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.
GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations
Massachusetts Institute of Technology（麻省理工学院）；Johannes Gutenberg University Mainz（美因茨约翰内斯古腾堡大学）；INRIA, U. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251（法国国家信息与自动化研究所、波尔多大学、法国国家科学研究中心、波尔多国立理工学院、数学与交叉研究实验室）
A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes
INSA Toulouse（图卢兹国立应用科学学院）；University of Montpellier, Institut Montpelliérain Alexander Grothendieck and Inria LEMON team（蒙彼利埃大学，亚历山大·格罗滕迪克蒙彼利埃研究所和Inria LEMON团队）
Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model
Université de Toulouse, UPS/INSA, IMT, CNRS UMR 5219（图卢兹大学）；DMA, Ecole Normale Supérieure, et CNRS UMR 8553（巴黎高等师范学院）；I3M, Univ. Montpellier 2 et CNRS UMR 5149（蒙彼利埃第二大学）
Discrete transparent boundary conditions for the linearized Green-Naghdi system of equations
Institut de Mathématiques de Toulouse（图卢兹数学研究所；UMR5219，图卢兹大学；法国国家科学研究中心，UPS IMT）；UMR5219, Université de Toulouse（图卢兹数学研究所；UMR5219，图卢兹大学；法国国家科学研究中心，INSA）；CNRS, UPS IMT；Institut de Mathématiques de Toulouse；UMR5219, Université de Toulouse；CNRS, INSA
An energy-consistent depth-averaged Euler system: derivation and properties
Inria（法国国家信息与自动化研究所）；CEREMA（法国中央城市与区域设备局）；CNRS（法国国家科学研究中心）；Laboratoire Jacques-Louis Lions（雅克-路易·利翁斯实验室）；Institut de Physique du Globe de Paris（巴黎地球物理学院）
