Upwind stabilized finite elements and residual based schemes for depth averaged free surface flow

In this talk we review some approaches used to simulate free surface flows by means of a class of stabilized finite element schemes.
This talk considers the development of numerical tools for the simulation of the propagation, breaking and runup of waves in the near shore region. Waves are modeled via a hybrid approach coupling (some form of) the Boussinesq equations in the propagation part, with the Shallow Water equations in the breaking region. We consider then a discretization approach capable of handing both limits, and based on upwind stabilized finite element and residual based schemes. In the talk we will highlight the main features of the upwind approach used for the simulation of planar waves (1D equations), and sketch the main ideas used to construct the 2D discretization, showing initial validation cases for the two limits (Boussinesq equations and Shallow Water).

contact: edie.miglio@polimi.it