For the simulation of multiscale gas flows, the numerical scheme should be valid and efficient in both rarefied and continuum regimes. For example, the Direct Simulation Monte Carlo (DSMC) method is not appropriate because of its huge computational cost in the continuum regime. Various kinds of hybrid methods with DSMC have been proposed to deal with this difficulty. One of them is the particle-particle hybrid method, which combines DSMC with another stochastic particle method that is based on an approximate kinetic model, such as the BGK-DSMC hybrid method. Since the same kind of computational particles is applied in the stochastic particle BGK (SPBGK) and DSMC methods, they can be implemented in a unified particle framework. Therefore, compared to the CFD-DSMC hybrid method, the BGK-DSMC hybrid method avoids difficulties caused by the amalgamation of two fundamentally different types of solvers. However, the traditional SPBGK method decouples the molecular motions and collisions in analogy to DSMC, and hence its transport properties deviate from physical values as the time step size increases. This defect significantly affects its computational accuracy and efficiency in the continuum regime. In the present paper, instead of the traditional SPBGK method, a unified stochastic particle BGK (USPBGK) method, which has second-order accuracy in time and space, is combined with DSMC. Comparing the computational performance of the USPBGK-DSMC and BGK-DSMC hybrid methods for numerical test cases of hypersonic flows past a cylinder and plume flows out of a planar micronozzle, one note that the proposed USPBGK-DSMC hybrid method can achieve higher efficiency for such multiscale gas flow simulations. In addition, an equilibrium-breakdown criterion based on the ratio of the time scales of the macroscopic flow field and molecule collision is proposed as a switching criterion for the new hybrid method. This criterion depends on the local Knudsen number and is easy to implement in a unified particle framework.

对于多尺度气流的模拟，数值方案在稀疏和连续区域均应有效且高效。例如，直接模拟蒙特卡洛（DSMC）方法不合适，因为它在连续体方式中的计算成本很高。已经提出了各种与DSMC的混合方法来解决这一难题。其中之一是粒子-粒子混合方法，该方法将DSMC与另一种基于近似动力学模型的随机粒子方法相结合，例如BGK-DSMC混合方法。由于在随机粒子BGK（SPBGK）和DSMC方法中应用了相同类型的计算粒子，因此可以在统一的粒子框架中实现它们。因此，与CFD-DSMC混合方法相比，BGK-DSMC混合方法避免了两种根本不同类型的求解器合并所带来的困难。但是，传统的SPBGK方法类似于DSMC来分离分子运动和碰撞，因此，随着时间步长的增加，其传输特性与物理值会发生偏差。此缺陷在连续区域中显着影响其计算精度和效率。在本文中，与传统的SPBGK方法不同，在时间和空间上具有二阶精度的统一的随机粒子BGK（USPBGK）方法与DSMC相结合。比较USPBGK-DSMC和BGK-DSMC混合方法在通过圆柱体的超音速流和从平面微喷嘴流出的羽流的数值测试案例的计算性能，有人指出，提出的USPBGK-DSMC混合方法可以为这种多尺度气流模拟实现更高的效率。此外，提出了一种基于宏观流场时间尺度与分子碰撞比例的平衡破坏准则作为新混合方法的转换准则。该标准取决于本地Knudsen数，并且易于在统一的粒子框架中实现。