We study the iterative methods for large moment systems derived from the linearized Boltzmann equation. By Fourier analysis, it is shown that the direct application of the block symmetric Gauss-Seidel (BSGS) method has slower convergence for smaller Knudsen numbers. Better convergence rates for dense flows are then achieved by coupling the BSGS method with the micro-macro decomposition, which treats the moment equations as a coupled system with a microscopic part and a macroscopic part. Since the macroscopic part contains only a small number of equations, it can be solved accurately during the iteration with a relatively small computational cost, which accelerates the overall iteration. The method is further generalized to the multiscale decomposition which splits the moment system into many subsystems with different orders of magnitude. Both one- and two-dimensional numerical tests are carried out to examine the performances of these methods. Possible issues regarding the efficiency and convergence are discussed in the conclusion.

翻译：本文研究由线性化玻尔兹曼方程导出的大型矩系统的迭代方法。通过傅里叶分析表明，直接应用块对称高斯-赛德尔（BSGS）方法在克努森数较小时收敛速度较慢。为提升稠密流场的计算效率，我们将BSGS方法与微宏观分解方法相结合，将矩方程视为由微观部分与宏观部分耦合而成的系统进行求解。由于宏观部分仅包含少量方程，可在迭代过程中以较小计算代价精确求解，从而加速整体迭代收敛。该方法进一步推广至多尺度分解框架，将矩系统按量级拆分为多个子系统。研究通过一维与二维数值实验验证了各方法的性能表现，并在结论部分讨论了计算效率与收敛性相关的潜在问题。