A polyatomic gas with slow relaxation of the internal modes in contact with a solid boundary is considered. In a previous paper [K. Aoki et al., Phys. Rev. E 102, 023104 (2020)], the two-temperature Navier-Stokes system, i.e., a set of compressible Navier-Stokes equations with the translational and internal temperatures, was derived from the ellipsoidal-statistical (ES) model of the Boltzmann equation for a polyatomic gas under the assumption that the Knudsen number is small and the ratio of the collisional mean free time to the relaxation time of the internal modes is as small as the Knudsen number. In the present study, the appropriate boundary conditions for the two-temperature Navier-Stokes system are derived by the analysis of the Knudsen layer on the basis of the ES model for a polyatomic gas and the Maxwell-type diffuse-specular reflection condition on the boundary. The resulting boundary conditions, which are of the type of slip boundary conditions, are summarized, together with the two-temperature Navier-Stokes equations, in a form that is applicable to practical applications immediately.

中文翻译：

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多原子气体的双温度 Navier-Stokes 方程的边界条件

考虑与固体边界接触的内部模式缓慢弛豫的多原子气体。在之前的一篇论文中 [K. 青木等。，物理。修订版 E 102, 023104 (2020)]，双温度 Navier-Stokes 系统，即一组具有平移和内部温度的可压缩 Navier-Stokes 方程，是从 Boltzmann 方程的椭球统计 (ES) 模型导出的假设克努森数很小，并且碰撞平均自由时间与内部模式的弛豫时间之比与克努森数一样小。在本研究中，基于多原子气体的 ES 模型和麦克斯韦型漫反射镜面反射条件，通过对 Knudsen 层的分析，推导出了两温度 Navier-Stokes 系统的适当边界条件。边界。所得边界条件属于滑动边界条件类型，总结如下：