There is a multitude of well balanced schemes for the shallow water models with source terms.
Which five of them can you recommend? The hydrostatic reconstruction is actually top on my list. So what do you think?
you may want to look at the implementation of shallow water eq. for solution of coastal innundation problems in 'ANUGA', a joint Geoscience Australia & ANU hydrodynamic model, see attached paper.
There has been great emphasis in the literature on the derivation of well balanced schemes for the shallow water (SHW) and similar equations in the case in which both the continuity equation and the momentum equation are in full flux form. However, for many applications (especially in subcritical regimes), in my opinion, there is no real necessity of employing the momentum equation in full flux form, since strict momentum conservation is often not really necessary (especially when dissipative terms are important and, as often happens, uncertain). In these cases the pressure gradient term is best written in non conservative form (see e.g. what is done in this paper
Rosatti, G., Bonaventura, L., Deponti, A., & Garegnani, G. (2011). An accurate and efficient semi‐implicit method for section‐averaged free‐surface flow modelling. International Journal for Numerical Methods in Fluids, 65(4), 448-473,
but there are many others also doing this). If you do that, the well balancing property is essentially automatic and granted for free and you do not need to worry about which approach to choose. Going deeper into well balancing issues is only really necessary when strict momentum conservation is essential (for example, when solving dam break problems). However, you can see from the previous paper that good solution for dam break problems can also be achieved for SHW equations formulated as suggested above.
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