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Nora Aïssiouene

 Engineer – researcher in applied Mathematics





2 rue Simone Iff – CS 42112 – 75589 Paris Cedex 12 – FRANCE

PhD thesis: Numerical analysis and discrete approximation of a dispersive Shallow Water model.

Download the thesis here.

Directed by  Edwige Godlewski and Jacques Sainte-Marie


In this PhD thesis we are interested in the numerical approximation of a dispersive shallow water system, aimed at modeling the free surface flows (e.g. ocean and rivers) and motivated by applications for natural hazards and sustainable energy resources. This model is a depth-averaged Euler system and takes into account a non-hydrostatic pressure which brings crucial information for understanding the behavior of the flow, particularly when dispersion occur.
We develop a numerical method for the one- and the two-dimensional dispersive shallow water system with a topography. The approach is based on a prediction-correction method initially introduced by Chorin-Temam, and we establish a global framework in order to easily increase the order of accuracy of the method.
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. We propose a variational formulation of the mixed problem which allows us to apply a finite element method with compatible spaces. In this framework we establish compatible boundary conditions between the prediction part and the correction part. The method is performed for the one-dimensional model and for the two-dimensional problem on unstructured grids. In order to make the method practical for real geophysical cases, we have derived a scheme able to treat wet/dry interfaces and to this end we give many examples to test its performance. Moreover, we provide a comparison of simulated solutions with data from laboratory experiments.

Some numerical simulations:



Solitary wave


Simulation using hydrostatic vs non-hydrostatic model





Aïssiouene, M. O. Bristeau, A. Mangeney, E. Godlewski, C. Parés, and J. Sainte-Marie. A numerical method for a two-dimensional dispersive Shallow Water system. Submitted, 2016.

Aïssiouene, M. O. Bristeau, E. Godlewski, and J. Sainte-Marie. A robust and stable numerical scheme for a depth-averaged Euler system. Submitted, 2016.

Aissiouene, 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.

Aïssiouene, T. Amtout, M. Brachet, E. Frénod, R. Hild, C. Prud’homme, A. Rousseau, S. Salmon. A coupled model for unsteady stokes/exner equations and numerical results with feel++ library. Submitted, CEMRACS 2015, 2015, Marseille, France.

Teaching activities

  • 2014: Calculus, 36 hours - UPMC (Jussieu)
  • 2015: Matrix calculus on Scilab, 36 hours  - UPMC (Jussieu)
  • 2015: Practical session: propagation of tsunamis , M2, 8 hours - IPGP Paris


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