete unified gas-kinetic scheme (DUGKS) (Guo et al 2013(Guo et al , 2015, the discrete velocity method (DVM) (Yang et al 2017), the Lattice Boltzmann model (LBM) (Succi 2001;Shan et al 2006;Watari 2009;Meng & Zhang 2011;Watari 2016;Meng et al 2012), and the discrete Boltzmann method (DBM) Gan et al 2015;Lin et al 2016;Lai et al 2016;Chen et al 2016;Lin et al 2017a,b;Gan et al 2018), etc. Generally, the process of simplification includes two parts.…”

Section: Introductionmentioning

confidence: 99%

Discrete Boltzmann method for non-equilibrium flows: Based on Shakhov model

Zhang

et al. 2019

Computer Physics Communications

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A general framework for constructing discrete Boltzmann model for non-equilibrium flows based on the Shakhov model is presented. The Hermite polynomial expansion and a set of discrete velocity with isotropy are adopted to solve the kinetic moments of discrete equilibrium distribution function. Such a model possesses both an adjustable specific heat ratio and Prandtl number, and can be applied to a wide range of flow regimes including continuous, slip, and transition flows. To recover results for actual situations, the nondimensionalization process is demonstrated. To verify and validate the new model, several typical non-equilibrium flows including the Couette flow, Fourier flow, unsteady boundary heating problem, cavity flow, and Kelvin-Helmholtz instability are simulated. Comparisons are made between the results of discrete Boltzmann model and those of previous models including analytic solution in slip flow, Lattice ES-BGK, and DSMC based on both BGK and hard-sphere models. The results show that the new model can accurately capture the velocity slip and temperature jump near the wall, and show excellent performance in predicting the non-equilibrium flow even in transition flow regime. In addition, the measurement of non-equilibrium effects is further developed and the non-equilibrium strength D * n in the n-th order moment space is defined. The nonequilibrium characteristics and the advantage of using D * n in Kelvin-Helmholtz instability are discussed. It concludes that the non-equilibrium strength D * n is more appropriate to describe the interfaces than the individual components of ∆ ∆ ∆ * n . Besides, the D * 3 and D * 3,1can provide higher resolution interfaces in the simulation of Kelvin-Helmholtz instability.

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Velocity slip and temperature jump simulations by the three-dimensional thermal finite-difference lattice Boltzmann method

Cited by 34 publications

References 31 publications

Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes

Natural convection with mixed insulating and conducting boundary conditions: low- and high-Rayleigh-number regimes

Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

Discrete Boltzmann method for non-equilibrium flows: Based on Shakhov model

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