High order well-balanced schemes

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A Survey of High Order Schemes for the Shallow Water Equations (2014, background): “It was then commented in [41] that the optimal choice of b j+1/2 remains an open problem.”
Well‐balanced positivity preserving central‐upwind scheme for the shallow water system with friction terms (2015, background): “Some of them preserve only “lake at rest” steady states, that is, u ≡ v ≡ 0, h+ B ≡ constant, [2, 4–6, 13, 22, 24, 27, 31, 36, 37], other can preserve a nonflat steady-state solution as well, [33, 39, 40, 43].”