A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow water equations has been first introduced in [A. Kurganov and D. Levy, M2AN Math. Model. Numer. Anal., 36, 397-425, 2002]. Depending on the reconstruction step, the second-order versions of the schemes there could be made either well-balanced or positivity preserving, but fail to satisfy both properties simultaneously.
No takes yet. Share an insight, caveat, or question.
Kurganov et al. (2007) studied this question.
Synapse has enriched 2 closely related papers on similar clinical questions. Consider them for comparative context: