Abstract In this paper, we consider the capabilities of the Boltzmann equation with the Shakhov and ellipsoidal models for the collision term to capture the characteristics of rarefied gas flows. The benchmark is performed by comparing the results obtained using these kinetic model equations with direct simulation Monte Carlo (DSMC) results for particles interacting via ab initiopotentials. The analysis is restricted to channel flows between parallel plates and we consider three flow problems, namely: the heat transfer between stationary plates, the Couette flow and the heat transfer under shear. The simulations are performed in the non-linear regime for the 3He, 4He, and Ne gases. The reference temperature ranges between 1 K and 3000 K for 3He and 4He and between 20 K and 5000 K for Ne. While good agreement is seen up to the transition regime for the direct phenomena (shear stress, heat flux driven by temperature gradient), the relative errors in the cross phenomena (heat flux perpendicular to the temperature gradient) exceed 10% even in the slip-flow regime. The kinetic model equations are solved using the finite difference lattice Boltzmann algorithm based on half-range Gauss-Hermite quadratures with the third order upwind method used for the implementation of the advection.

中文翻译：

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玻尔兹曼方程的 Shakhov 和椭球模型与基于 ab initio 的粒子相互作用的 DSMC 的比较

摘要 在本文中，我们考虑了具有 Shakhov 和椭球模型的 Boltzmann 方程在碰撞项中捕捉稀薄气体流动特征的能力。基准是通过将使用这些动力学模型方程获得的结果与直接模拟蒙特卡罗 (DSMC) 的粒子通过 ab initiopotentials 相互作用的结果进行比较来执行的。分析仅限于平行板之间的通道流动，我们考虑三个流动问题，即：固定板之间的传热、Couette 流和剪切下的传热。对于 3He、4He 和 Ne 气体，模拟是在非线性状态下进行的。3He 和 4He 的参考温度范围在 1 K 到 3000 K 之间，Ne 的参考温度范围在 20 K 到 5000 K 之间。虽然在直接现象（剪切应力、温度梯度驱动的热通量）的过渡状态中看到了很好的一致性，但交叉现象（垂直于温度梯度的热通量）的相对误差甚至在滑移中也超过了 10%。流态。动力学模型方程使用基于半程高斯-厄米积分的有限差分格子 Boltzmann 算法求解，其中三阶迎风方法用于实现对流。