求解一维双曲守恒律方程的高分辨率格式  

A High-Resolution Scheme for Solving One-Dimensional Hyperbolic Conservation Law Equations

作　　者：汪浏博 陈柳诗 王晴 

机构地区：[1]长安大学理学院,陕西 西安

出　　处：《应用数学进展》2024年第3期900-911,共12页Advances in Applied Mathematics

摘　　要：对于双曲守恒律方程,当存在激波或间断时,熵相容格式会出现非物理振荡,为抑制振荡同时提高格式的分辨率,利用限制器构造高分辨率格式,对已有的sweby及MC限制器进行改进,将改进后的限制器添加至熵相容格式中。在一维双曲守恒律上进行数值实验结果表明,所构造的高分辨率熵相容格式具有鲁棒性、无振荡性等良好特性。For the hyperbolic conservation law equations, when shock waves or discontinuities are present, entropy-consistent schemes may exhibit non-physical oscillations. To suppress these oscillations and enhance the resolution of the scheme, high-resolution formats are constructed using limiters. We propose improvements to the existing Sweby and MC limiters and incorporate the enhanced limiters into the entropy-consistent scheme. Numerical experiments on one-dimensional hyperbolic conservation laws demonstrate that the developed high-resolution, entropy-consistent scheme ex-hibits robustness and freedom from oscillations, highlighting its favorable characteristics.

关 键 词：双曲守恒方程 熵稳定格式 高分辨率 斜率限制器 

分 类 号：G63[文化科学—教育学]