Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics
Entropy-stable Gauss collocation methods for ideal magneto-hydrodynamics
复制标题
理想磁流体动力学的熵稳定高斯配置方法
DOI：
10.1016/j.jcp.2022.111851
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发表时间：
2023
影响因子：
4.1
通讯作者：
Gassner, Gregor J.
中科院分区：
文献类型：
--
作者：
Rueda-Ramírez, Andrés M.;Hindenlang, Florian J.;Chan, Jesse;Gassner, Gregor J.
本文提出了一种基于三维曲线网格的熵稳定Gauss配置间断Galerkin（DG）方法，用于求解具有广义拉格朗日乘子（GLM）发散清除机制的单流体磁流体动力学（MHD）方程。为了保持连续熵分析并确保发散清除技术中的伽利略不变性，GLM-MHD系统需要使用非保守项。传统上，熵稳定DG离散化使用DG方法的同位节点变体，也称为Legendre-Gauss-Lobatto（LGL）点上的不连续Galerkin谱元方法（DGSEM）。最近，Chan等人[1]，“Efficient Entropy Stable Gauss Collocation Methods”。SIAM（2019）]提出了一种熵稳定的DGSEM方案，该方案使用Legendre-Gauss点（而不是LGL点）作为守恒律。我们的主要贡献是将Chan等人的离散方法推广到非保守GLM-MHD系统，并在三维曲线网格上数值验证了新格式的熵行为和收敛性。此外，我们测试的鲁棒性和准确性，我们的计划与磁流体动力学开尔文-亥姆霍兹不稳定性问题。数值实验表明，高斯点上GLM-MHD系统的熵稳定DGSEM比LGL系统的DGSEM更精确。
In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: the single-fluid magneto-hydrodynamics (MHD) equations with a generalized Lagrange multiplier (GLM) divergence cleaning mechanism. For the continuous entropy analysis to hold and to ensure Galilean invariance in the divergence cleaning technique, the GLM-MHD system requires the use of non-conservative terms.Traditionally, entropy-stable DG discretizations have used a collocated nodal variant of the DG method, also known as the discontinuous Galerkin spectral element method (DGSEM) on Legendre-Gauss-Lobatto (LGL) points. Recently, Chan et al. [1, “Efficient Entropy Stable Gauss Collocation Methods”. SIAM (2019)] presented an entropy-stable DGSEM scheme that uses Legendre-Gauss points (instead of LGL points) for conservation laws. Our main contribution is to extend the discretization technique of Chan et al. to the non-conservative GLM-MHD system.We provide a numerical verification of the entropy behavior and convergence properties of our novel scheme on 3D curvilinear meshes. Moreover, we test the robustness and accuracy of our scheme with a magneto-hydrodynamic Kelvin-Helmholtz instability problem. The numerical experiments suggest that the entropy-stable DGSEM on Gauss points for the GLM-MHD system is more accurate than the LGL counterpart.