Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization

38/2017

Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization

Thursday 13th July 2017

Bonaventura, L.; Fernandez Nieto, E.; Garres Diaz, J.; Narbona Reina, G.;

We propose an extension of the discretization approaches for mul- tilayer shallow water models, aimed at making them more exible and ecient for realistic applications to coastal ows. A novel discretiza- tion approach is proposed, in which the number of vertical layers and their distribution are allowed to change in dierent regions of the com- putational domain. Furthermore, semi-implicit schemes are employed for the time discretization, leading to a signicant eciency improve- ment for subcritical regimes. We show that, in the typical regimes in which the application of multilayer shallow water models is justied, the resulting discretization does not introduce any major spurious fea- ture 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 prob- lem is presented, showing a remarkable improvement with respect to standard discretization approaches.

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L.Bonaventura,E.D.Fernandez Nieto,J.Garres Diaz,G.Narbona~Reina, Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization, Journal of Computational Physics, Vol. 364, pp. 209-234, 2018