The active-layer model used to account for mixed-size sediment morphodynamic processes may be ill-posed under certain circumstances. Well-posedness guarantees the existence of a unique solution continuously depending on the problem data. When a model becomes ill-posed, infinitesimal perturbations to a solution grow infinitely fast. Apart from the fact that this behaviour cannot represent a physical process, numerical simulations of an ill-posed model continue to change as the grid is refined. For this reason, ill-posed models cannot be used as predictive tools. There exists a regularisation strategy based on a preconditioning method that guarantees that the one-dimensional active-layer model is well-posed. Here, we show that the extension of this strategy to two dimensions does not regularise the model and we propose a different regularisation strategy based on diffusion that guarantees that both the one-dimensional and two-dimensional active-layer models are well-posed. We implement the strategy in Delft3D Flexible Mesh and show an application.
Víctor Chavarrías (Fri,) studied this question.