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
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。
Abstract: 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.
文章引用：汪浏博, 陈柳诗, 王晴. 求解一维双曲守恒律方程的高分辨率格式[J]. 应用数学进展, 2024, 13(3): 900-911. https://doi.org/10.12677/AAM.2024.133085

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