A new spectral method using legendre wavelets for shallow water model in limited-area

7th International Conference on Applied Physics and Mathematics

物理学;数学

Yin, Fukang^1 ; Song, Junqiang^1 ; Wu, Jianping^1 ; Cao, Xiaoqun^1

Academy of Ocean and Engineering, National University of Defense Technology, Changsha

410073, China^1

关键词: Advection equations;    Collocation method;    Error characteristics;    Exponential convergence;    Numerical solution;    Realistic applications;    Shallow water equations;    Shallow water model;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/814/1/012014/pdf
DOI  :  10.1088/1742-6596/814/1/012014

来源: IOP

【 摘 要 】

This paper presents a new spectral method using Legendre wavelets (named LWSTCM), which complete the stepping in spectral space while deal with boundary conditions in grid-point space by collocation method, for the numerical solution of shallow water model in limited-area. In order to deal with the overlapping boundaries, some proper schemes are considered for exchanging the information on the boundaries between sub-domains. 1-D advection equation is used to analysis the exponential convergence property and error characteristics of LWSTCM. Finally, we study LWSTCM on 2-D shallow water equations for a more realistic application. The numerical results are compared with existing numerical solutions found in the literature and demonstrate the validity and applicability of the presented method.