No. 2021.08
A class of boundary conditions for time-discrete Green-Naghdi equations with bathymetry
S. Noelle, M. Parisot, and T. Tscherpel
Subject: Shallow water flow, Green-Naghdi equations, dispersive equations, boundary conditions, prediction correction scheme, projection method, entropy satisfying scheme
Abstract
This work is devoted to the structure of the time-discrete Green–Naghdi equations including bathymetry. We use the projection structure of the equations to characterize homogeneous and inhomogeneous boundary conditions for which the semidiscrete equations are well posed. This structure allows us to propose efficient and robust numerical treatment of the boundary conditions that ensures entropy stability of the scheme by construction. Numerical evidence is provided to illustrate that our approach is suitable for situations of practical interest that are not covered by existing theory.
Reference
SIAM J. Numer. Anal. 60 (2022), no. 5, 2681–2712