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.

翻译：在本文中,我们显示,如果非保守性术语可以作为局部贡献和对称贡献的产物来写成,那么按部分(SBP)对双曲平衡法一般非保守性系统进行对角-向量比较,可以改写成数量型的有限公式,也称为通量差异公式,如果非保守性术语可以作为局部贡献和对称贡献的产物来写成。此外,我们表明,由于存在通量差异公式,因此能够使用最近的子细胞限制战略来提高高分级分立的稳健性。为了证明新的通量差异公式的实用性,我们建立了混合计划,将高端SBP方法(不连续的Galerkin光谱元素法和高端SBP有限差异法)与在次细胞一级兼容的低序有限量(FV)计划结合起来。我们运用混合计划来解决具有强烈冲击力的磁力动力学(MHD)问题。