Split Form Shallow Water Equations

[fluidnumerics-joe]

The nonlinear shallow water solvers, in 1-D and 2-D, exhibit spurious flows when topography is spatially variable.

Gassner, Winters, & Kopriva (2016) and Wintermeyer et al. (2017) have shown that a discretization based on the split form of the shallow water equations is well-balanced (preserves lake-at-rest) and is entropy conservative, provided an appropriate Riemann flux is given. Additionally, they've shown that minimal modifications are needed to adjust a conservative form solver to obtain an equivalent implementation.