Assessment of the ellipsoidal-statistical Bhatnagar–Gross–Krook model for force-driven Poiseuille flows

Meng, Juan; Wu, Lei; Reese, Jason M.; Zhang, Yonghao

doi:10.1016/j.jcp.2013.05.045

Cited by 36 publications

(26 citation statements)

References 26 publications

(57 reference statements)

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“…Figure 9 shows that the normalized MFR reduces with increasing external acceleration. This is consistent with results from Boltzmann-type kinetic equations (Aoki, Takata & Nakanishi 2002;Meng et al 2013). Generally speaking, because of the viscous heating, a larger external acceleration results in a higher gas temperature and consequently a larger effective Knudsen number Kn e .…”

Section: For Various Values Of L/σ and The Global Knudsen Numbersupporting

confidence: 90%

Non-equilibrium dynamics of dense gas under tight confinement

Liu

Reese

et al. 2016

J. Fluid Mech.

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The force-driven Poiseuille flow of dense gases between two parallel plates is investigated through the numerical solution of the generalized Enskog equation for two-dimensional hard discs. We focus on the competing effects of the mean free path λ, the channel width L and the disc diameter σ . For elastic collisions between hard discs, the normalized mass flow rate in the hydrodynamic limit increases with L/σ for a fixed Knudsen number (defined as Kn = λ/L), but is always smaller than that predicted by the Boltzmann equation. Also, for a fixed L/σ , the mass flow rate in the hydrodynamic flow regime is not a monotonically decreasing function of Kn but has a maximum when the solid fraction is approximately 0.3. Under ultra-tight confinement, the famous Knudsen minimum disappears, and the mass flow rate increases with Kn, and is larger than that predicted by the Boltzmann equation in the free-molecular flow regime; for a fixed Kn, the smaller L/σ is, the larger the mass flow rate. In the transitional flow regime, however, the variation of the mass flow rate with L/σ is not monotonic for a fixed Kn: the minimum mass flow rate occurs at L/σ ≈ 2-3. For inelastic collisions, the energy dissipation between the hard discs always enhances the mass flow rate. Anomalous slip velocity is also found, which decreases with increasing Knudsen number. The mechanism for these exotic behaviours is analysed.

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Section: For Various Values Of L/σ and The Global Knudsen Numbersupporting

confidence: 90%

Non-equilibrium dynamics of dense gas under tight confinement

Liu

Reese

et al. 2016

J. Fluid Mech.

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“…2(a-f) that the results obtained by the USP-ESBGK method agree well with the corresponding DSMC results for the cases 1-3, except that there is small deviation for the temperature distribution at Kn=0.1 as shown in Fig. 2(b), due to the limitation of the simplified collision term in the ESBGK model [46]. Note that an accurate DSMC calculations require that the cell sizes are smaller than molecular mean free path and the time steps are smaller than mean collision time, while the USP-ESBGK method can get accurate results using much larger cell sizes and time steps.…”

Section: Poiseuille Flowsupporting

confidence: 75%

A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows

Fei

Zhang

et al. 2020

Journal of Computational Physics

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The stochastic particle method based on Bhatnagar-Gross-Krook (BGK) or ellipsoidal statistical BGK (ESBGK) model approximates the pairwise collisions in the Boltzmann equation using a relaxation process.Therefore, it is more efficient to simulate gas flows at small Knudsen numbers than the counterparts based on the original Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) method. However, the traditional stochastic particle BGK method decouples the molecular motions and collisions in analogy to the DSMC method, and hence its transport properties deviate from physical values as the time step increases. This defect significantly affects its computational accuracy and efficiency for the simulation of multiscale flows, especially when the transport processes in the continuum regime is important. In the present paper, we propose a unified stochastic particle ESBGK (USP-ESBGK) method by combining the molecular convection and collision effects. In the continuum regime, the proposed method can be applied using large temporal-spatial discretization and approaches to the Navier-Stokes solutions accurately. Furthermore, it is capable to simulate both the small scale non-equilibrium flows and large scale continuum flows within a unified framework efficiently and accurately. The applications of USP-ESBGK method to a variety of benchmark problems, including Couette flow, thermal Couette flow, Poiseuille flow, Sod tube flow, cavity flow, and flow through a slit, demonstrated that it is a promising tool to simulate multiscale gas flows ranging from rarefied to continuum regime.

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“…We consider monatomic gas in this simulation. To follow the study [20], the Knudsen number is defined as,…”

Section: Force Driven Poiseuille Flowmentioning

confidence: 99%

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

Chen

Cai

2015

Adv. Appl. Math. Mech.

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The Ellipsoidal Statistical model (ES-model) and the Shakhov model (Smodel) were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heat flux. With the introduction of a new parameter to combine the ES-model and S-model, a generalized kinetic model can be developed. This new model can give the correct Navier-Stokes equations in the continuum flow regime. Through the adjustment of the new parameter, it provides abundant dynamic effect beyond the ES-model and S-model. Changing the free parameter, the physical performance of the new model has been tested numerically. The unified gas kinetic scheme (UGKS) is employed for the study of the new model. In transition flow regime, many physical problems, i.e., the shock structure and micro-flows, have been studied using the generalized model. With a careful choice of the free parameter, good results can be achieved for most test cases. Due to the property of the Boltzmann collision integral, the new parameter in the generalized kinetic model cannot be fully determined. It depends on the specific problem. Generally speaking, the Smodel predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model, while ES-model performs better in the cases where the flow is mostly driven by temperature gradient, such as a channel flow with large boundary temperature variation at high Knudsen number.

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Assessment of the ellipsoidal-statistical Bhatnagar–Gross–Krook model for force-driven Poiseuille flows

Cited by 36 publications

References 26 publications

Non-equilibrium dynamics of dense gas under tight confinement

Non-equilibrium dynamics of dense gas under tight confinement

A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

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