Modelling degradational rivers

Throughout the last two centuries engineers have intervened large rivers for the sake of, among others, improving navigability and preventing flooding (Lonnquest et al., 2014). These interventions have induced morphodynamic changes that we still face nowadays. One if the consequences of past interventions is the ongoing bed degradation occurring in several large rivers including the Rhine River in the Netherlands (Blom, 2016). Measures aimed at preventing further degradation require predicting the effects of such interventions using morphodynamic models. A problem arises when using a morphodynamic model to predict degradational conditions of a river: the model may become ill-posed. An ill-posed model becomes useless in practice, as unphysical oscillations appear in the results. The origin of the oscillations lays in the unsuitability of the model to represent the physical processes under consideration and for this reason the emergence of oscillations is independent of the numerical solver. The most striking feature of an ill-posed model is that the result does not converge when the numerical grid is refined. Worded differently, when using smaller grid cells unphysical oscillations grow faster leading to ever changing results. In this paper we present two alternative strategies to prevent ill-posedness in morphodynamic modelling.