Abstract Low speed thermal transpiration gas flows through micro-channels are simulated by the direct simulation BGK (DSBGK) method that is based on the Bhatnagar-Gross-Krook model equation. Different from the ordinary application of BGK equation having the viscosity matched, we selected its relaxation time according to the thermal conductivity coefficient and thus significantly improved the accuracy. In comparing the detailed flow field solutions of a 2D Knudsen pump, the validation by the standard direct simulation Monte Carlo (DSMC) method shows that the improved BGK equation has about the same accuracy as the Shakhov equation that is solved by the well-developed gas kinetic unified algorithm (GKUA). We also present the ordinary application of BGK equation with noticeable error to clearly show the difference made in our study. Then, the efficient DSBGK method is applied to simulate the low-speed rarefied gas flows in 3D real-size thermal transpiration problem to show its applicability and its validity is verified by comparing with the experimental measurement of mass flow rates. The DSBGK simulation results have excellent agreement with experimental data for three types of gases over a wide range of Knudsen number. Additionally, the channel end effect is also studied and discussed as a prerequisite for high-fidelity modeling, otherwise it will be mistakenly interpreted as the variation of accommodation coefficients of the molecular reflection process on the solid boundary.

中文翻译：

---

低速热蒸腾气体流过微通道的高效 DSBGK 模拟

摘要 采用基于Bhatnagar-Gross-Krook模型方程的直接模拟BGK(DSBGK)方法模拟了低速热蒸腾气流通过微通道。不同于通常应用粘度匹配的BGK方程，我们根据导热系数选择其弛豫时间，从而显着提高了精度。在对比二维 Knudsen 泵的详细流场解时，通过标准直接模拟蒙特卡罗 (DSMC) 方法的验证表明，改进的 BGK 方程与由发育良好的气体求解的 Shakhov 方程具有大致相同的精度动力学统一算法（GKUA）。我们还介绍了具有明显误差的 BGK 方程的普通应用，以清楚地显示我们研究中的差异。然后，将高效的DSBGK方法用于模拟3D真实尺寸热蒸腾问题中的低速稀薄气体流动，以展示其适用性，并通过与质量流量的实验测量进行比较验证其有效性。DSBGK 模拟结果与三种气体在很宽的克努森数范围内的实验数据非常吻合。此外，还将通道端效应作为高保真建模的先决条件进行了研究和讨论，否则将被错误地解释为固体边界上分子反射过程的调节系数的变化。