Variational approach for the multiscale modeling of an estuarian river. Part 1 : Derivation and numerical approximation of a 2D horizontal model

The paper is devoted to the 2D hydrodynamical modeling and numerical approximation of an estuarian river flow. A new 2D horizontal model is derived and analyzed as a conforming approximation of the 3D time-discretized problem. It provides the three-dimensional velocity field as well as the pressure, which remains an unknown of the problem. Thanks to the framework of weak formulations, we avoid any closure problem usually encountered in the shallow water system and we can next employ finite elements for the approximation of the 2D model. The discrete problem is shown to be well-posed and finally, numerical tests are presented. The developed code is validated by means of comparisons with the classical shallow water model as well as with measured data