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## Section: New Results

### Stabilized SEM approximation of the 2D Saint-Venant system

Participant : Richard Pasquetti.

Following a study restricted to one space dimension, R. Pasquetti has developped a stabilized Spectral Element approximation of the two-dimensional Saint-Venant system. This stabilized SEM model uses the entropy viscosity method (EVM), that is a non linear viscous stabilization with viscosity proportional to the entropy production and bounded from above by a first order viscosity. We have especially focused on problems involving dry-wet transitions and proposed an elaborated variant of the EVM that allows to support the presence of dry zones. The algorithm has been tested against benchmarks problems, involving planar oscillations and axisymmetric oscillations in a paraboloid, for which exact solutions are known. The method was also checked successfully for flows combining dry-wet transitions and shocks. Part of this study was carried out in the National Center for Theoretical Science (Taipei, Taiwan). The work was presented at the ICOSAHOM 2016 congress (Rio, June 2016, see [16]).