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

[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.

[发布机构] Academy of Ocean and Engineering, National University of Defense Technology, Changsha; 410073, China^1

[效力级别] 数学

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