期刊
JOURNAL OF SCIENTIFIC COMPUTING
卷 47, 期 3, 页码 281-302出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-010-9437-3
关键词
Lax-Wendroff-type time discretization; Weighted essentially non-oscillatory schemes; Shallow water equations; High order accuracy
资金
- NSFC [40906048, 10931004]
- Nanjing University of Information Science Technology [20090203]
In this paper we study a Lax-Wendroff-type time discretization procedure for the finite difference weighted essentially non-oscillatory (WENO) schemes to solve one-dimensional and two-dimensional shallow water equations with source terms. In order to maintain genuinely high order accuracy and suit to problems with a rapidly varying bottom topography we use WENO reconstruction not only to the flux but also to the source terms of algebraical modified shallow water equations. Extensive simulations are performed, as a result, the WENO schemes with Lax-Wendroff-type time discretization can maintain nonoscillatory properties and more cost effective than that with Runge-Kutta time discretization.
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