Séance Séminaire

Séminaire ACSIOM

Simulation of a tsunami propagation using a non-hydrostatic model

We present a new numerical method to solve the two-dimensional dispersive shallow water system with topography proposed recently by [3]. This model is a depth averaged Euler system and takes into account a non-hydrostatic pressure. Interestingly, this model is close to but not the same as the Green-Naghdi model. An incompressible system has to be solved to find the numerical solution of this model. The solution method [1,2] is based on a prediction-correction scheme initially introduced by Chorin-Temam[4] for the Navier-Stokes system. The prediction part leads to solving a shallow water system for which we use finite volume methods, while the correction part leads to solving a mixed problem in velocity and pressure. For the correction part, we apply a finite element method with compatible spaces on unstructured grids. Several numerical tests are performed to evaluate the efficiency of the proposed method, in particular, we simulate a tsunami propagation and compare the results for both hydrostatic and non-hydrostatic models. References [1] N. Aïssiouene, M.-O. Bristeau, E. Godlewski, and J. Sainte-Marie. A combined finite volume - finite element scheme for a dispersive shallow water system. Networks and Heterogeneous Media, 11(1):1-27, 2016. [2] N. Aïssiouene, Numerical analysis and discrete approximation of a dispersive shallow water model, Thesis, 2016 [3] M.-O. Bristeau, A. Mangeney, J. Sainte-Marie, and N. Seguin. An energy consistent depth-averaged Euler system: Derivation and properties. Discrete and Continuous Dynamical Systems - Series B , 20(4):961-988, 2015. [4] R. Rannacher. On Chorin's projection method for the incompressible Navier- Stokes equations. In G. Heywood, John, K. Masuda, R. Rautmann, and A. Solonnikov, Vsevolod, editors, The Navier-Stokes Equations II | Theory and Numerical Methods , volume 1530 of Lecture Notes in Mathematics , pages 167-183. Springer Berlin Heidelberg, 1992.