论文标题
通过非保守系统的零件离散化的分裂形式总和的通量差异公式：用于磁性流动力的子限制的应用
A Flux-Differencing Formula for Split-Form Summation By Parts Discretizations of Non-Conservative Systems: Applications to Subcell Limiting for magneto-hydrodynamics
论文作者
论文摘要
在本文中，我们表明，如果副本平衡定律的一般非保守性系统的零件（SBP）离散化可以作为有限体积型公式进行重写，如果非保守性术语可以作为当地撰写和对称的贡献。此外，我们表明，通量差异公式的存在使使用最近的子限制策略可以提高高阶离散化的鲁棒性。 为了证明新型通量差异公式的实用性，我们构建了混合方案，这些混合方案将高阶SBP方法（不连续的Galerkin频谱元素方法和高阶SBP有限差方法）与兼容的低阶有限体积（FV）方案在子键水平上进行。我们应用混合方案来解决具有强烈冲击的挑战性磁流失动力学（MHD）问题。
In this paper, we show that diagonal-norm summation by parts (SBP) discretizations of general non-conservative systems of hyperbolic balance laws can be rewritten as a finite-volume-type formula, also known as flux-differencing formula, if the non-conservative terms can be written as the product of a local and a symmetric contribution. Furthermore, we show that the existence of a flux-differencing formula enables the use of recent subcell limiting strategies to improve the robustness of the high-order discretizations. To demonstrate the utility of the novel flux-differencing formula, we construct hybrid schemes that combine high-order SBP methods (the discontinuous Galerkin spectral element method and a high-order SBP finite difference method) with a compatible low-order finite volume (FV) scheme at the subcell level. We apply the hybrid schemes to solve challenging magnetohydrodynamics (MHD) problems featuring strong shocks.
