Flux Globalization Based Well-Balanced Central-Upwind Schemes for Hydrodynamic Equations with General Free Energy

Abstract We develop flux globalization based well-balanced central-upwind schemes for hydrodynamic equations with general free energy. The proposed are in the sense that they capable of exactly preserving quite complicated steady-state solutions and also capturing traveling waves, even when vacuum regions present. In order to accurately track interfaces near parts solution, we use technique introduced Chertock et al. (J Sci Comput 90:Paper No. 9, 2022) design a hybrid approach: inside no regions, scheme, while elsewhere implement scheme similar one Bollermann 56:267–290, 2013) context wet/dry fronts shallow water equations. advantages demonstrated on number challenging numerical examples.