The discrete velocity method (DVM) for rarefied flows and the unified methods (based on the DVM framework) for flows in all regimes, from continuum one to free molecular one, have worked well as precise flow solvers over the past decades and have been successfully extended to other important physical fields. Both DVM and unified methods endeavor to model the gas-gas interaction physically. However, for the gas-surface interaction (GSI) at the wall boundary, they have only use the full accommodation boundary up to now, which can be viewed as a rough Maxwell boundary with a fixed accommodation coefficient (AC) at unity, deviating from the real value. For example, the AC for metal materials typically falls in the range of 0.8 to 0.9. To overcome this bottleneck and extend the DVM and unified methods to more physical boundary conditions, an algorithm for Maxwell boundary with an adjustable AC is established into the DVM framework. The Maxwell boundary model splits the distribution of the bounce-back molecules into specular ones and Maxwellian (normal) ones. Since the bounce-back molecules after the spectral reflection does not math with the discrete velocity space (DVS), both macroscopic conservation (from numerical quadrature) and microscopic consistency in the DVS are hard to achieve in the DVM framework. In this work, this problem is addressed by employing a combination of interpolation methods for mismatch points in DVS and an efficient numerical error correction method for micro-macro consistency. On the other hand, the current Maxwell boundary for DVM takes the generality into consideration, accommodating both the recently developed efficient unstructured velocity space and the traditional Cartesian velocity space. Moreover, the proposed algorithm allows for calculations of both monatomic gases and diatomic gases with internal degrees in DVS. Finally, by being integrated with the unified gas-kinetic scheme within the DVM framework, the performance of the present GSI algorithm is validated through a series of benchmark numerical tests across a wide range of Knudsen numbers.

中文翻译：

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用于预测稀薄流和多尺度流的离散速度方法的气体-表面相互作用算法：用于 Maxwell 边界模型


用于稀疏流的离散速度法 （DVM） 和用于所有状态（从连续体 1 到自由分子 1）的流的统一方法（基于 DVM 框架）在过去几十年中作为精确的流动求解器运行良好，并已成功扩展到其他重要的物理领域。DVM 和统一方法都试图对气体-气体相互作用进行物理建模。然而，对于壁边界处的气体-表面相互作用 （GSI），到目前为止他们只使用了完整的住宿边界，这可以看作是一个粗糙的麦克斯韦边界，在单位时具有固定的住宿系数 （AC），偏离了实际值。例如，金属材料的 AC 通常在 0.8 到 0.9 的范围内。为了克服这一瓶颈并将 DVM 和统一方法扩展到更多的物理边界条件，在 DVM 框架中建立了一种具有可调 AC 的 Maxwell 边界算法。麦克斯韦边界模型将反弹分子的分布分为镜面分布和麦克斯韦（正常）分布。由于光谱反射后的反弹分子没有与离散速度空间 （DVS） 进行数学运算，因此在 DVM 框架中很难实现 DVS 中的宏观守恒（来自数值正交）和微观一致性。在这项工作中，通过对 DVS 中的失配点采用插值方法和用于微观-宏观一致性的有效数值纠错方法的组合来解决这个问题。另一方面，当前 DVM 的 Maxwell 边界考虑了通用性，同时容纳了最近开发的高效非结构化速度空间和传统的笛卡尔速度空间。 此外，所提出的算法允许在 DVS 中计算具有内部度数的单原子气体和双原子气体。最后，通过与 DVM 框架内的统一气体动力学方案集成，通过对各种克努森数的一系列基准数值测试验证了当前 GSI 算法的性能。