基于限制器的理想磁流体力学方程全离散熵稳定显式DG格式
Limiter-based fully-discrete entropy stable explicit DG schemes for ideal MHD equations
- University of Science and Technology of China（中国科学技术大学）
- The University of Alabama（阿拉巴马大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一类基于广义路径分解框架和ES限制器的全离散熵稳定DG格式，用于理想MHD方程，满足单元熵不等式并具有低耗散和强鲁棒性。
AI中文摘要：
我们针对可压缩理想磁流体力学（MHD）方程提出了一类高阶全离散熵稳定（ES）显式间断伽辽金（DG）求解器。我们的主要理论贡献是为Godunov对称形式下的MHD方程引入了一个新的广义路径分解框架。通过创新性地将非守恒源项的内部体积积分解释为沿由解多项式构造的广义路径的路径积分，我们建立了全离散DG格式的弱单元熵不等式。这一总体框架也适用于其他基于对称形式的现有DG求解器。结合精心设计的ES限制器，所提出的格式满足真正的全离散单元熵不等式。利用这一性质，可以获得Lax-Wendroff型定理，以证明解极限满足熵条件。最后，该格式自然与局部无散度空间兼容。广泛的数值实验表明该格式具有低数值耗散和强鲁棒性。
英文摘要：
We propose a class of high-order fully-discrete entropy stable (ES) explicit discontinuous Galerkin (DG) solvers for the compressible ideal magnetohydrodynamics (MHD) equations. Our main theoretical contribution is the introduction of a novel generalized-path-decomposition framework for MHD equations in Godunov's symmetric form. By innovatively interpreting the interior volume integral of the non-conservative source term as a path integral along a generalized path constructed by the solution polynomial, we establish the weak cell entropy inequality for the fully-discrete DG schemes. This overarching framework also accommodates other existing DG solvers based on the symmetric form. Combined with a carefully designed ES limiter, the proposed scheme satisfies the genuine fully-discrete cell entropy inequality. With this property, a Lax--Wendroff-type theorem can be obtained to show that the solution limit satisfies the entropy condition. Finally, the scheme is naturally compatible with the locally divergence-free space. Extensive numerical experiments demonstrate the scheme's low numerical dissipation and strong robustness.
