Generating boundary conditions for a Boussinesq system

We present a new method for the numerical implementation of generating boundary conditions for a one dimensional Boussinesq system. This method is based on a reformulation of the equations and a resolution of the dispersive boundary layer that is created at the boundary when the boundary conditions are non homogeneous. This method is implemented for a simple first order finite volume scheme and validated by several numerical simulations. Contrary to the other techniques that can be found in the literature, our approach does not cause any increase in computational time with respect to periodic boundary conditions. *DL is supported by the Fondation Del Duca de l'Académie des Sciences, the ANR grants ANR-17-CE40-0025 NABUCO and ANR-18-CE40-0027-01 Singflows, and the Conseil Régional d'Aquitaine.