基于斜率限制器下求解 二维时间分数阶 Burgers 方程的 多重网格法
A Multi-Grid Method for SolvingTwo-Dimensional Temporal Fractional Burgers Equations Based on Slope Limiter
DOI: 10.12677/AAM.2024.1312503, PDF,   
作者: 李林娜：长沙理工大学，数学与统计学院，湖南 长沙
关键词: 二维时间分数阶 Burgers 方程；多重网格法；Two-Dimensional Time Fractional Burgers Equations； Multigrid Method
摘要: 本文研究求解二维时间分数阶 Burgers 方程的多重网格法：在离散过程中，我们采用 L1差分格 式离散时间分数阶导数，对流项运用 Lax-Friedrichs 通量近似计算。实验结果表明该方法可以很 好地模拟间断。
Abstract: In this paper, we study the multi-grid method for solving the two-dimensional frac- tional Burgers equation in time: In the discretization process, we use the discretized fractional derivative of time in the L1 difference format, and the Lax-Friedrichs flux approximation is used for the convection term. Experimental results show that the proposed method can simulate discontinuities well.
文章引用：李林娜. 基于斜率限制器下求解 二维时间分数阶 Burgers 方程的 多重网格法[J]. 应用数学进展, 2024, 13(12): 5217-5224. https://doi.org/10.12677/AAM.2024.1312503

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