发表机构
University of Notre Dame（圣母大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种高阶全显式算子分裂方法求解2.5D理想MHD，结合熵稳定DGSEM与兼容有限元，实现精确无散度更新和熵稳定，并通过多种数值实验验证其精度与稳健性。
AI 中文摘要
我们为笛卡尔网格上的2.5D理想磁流体动力学开发了一种高阶、全显式的算子分裂方法。流体动力学子流通过一种配备逐级振荡消除和保正限制器的熵稳定间断伽辽金谱元方法推进。磁-速度子流使用兼容有限元和电场及电流密度的质量集中重构。其离散旋度更新精确保持全局$H(\mathrm{div})$无散度子空间，而理想半离散化平衡动能、磁能和内能。旋度形式的人工电阻率和方向分辨速度滤波器将移除的磁能和动能返回到内能；因此，稳定的磁阶段保持正内能并满足离散熵不等式。两个求解器通过二阶流体动力学-磁-流体动力学Strang分裂组合，产生一个无矩阵方案，在接受的步骤上保持全局质量、节点可接受性和磁散度。光滑Alfvén波和对流涡测试揭示了磁多项式阶数的奇偶收敛模式，验证了二阶时间精度，并表明稳定化保持了高阶精度。场环、Orszag-Tang、转子、MHD爆炸波和Kelvin-Helmholtz计算展示了非光滑多维流动的稳健性能，并表明人工电阻率抑制网格尺度磁振荡，同时保留解析结构。
英文摘要
We develop a high-order, fully explicit operator-splitting method for 2.5D ideal magnetohydrodynamics on Cartesian meshes. The hydrodynamic subflow is advanced by an entropy-stable discontinuous Galerkin spectral element method equipped with stagewise oscillation elimination and a positivity-preserving limiter. The magnetic--velocity subflow uses compatible finite elements and mass-lumped reconstructions of electric field and current density. Its discrete-curl update exactly preserves the global $H(\mathrm{div})$ divergence-free subspace, while the ideal semidiscretization balances kinetic, magnetic, and internal energy. Curl-form artificial resistivity and a direction-resolved velocity filter return removed magnetic and kinetic energy to internal energy; consequently, the stabilized magnetic stage preserves positive internal energy and satisfies a discrete entropy inequality. The two solvers are composed by a second-order hydrodynamic--magnetic--hydrodynamic Strang splitting, yielding a matrix-free scheme that retains global mass, nodal admissibility, and magnetic divergence on accepted steps. Smooth Alfvén-wave and advected-vortex tests reveal an even--odd convergence pattern in the magnetic polynomial degree, verify second-order temporal accuracy, and show that stabilization preserves high-order accuracy. Field-loop, Orszag--Tang, rotor, MHD blast-wave, and Kelvin--Helmholtz calculations demonstrate robust performance for nonsmooth multidimensional flows and show that artificial resistivity suppresses grid-scale magnetic oscillations while retaining the resolved structures.
Comments43 pages, 8 figures
