This paper focuses on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methodsrepresented by unified gas-kinetic scheme (UGKS) and discrete unified gas-kinetic scheme (DUGKS), which concentrate on the evolution of the distribution function at the cell interface, in the present scheme the flux for macroscopic variables is split into the equilibrium part and the nonequilibrium part, and the nonequilibrium flux is calculated by integrating the discrete distribution function at the cell center, which overcomes the excess numerical dissipation of the conventional DVM in the continuum flow regime. Afterwards, the macroscopic variables are finally updated by simply integrating the discrete distribution function at the cell center, or by a blend of the increments based on the macroscopic and the microscopic systems, and the multiscale property is achieved. Several test cases, involving unsteady, steady, high speed, low speed gas flows in all flow regimes, have been performed, demonstrating the good performance of the multiscale DVM from free molecule to continuum Navier-Stokes solutions and the multiscale property of the scheme is proved.

本文致力于将常规离散速度方法（DVM）改进为在有限体积框架下针对所有流动状态下的气体流动的多尺度方案。与统一气体动力学方案（UGKS）和离散统一气体动力学方案（DUGKS）代表的典型的多尺度动力学方法不同，后者专注于细胞界面分布函数的演化，在本方案中，宏观变量的通量为分为平衡部分和非平衡部分，并通过在单元中心积分离散分布函数来计算非平衡通量，从而克服了传统DVM在连续流状态下的多余数值耗散。之后，最后，通过简单地在单元中心集成离散分布函数或通过基于宏观和微观系统的增量混合来最终更新宏观变量，即可实现多尺度特性。已经进行了几个测试案例，涉及在所有流态下的不稳定，稳定，高速，低速气流，证明了多尺度DVM从自由分子到连续Navier-Stokes解决方案的良好性能，并且该方案的多尺度性质是证实。