The kinetic theory provides a good basis for developing numerical methods for multiscale gas flows covering a wide range of flow regimes. A particular challenge for kinetic schemes is whether they can capture the correct hydrodynamic behaviors of the system in the continuum regime (i.e., as the Knudsen number $\epsilon\ll 1$ ) without enforcing kinetic scale resolution. At the current stage, the main approach to analyze such property is the asymptotic preserving (AP) concept, which aims to show whether the kinetic scheme reduces to a solver for the hydrodynamic equations as $\epsilon \to 0$. However, the detailed asymptotic properties of the kinetic scheme are indistinguishable as $\epsilon$ is small but finite under the AP framework. In order to distinguish different characteristics of kinetic schemes, in this paper we introduce the concept of unified preserving (UP) aiming at assessing asmyptotic orders (in terms of $\epsilon$) of a kinetic scheme by employing the modified equation approach and Chapman-Enskon analysis. It is shown that the UP properties of a kinetic scheme generally depend on the spatial/temporal accuracy and closely on the inter-connections among the three scales (kinetic scale, numerical scale, and hydrodynamic scale). Specifically, the numerical resolution and specific discretization determine the numerical flow behaviors of the scheme in different regimes, especially in the near continuum limit. As two examples, the UP analysis is applied to the discrete unified gas-kinetic scheme (DUGKS) and a second-order implicit-explicit Runge-Kutta (IMEX-RK) scheme to evaluate their asymptotic behaviors in the continuum limit.

翻译：动能理论为制定涵盖多种流动体系的多比例气体流动的数字方法提供了良好的基础。动能机制面临的一个特殊挑战是,它们能否在不执行动能比例尺分辨率分辨率的情形下,在连续系统(即Knudsen nudsen nu= $\epsilon\ll 1美元)中捕捉到系统的正确流体动力行为(即Knudsen nutsen nu= $\epsilon\ll 1美元),而没有执行动能比例尺分辨率的分辨率分辨率。在现阶段,分析这种特性的主要方法是无运动保存(AP)概念,其目的是显示运动机能计划是否降低为流体动力方程式的解析器($\epslon=0美元至0美元)。然而,动能系统的详细的动力动力学特性是不可分化的($\central-encialalalal-liformal-listal-listal-ladeal-deal-lacal-deal-deal-liversal-deal-deal-deal-deal-deal-deal-livertradeal-deal-deal-de sal-al-deal-deal-deal-deal-deal-deal-al-deal-deal-deal-deal-deal-al-al-deal-al-deal-deal-al-al-al-al-al-al-deal-deal-deal-de sal-deal-deal-deal-al-al-al-al-al-al-deal-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-deal-deal-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-al-de-deal-al-al-deal-al-al-de-de-al-al-al-al-al-al-de