Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization
For computational fluid dynamics researchers working on coastal flow simulations, this method improves efficiency and flexibility of multilayer shallow water models.
The paper extends multilayer shallow water models by allowing a locally variable number of layers and using semi-implicit time discretization, achieving significant computational cost reductions in subcritical regimes and complex bathymetry areas, with a sediment transport example showing remarkable improvement over standard approaches.
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in which the number of vertical layers and their distribution are allowed to change in different regions of the computational domain. Furthermore, semi-implicit schemes are employed for the time discretization, leading to a significant efficiency improvement for subcritical regimes. We show that, in the typical regimes in which the application of multilayer shallow water models is justified, the resulting discretization does not introduce any major spurious feature and allows again to reduce substantially the computational cost in areas with complex bathymetry. As an example of the potential of the proposed technique, an application to a sediment transport problem is presented, showing a remarkable improvement with respect to standard discretization approaches.