Mass and momentum conservation in the simplified flood routing models

SummaryIn the paper the conservative properties of the simplified flood routing models in form of the advective or advective–diffusive transport equation are analysed. The aim of the analysis is to explain the reasons of the mass balance error, which is observed in the numerical solutions of both non-linear kinematic and diffusive wave equations. It appeared that depending on the assumed conservative form of the kinematic wave equation, this model satisfies either the global mass conservation law or the global momentum conservation law. Both laws are satisfied simultaneously by the linear equation only. Moreover it is shown that for the non-linear diffusive wave model with the flow discharge Q(x, t) as unknown, the mass and momentum balance errors cannot be eliminated. This is caused by the presence of a diffusion term in the non-divergent form, which arises during the derivation the non-linear diffusive wave model.