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

作　　者：罗艺 

机构地区：[1]重庆交通大学数学与统计学院,重庆

出　　处：《应用数学进展》2025年第2期376-387,共12页Advances in Applied Mathematics

基　　金：重庆市研究生校级科研创新项目(2024S0134)。

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。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.

关 键 词：Lax-Wendroff型时间离散方法 中心间断伽辽金方法 双曲型守恒律方程 

分 类 号：O17[理学—数学]