A CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive property

JOURNAL OF COMPUTATIONAL PHYSICS

卷:399

Article

Li, Maojun¹  Xu, Liwei¹  Cheng, Yongping² 

[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

[2] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

关键词: Enhanced dispersive property;    Green-Naghdi model;    Central discontinuous Galerkin method;    Finite element method;    Positivity-preserving property;    Well-balanced scheme;   

DOI  :  10.1016/j.jcp.2019.108953

来源: Elsevier

【 摘 要 】

In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For numerics, the Green-Naghdi model is rewritten into a formulation coupling a pseudoconservative system and a set of pseudo-elliptic equations. Since the pseudo-conservative system is no longer hyperbolic and its Riemann problem can only be approximately solved, we consider the utilization of the central discontinuous Galerkin method, which possesses an important feature of the needlessness of Riemann solvers. Meanwhile, the stationary elliptic part will be solved using the finite element method. Both the well-balanced and the positivity-preserving features, which are highly desirable in the simulation of the shallow water wave, will be embedded into the proposed numerical scheme. The accuracy and efficiency of the numerical model and method will be illustrated through numerical tests. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free