Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution

Yang, James; Yan, Chih-Yuan; Diaz, Manuel A.; Huang, Juan; Li, Zhihui; Zhang, Hanxin

doi:10.1098/rspa.2013.0413

Cited by 7 publications

(17 citation statements)

References 30 publications

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“…Here, we test our solution method by solving two-dimensional Riemann problems of semiclassical rarefied gas dynamics. In order to compare the present results of τ −→ 0 with those of Yang et al [28] which corresponding to τ = 0, we have employed the same numerical method and the same mesh system as in [28]. Although the initial set-up of the present two-dimensional Riemann problem is the same as that in [28], however, due to finite relaxation time, the dissipative effects are not negligible and will cause the evolution and interaction of discontinuities to display more broad profiles in general depending on the value of relaxation time (or Knudsen number).…”

Section: Numerical Resultsmentioning

confidence: 72%

“…In recent years, notable numerical methods to describe the ideal quantum gas flows have been developed [25][26][27]. Numerical experiments with f = f ES in equation (2.1), corresponding to relaxation time τ = 0, have been presented [28]. This work is a sequel to Yang et al [28] and the effect of finite relaxation time which covers different non-equilibrium flow regimes is examined.…”

Section: Semiclassical Boltzmann Ellipsoidal-statistical Kinetic Modementioning

confidence: 99%

“…Numerical experiments with f = f ES in equation (2.1), corresponding to relaxation time τ = 0, have been presented [28]. This work is a sequel to Yang et al [28] and the effect of finite relaxation time which covers different non-equilibrium flow regimes is examined. It is worth pointing out that in the equilibrium flow (τ = 0), one only has the unknown f ES and the macroscopic quantities from f ES , n(x, t), u(x, t) and W αβ (x, t), are given by equation (2.3).…”

Section: Semiclassical Boltzmann Ellipsoidal-statistical Kinetic Modementioning

confidence: 99%

“…The full semiclassical Boltzmann equation and its related theory can be found in [1,2]. Here we follow the development in [28] and consider the semiclassical Boltzmann ES model equation by Wu et al [23] ∂f ∂t…”

Section: Semiclassical Boltzmann Ellipsoidal-statistical Kinetic Modementioning

confidence: 99%

“…The numerical flux for a second-order TVD scheme using flux limiter can be found in [28], and that for a fifth-order WENO scheme (WENO3, (r = 3)) can be found in [34] and will not be repeated here. The class of asymptotic preserving schemes for the kinetic equations and related problems with stiff sources can be beneficially applied as well [36,40].…”

Section: Solution Algorithms In Phase Space (A) Implementation Of Dismentioning

confidence: 99%

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Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

et al. 2014

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Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidalstatistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied.

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Section: Numerical Resultsmentioning

confidence: 72%

Section: Semiclassical Boltzmann Ellipsoidal-statistical Kinetic Modementioning

confidence: 99%

Section: Semiclassical Boltzmann Ellipsoidal-statistical Kinetic Modementioning

confidence: 99%

Section: Semiclassical Boltzmann Ellipsoidal-statistical Kinetic Modementioning

confidence: 99%

Section: Solution Algorithms In Phase Space (A) Implementation Of Dismentioning

confidence: 99%

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Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

et al. 2014

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Stationary Quantum BGK Model for Bosons and Fermions in a Bounded Interval

Bae

Yun

2019

J Stat Phys

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In this paper, we consider the existence problem for a stationary relaxational models of the quantum Boltzmann equation. More precisely, we establish the existence of mild solution to the fermionic or bosonic quantum BGK model in a slab with inflow boundary data. Unlike the classical case, it is necessary to verify that the quantum local equilibrium state is well-defined, and the transition from the non-condensed state to the condensated state (Bosons), or from the non-saturated state to the saturated state (Fermions) does not arise in our solution space. 3 5 , (1.4)

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A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: Homogeneous relaxation and transport coefficients

2019

Journal of Computational Physics

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A fast spectral method (FSM) is developed to solve the Uehling-Uhlenbeck equation for quantum gas mixtures with generalized differential cross-sections. The computational cost of the proposed FSM is O(M dv−1 N dv +1 log N), where d v is the dimension of the problem, M dv −1 is the number of discrete solid angles, and N is the number of frequency nodes in each direction. Spatially-homogeneous relaxation problems are used to demonstrate that the FSM conserves mass and momentum/energy to the machine and spectral accuracy, respectively. Based on the variational principle, transport coefficients such as the shear viscosity, thermal conductivity, and diffusion are calculated by the FSM, which compare well with analytical solutions. Then, we apply the FSM to find the accurate transport coefficients through an iterative scheme for the linearized quantum Boltzmann equation. The shear viscosity and thermal conductivity of the three-dimensional quantum Fermi and Bose gases interacting through hard-sphere potential are calculated. For Fermi gas, the relative difference between the accurate and variational transport coefficients increases with the fugacity; for Bose gas, the relative difference in the thermal conductivity has similar behavior as the gas moves from the classical to the degenerate limits, but that in the shear viscosity decreases. Finally, the shear viscosity and diffusion coefficient have also been calculated for a two-dimensional equal-mole mixture of Fermi gases. When the molecular mass of the two components are the same, our numerical results agree well with the variational solution. However, when the molecular mass ratio is not one, large discrepancies between the accurate and variational results are observed; our results are reliable because (i) the method relies on no assumption and (ii) the ratio between shear viscosity and entropy density satisfies the minimum bound predicted by the string theory.

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Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution

Cited by 7 publications

References 30 publications

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

Stationary Quantum BGK Model for Bosons and Fermions in a Bounded Interval

A fast spectral method for the Uehling-Uhlenbeck equation for quantum gas mixtures: Homogeneous relaxation and transport coefficients

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