标题： 一种用于高阶矩模型微流的高效稳态求解器 显示英文标题

标题： An Efficient Steady-State Solver for Microflows with High-Order Moment Model

摘要： 在[Z. Hu, R. Li和Z. Qiao的论文“通过使用低阶模型修正加速玻尔兹曼方程高阶矩模型的微流模拟”，发表于《J. Comput. Phys.》，327卷，225-244页，2016年]中，成功展示了使用低阶矩模型修正是加速玻尔兹曼方程高阶矩模型稳态计算的一种有前景的方法。为了开发现有的求解器，本文研究了以下几个方面。首先，采用具有线性重构的有限体积法进行高分辨率空间离散化，从而在不损失精度的情况下显著减少空间自由度。其次，通过在修正步骤中引入一个适当的参数$\tau$，发现求解器的性能可以显著提高，即求解器将涉及更多层次，从而进一步加速方法的收敛。第三，在每一层中采用Heun方法作为平滑器，以增强求解器的鲁棒性。进行了微流中的数值实验，以证明新求解器的效率并研究其行为。此外，测试了几种用于选择求解器阶数序列的阶数降低策略，并发现策略$m_{l-1} = \lceil m_{l} / 2 \rceil$最为有效。 显示英文摘要

摘要： In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order moment model correction is a promising idea to accelerate the steady-state computation of high-order moment models of the Boltzmann equation. To develop the existing solver, the following aspects are studied in this paper. First, the finite volume method with linear reconstruction is employed for high-resolution spatial discretization so that the degrees of freedom in spatial space could be reduced remarkably without loss of accuracy. Second, by introducing an appropriate parameter $\tau$ in the correction step, it is found that the performance of the solver can be improved significantly, i.e., more levels would be involved in the solver, which further accelerates the convergence of the method. Third, Heun's method is employed as the smoother in each level to enhance the robustness of the solver. Numerical experiments in microflows are carried out to demonstrate the efficiency and to investigate the behavior of the new solver. In addition, several order reduction strategies for the choice of the order sequence of the solver are tested, and the strategy $m_{l-1} = \lceil m_{l} / 2 \rceil$ is found to be most efficient.