In this paper, we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations (MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation (NACDE) and Navier-Stokes equations (NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, two benchmark problems, Gauss hill problem and Poiseuille flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results are not only in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis.

翻译：本文首先提出了通用传播多重弛豫时间格子玻尔兹曼（GPMRT-LB）模型，并基于守恒矩推导了相应的宏观有限差分（GPMFD）格式。进而采用麦克斯韦迭代方法，在扩散尺度与声学尺度下分别分析了GPMRT-LB模型与GPMFD格式的截断误差及修正方程（MEs）。针对非线性各向异性对流扩散方程（NACDE）和纳维-斯托克斯方程（NSEs），本文进一步推导了GPMRT-LB模型与GPMFD格式的一阶与二阶修正方程。特别地，针对具有恒定速度与扩散系数的一维对流扩散方程（CDE），在扩散尺度下构建了四阶GPMRT-LB（F-GPMRT-LB）模型及相应的四阶GPMFD（F-GPMFD）格式。最后，采用高斯丘陵问题与二维泊肃叶流动两个基准算例验证了GPMRT-LB模型与GPMFD格式，数值结果不仅与相应解析解高度吻合，且具备空间二阶收敛率。此外，一维对流扩散方程的数值研究表明，F-GPMRT-LB模型与F-GPMFD格式可实现空间四阶精度，与理论分析结果一致。