A reformulation of the shallow water equations enables staggered DG fluxes whose non-conservative terms vanish at equilibrium, allowing node-wise subcell limiting that remains exactly well-balanced.
Renac, Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows, Journal of Computational Physics 382 (2019) 1–26
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Well-Balanced Subcell Limiting for Discontinuous Galerkin Discretizations of the Shallow-Water Equations
A reformulation of the shallow water equations enables staggered DG fluxes whose non-conservative terms vanish at equilibrium, allowing node-wise subcell limiting that remains exactly well-balanced.