In this paper, authors focus effort 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 methods 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.

中文翻译：

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模型动力学方程的多尺度离散速度方法

在本文中，作者致力于将传统的离散速度方法 (DVM) 改进为在所有流态下的气体流动的有限体积框架中的多尺度方案。与典型的多尺度动力学方法统一气体动力学方案 (UGKS) 和离散统一气体动力学方案 (DUGKS) 不同，它们专注于单元界面处分布函数的演变，在本方案中，宏观变量的通量是分开的分为平衡部分和非平衡部分，通过对单元中心的离散分布函数进行积分计算非平衡通量，克服了传统DVM在连续流态下的过度数值耗散。然后，通过对单元中心离散分布函数的简单积分，或基于宏观和微观系统的增量混合，最终更新宏观变量，实现多尺度特性。已经执行了几个测试案例，涉及所有流态下的不稳定、稳定、高速、低速气流，证明了从自由分子到连续 Navier-Stokes 解的多尺度 DVM 的良好性能，并且该方案的多尺度特性是证明了。