浅水磁流体方程的高分辨率熵稳定格式
High-Resolution Entropy Stable Scheme for Shallow Water Magnetohydrodynamics Equations
摘要: 本文构造了一种求解浅水磁流体方程(Shallow Water Magnetohydrodynamics Equations，简称为SWMHD方程)的高分辨率熵稳定格式(ES2)。主要构造过程是将一种基于MUSCL (Monotone Up-stream-centred Scheme for Conservation Laws)型重构方法的新型斜率限制器应用于SWMHD方程的熵稳定格式(ES)中，得到了具有二阶精度的高分辨率熵稳定格式，该格式在间断区域通过合理控制耗散的方式有效地抑制了非物理现象的产生。将新构造的格式(ES2)和熵稳定格式(ES)，熵守恒格式(C)应用于一维和二维SWMHD方程问题求解中，数值结果表明，该格式能够准确地捕捉解的结构，在光滑区域达到了高阶精度，且在间断区域没有非物理振荡。
Abstract: In this paper, a high-resolution entropy stable scheme (ES2) is constructed to solve the shallow wa-ter magnetohydrodynamics equations (SWMHD equation). The main construction process is to ap-ply a new slope limiter based on MUSCL (Monotone Upstream-centred Scheme for Conservation Laws) type reconstruction method to the entropy stable scheme (ES) of the SWMHD equation, and obtain a high-resolution entropy stable scheme with second-order accuracy, which effectively sup-presses the occurrence of non-physical phenomena by reasonably controlling dissipation in the discontinuous region. The newly constructed scheme (ES2), entropy stable scheme (ES), and entro-py conservation scheme (C) are applied to solve the one-dimensional and two-dimensional SWMHD equation problems, and the numerical results show that the scheme can accurately capture the structure of the solutions, achieve high-order accuracy in the smooth region, and have no non-physical oscillations in the discontinuous region.
文章引用：王晴, 封建湖, 陈柳诗. 浅水磁流体方程的高分辨率熵稳定格式[J]. 应用数学进展, 2023, 12(9): 4076-4089. https://doi.org/10.12677/AAM.2023.129400

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