Balanced semi-implicit Roe scheme for open channel flow equations

In this paper, we present an extension of balanced upwind explicit finite volume schemes designed in Vuković and Sopta (SIAM J Sci Comput 24(5):1630–1649, 2003) to semi-implicit ones. Particularly, those schemes are applied to open-channel flows with general geometries and we verify the exact conservation property (C-property). We present the algorithm, the proof of exact C-property and results for several test cases. Also, we test and compare balanced semi-implicit and explicit schemes on standard test cases and on cases involving friction, non-uniform bed slopes and strong channel width variations.