一维双曲型守恒律方程的Lax-Wendroff型中心间断伽辽金方法
Lax-Wendroff Type Central Discontinuous Galerkin Method for One-Dimensional Hyperbolic Conservation Law Equations
摘要: 物理系统中波动、传播等现象通常用双曲型守恒律方程的数学模型来描述，特别是在流体力学领域尤为重要。针对此类方程，我们考虑了Lax-Wendroff型中心间断伽辽金方法。该方法首先采用Lax-Wendroff型时间离散方法，也就是通过泰勒级数展开处理时间导数，然后在空间上运用中心间断伽辽金方法，从而避免了传统的多步时间积分方法。最后我们对多个双曲型守恒律方程开展数值实验，验证所提出方法在计算效率和精度上的有效性。
Abstract: In physical systems, phenomena like wave fluctuation and propagation are often described using hyperbolic conservation law equations, which play a crucial role in fluid mechanics. To solve these equations, we employ the Lax-Wendroff central discontinuous Galerkin method. This approach begins with the Lax-Wendroff time discretization, where time derivatives are managed through a Taylor series expansion. It then incorporates the central discontinuous Galerkin method for spatial discretization and effectively eliminates the need for traditional multi-step time integration schemes. Finally, numerical experiments on various hyperbolic conservation law equations are constructed to validate the effectiveness of our method in terms of both computational efficiency and accuracy.
文章引用：罗艺. 一维双曲型守恒律方程的Lax-Wendroff型中心间断伽辽金方法[J]. 应用数学进展, 2025, 14(2): 376-387. https://doi.org/10.12677/aam.2025.142078

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