相对论流体力学方程的MUSCL-型熵相容格式
The MUSCL-Type Entropy Consistent Schemes for Relativistic Hydrodynamics Equations
摘要: 本文基于MUSCL-Hancock数据重构方法提出了一种求解相对论流体力学方程的高分辨率熵相容格式(EC-MHM格式)。首先将一个修正的斜率限制器应用到MUSCL-Hancock方法的数据重构中，使之与熵相容格式结合，从而得到高分辨率的熵相容通量；在时间上，主要利用双曲守恒律方程的守恒型差分形式来更新下一时间层，从而提高了格式的计算效率。文中还证明了熵相容格式的收敛性。新格式在解的光滑区域具有高精度的特性，然而在间断区域，EC-MHM格式可以有效抑制非物理现象的发生；最后通过一系列数值算例验证了新格式具有无振荡、高分辨率等良好性能。
Abstract: This paper presents a high-resolution entropy-consistent scheme, termed the EC-MHM (Entropy-consistent, MUSCL-type High-resolution Method), for solving relativistic hydrodynamics equations, based on the MUSCL-Hancock data reconstruction methodology. Firstly, a modified slope limiter is applied to the data reconstruction of MUSCL-Hancock method, and combine it with the entropy consistent scheme, so as to obtain the high resolution entropy consistent flux. For the discretization of time derivative, the conservative finite difference scheme of hyperbolic conservation laws is adopted to update the solution at the next time level. The convergence of the entropy consistent scheme is also proved. In regions where the solution is smooth, the EC-MHM scheme exhibits high precision characteristics. Conversely, in discontinuous zones, the EC-MHM can effectively prevent the occurrence of non-physical phenomena. Finally, a series of numerical examples are simulated, and the new scheme is proved to have good properties such as no oscillation and high resolution.
文章引用：任书锐, 封建湖, 任潇潇. 相对论流体力学方程的MUSCL-型熵相容格式[J]. 应用数学进展, 2024, 13(12): 5184-5197. https://doi.org/10.12677/aam.2024.1312501

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