论文标题
Navier-Stokes和非线性对流扩散方程的矩形多余时间晶格Boltzmann方法：一般平衡和一些重要问题
Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues
论文作者
论文摘要
在本文中，我们为Navier-Stokes方程（NSES）和非线性对流 - 对流 - 扩散方程（NCDE）开发了一种通用的矩形多余时间晶格Boltzmann（RMRT-LB）方法，通过扩展我们最近的MRT-LB方法的统一框架[Z.H. Z.H.柴和卑诗省史，物理。 Rev. E 102，023306（2020）]，其中矩形平衡分布函数（REDF）[J.H.卢等人，菲尔。反式。 R. Soc。使用矩形晶格上的369，2311-2319（2011）。由于矩形晶格上离散速度的各向异性，REDF的三阶力矩与流行的LB方法不一致，因此，MRT-LB方法的先前统一框架无法直接应用于NSES，使用REDF在矩形RDDDQQ lattice上使用REDF。可以通过直接选择与动力学粘度和散装粘度有关的松弛子量$ \ mathbf {s} _2 $，通过直接选择Subs-Matrix $ \ Mathbf {s} _2 $从RMRT-LB方法中恢复宏观NSE。虽然矩形晶格并未导致REDF的零时，一阶和二阶矩的变化，因此MRT-LB方法的统一框架可以直接应用于NCDE。 It should be noted that the RMRT-LB model for NSEs can be derived on the rDdQq lattice, including rD2Q9, rD3Q19, and rD3Q27 lattices, and the RMRT-LB versions (if existed) of the previous MRT-LB models can be obtained, including those based on raw (natural)-moment, central-moment, Hermite-moment, and central赫尔米特时刻分别。
In this paper, we develop a general rectangular multiple-relaxation-time lattice Boltzmann (RMRT-LB) method for the Navier-Stokes equations (NSEs) and nonlinear convection-diffusion equation (NCDE) by extending our recent unified framework of MRT-LB method [Z.H. Chai and B.C. Shi, Phys. Rev. E 102, 023306 (2020)], where a rectangular equilibrium distribution function (REDF) [J.H. Lu et al, Phil. Trans. R. Soc. A 369, 2311-2319 (2011)] on a rectangular lattice is utilized. Due to the anisotropy of discrete velocities on a rectangular lattice, the third-order moment of REDF is inconsistent with that of popular LB method, and thus the previous unified framework of MRT-LB method cannot be directly applied to the NSEs using the REDF on the rectangular rDdQq lattice. The macroscopic NSEs can be recovered from the RMRT-LB method through the direct Taylor expansion method by properly selecting the relaxation sub-matrix $\mathbf{S}_2$ which is related to kinetic viscosity and bulk viscosity. While the rectangular lattice does not lead to the change of the zero-th, first and second-order moments of REDF, thus the unified framework of MRT-LB method can be directly applied to the NCDE. It should be noted that the RMRT-LB model for NSEs can be derived on the rDdQq lattice, including rD2Q9, rD3Q19, and rD3Q27 lattices, and the RMRT-LB versions (if existed) of the previous MRT-LB models can be obtained, including those based on raw (natural)-moment, central-moment, Hermite-moment, and central Hermite-moment, respectively.
