Conservative discontinuous Galerkin methods for the nonlinear Serre equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:421

Article

Zhao, Jianli¹  Zhang, Qian^1,3  Yang, Yang²  Xia, Yinhua¹ 

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

[3] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China

关键词: Serre equations;    Discontinuous Galerkin methods;    Conservative schemes;    Well-balanced schemes;   

DOI  :  10.1016/j.jcp.2020.109729

来源: Elsevier

【 摘 要 】

In this paper, we develop three conservative discontinuous Galerkin (DG) schemes for the one-dimensional nonlinear dispersive Serre equations, including two conserved schemes for the equations in conservative form and a Hamiltonian conserved scheme for the equations in non-conservative form. One of the schemes owns the well-balanced property via constructing a high order approximation to the source term for the Serre equations with a non-flat bottom topography. By virtue of the Hamiltonian structure of the Serre equations, we introduce an Hamiltonian invariant and then develop a DG scheme which can preserve the discrete version of such an invariant. Numerical experiments in different cases are performed to verify the accuracy and capability of these DG schemes for solving the Serre equations. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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