Stability analysis of inverse Lax–Wendroff boundary treatment of high order compact difference schemes for parabolic equations
Stability analysis of inverse Lax–Wendroff boundary treatment of high order compact difference schemes for parabolic equations
复制标题
抛物型方程高阶紧差分格式逆Lax-Wendroff边界处理的稳定性分析
DOI：
10.1016/j.cam.2021.113711
复制
发表时间：
2022
影响因子：
2.4
通讯作者：
Chi-Wang Shu
中科院分区：
文献类型：
--
作者：
Tingting Li;Jianfang Lu;Chi-Wang Shu
本文研究了抛物型方程高阶紧致差分方法数值边界处理的稳定性。紧致差分格式可以在相对较小的尺度下达到很高的精度。为了匹配内部区域中紧致格式的收敛阶，我们采用简化的逆Lax-Wendroff（SILW）过程（Tan等人，2012; Li等人，2017）作为我们的数值边界处理。在全离散情况下，采用三阶总变差递减（TVD）龙格-库塔法（Shu和Osher，1988）作为我们的时间推进方法。采用两种分析技术来检查算法的稳定性，一种是基于Godunov-Ryabenkii理论，另一种是特征值谱可视化方法（Vilar和Shu，2015）。半离散和全离散的情况下进行了研究，这两种不同的分析技术产生一致的结果。数值实验结果验证了理论分析的正确性。
In this paper, we study the stability of a numerical boundary treatment of high order compact finite difference methods for parabolic equations. The compact finite difference schemes could achieve very high order accuracy with relatively small stencils. To match the convergence order of the compact schemes in the interior domain, we take the simplified inverse Lax–Wendroff (SILW) procedure (Tan et al., 2012; Li et al., 2017) as our numerical boundary treatment. The third order total variation diminishing (TVD) Runge–Kutta method (Shu and Osher, 1988) is taken as our time-stepping method in the fully-discrete case. Two analysis techniques are adopted to check the algorithm’s stability, one is based on the Godunov–Ryabenkii theory, and the other is the eigenvalue spectrum visualization method (Vilar and Shu, 2015). Both the semi-discrete and fully-discrete cases are investigated, and these two different analysis techniques yield consistent results. Several numerical experimental results are shown to validate the theoretical results.