Institute of Multidisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology, Wuhan 430074, China.
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
Phys Rev E. 2023 Feb;107(2-2):025304. doi: 10.1103/PhysRevE.107.025304.
In this paper, a discrete unified gas kinetic scheme (DUGKS) is proposed for continuum compressible gas flows based on the total energy kinetic model [Guo et al., Phys. Rev. E 75, 036704 (2007)1539-375510.1103/PhysRevE.75.036704]. The proposed DUGKS can be viewed as a special finite-volume lattice Boltzmann method for the compressible Navier-Stokes equations in the double distribution function formulation, in which the mass and momentum transport are described by the kinetic equation for a density distribution function (g), and the energy transport is described by the other one for an energy distribution function (h). To recover the full compressible Navier-Stokes equations exactly, the corresponding equilibrium distribution functions g^{eq} and h^{eq} are expanded as Hermite polynomials up to third and second orders, respectively. The velocity spaces for the kinetic equations are discretized according to the seventh and fifth Gauss-Hermite quadratures. Consequently, the computational efficiency of the present DUGKS can be much improved in comparison with previous versions using more discrete velocities required by the ninth Gauss-Hermite quadrature.
本文基于总能量动力学模型[Guo 等人，Phys. Rev. E 75, 036704 (2007)1539-375510.1103/PhysRevE.75.036704]，提出了一种用于连续可压缩气体流动的离散统一气体动力学方案(DUGKS)。所提出的 DUGKS 可以看作是双分布函数形式下可压缩 Navier-Stokes 方程的特殊有限体积格子玻尔兹曼方法，其中质量和动量输运由密度分布函数 (g) 的动力学方程描述，能量输运由另一个能量分布函数 (h) 的动力学方程描述。为了精确恢复完整的可压缩 Navier-Stokes 方程，相应的平衡分布函数 g^{eq} 和 h^{eq} 分别展开为三阶和二阶的 Hermite 多项式。动力学方程的速度空间根据第七和第五高斯-赫尔墨特求积公式离散化。因此，与使用第九高斯-赫尔墨特求积需要更多离散速度的先前版本相比，本 DUGKS 的计算效率可以大大提高。
