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 semi-discrete 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.

翻译：这项工作致力于时间分解的绿色-纳格迪方程式的结构,包括测深。我们用方程式的预测结构来描述半分解方程式完全覆盖的同质和不相容的边界条件。这一结构使我们能够提出高效和稳健的边界条件数字处理方法,通过构建确保计划的酶稳定性。提供了数字证据,以说明我们的方法适合现有理论没有涵盖的实际利益情况。