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In this paper, we show that diagonal-norm summation by parts (SBP)discretizations of general non-conservative systems of hyperbolic balance lawscan be rewritten as a finite-volume-type formula, also known asflux-differencing formula, if the non-conservative terms can be written as theproduct of a local and a symmetric contribution. Furthermore, we show that theexistence of a flux-differencing formula enables the use of recent subcelllimiting strategies to improve the robustness of the high-orderdiscretizations.  To demonstrate the utility of the novel flux-differencing formula, weconstruct hybrid schemes that combine high-order SBP methods (the discontinuousGalerkin spectral element method and a high-order SBP finite difference method)with a compatible low-order finite volume (FV) scheme at the subcell level. Weapply the hybrid schemes to solve challenging magnetohydrodynamics (MHD)problems featuring strong shocks.

A Flux-Differencing Formula for Split-Form Summation By Parts  Discretizations of Non-Conservative Systems: Applications to Subcell Limiting  for magneto-hydrodynamics