Figure 13: (a) Comparison between the experimental velocities and the simulated ones for the thirteen points defined over Fig. 11-(b).
7 Conclusion
In this paper, we have presented a layer-averaged version of the 3d incompressible, hydrostatic Euler and Navier-Stokes systems with free surface. Compared to previous works of some of the authors, the numerical scheme is improved (implicit treatment of the vertical exchanges, description of the topography source term,...) and hence, based on a kinetic interpretation of the system for the Euler part, we have derived a stable, robust and efficient numerical scheme in a finite volume/finite element framework on fixed unstructured meshes. The numerical scheme is endowed with strong stability properties (domain invariant, well-balancing, wet/dry interfaces treatment,...).
The numerical scheme is successfully validated with analytical solutions and is shown to be applicable to simulate complex test cases, like a tsunami propagation over a real bathymetry, proving its accuracy and efficiency.
Acknowledgements The authors thank Quentin Blétery for his involvement in the analysis of the 2014 Iquique earthquake (paragraph 6.3). We also thank Raphaël Grandin for its contribution in the computations of the bottom displacements necessary for the tsunami simulations. This work has been partially funded by the ERC Contract No. ERC-CG-2013-PE10-617472 SLIDEQUAKES. The authors also acknowledge the Inria Project Lab "Algae in Silico" for its financial support.
References
[1] N. Aïssiouene, M.-O. Bristeau, E. Godlewski, A. Mangeney, C. Parés, and J. Sainte-Marie, A two-dimensional method for a family of dispersive shallow water model, working paper or preprint, May 2019.
[2] E. Audusse, A multilayer Saint-Venant model : Derivation and numerical validation, Discrete Contin. Dyn. Syst. Ser. B 5 (2005), no. 2, 189–214.