求解双曲守恒律方程的MUSCL-Hancock熵相容格式
MUSCL-Hancock Entropy Consistent Scheme for Solving Hyperbolic Conservation Laws
摘要: 本文提出了一种基于MUSCL-Hancock方法求解双曲守恒律方程的熵相容格式(EC-MHM格式)，新格式在空间上利用MUSCL-Hancock方法对数据进行重构，并对重构后的斜率进行修正，得到高分辨率的熵相容通量；在时间上，利用双曲守恒律方程的差分形式更新下一时刻的值，更新下一时刻变量值时只需计算一次数值通量，从而提高了格式的计算效率；最后对不同的双曲守恒律方程进行数值模拟，结果表明，EC-MHM格式具有无振荡、高分辨率、高精度等良好特性。
Abstract: In this paper, an entropy consistent scheme (EC-MHM scheme) based on the MUSCL-Hancock meth-od for hyperbolic conservation laws is proposed. The new scheme uses the MUSCL-Hancock method to reconstruct the data spatially, and corrects the slope after the reconstruction to obtain a high-resolution entropy consistent flux. The value of the new time moment is updated by conserva-tive difference scheme of the hyperbolic conservation laws, and the numerical flux only needs to be calculated once when the variable value of the next moment is updated, which improves the com-putational efficiency of the scheme. Different hyperbolic conservation laws are numerically solved, and the numerical results show that the EC-MHM scheme has good characteristics such as non-oscillation, high resolution, and robustness.
文章引用：陈柳诗, 封建湖, 王晴. 求解双曲守恒律方程的MUSCL-Hancock熵相容格式[J]. 应用数学进展, 2023, 12(9): 3886-3898. https://doi.org/10.12677/AAM.2023.129382

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