A modified leapfrog scheme for shallow water equations

被引：7
作者：
Sun, Wen-Yih [1 ,2 ,3 ]
Sun, Oliver M. T. [4 ]
机构：
[1] Purdue Univ, Dept Earth & Atmospher Sci, W Lafayette, IN 47907 USA
[2] Nagoya Univ, HyARC, Chikusa Ku, Nagoya, Aichi 4648601, Japan
[3] Natl Cent Univ, Dept Atmospher Sci, Tao Yuan, Taiwan
[4] Woods Hole Oceanog Inst, Dept Phys Oceanog, Woods Hole, MA 02543 USA
来源：
COMPUTERS & FLUIDS | 2011年 / 52卷
关键词：
Shallow water equations; Leapfrog scheme; Courant number; Eigenvalue; Semi-implicit; Finite-volume; Stability;
D O I：
10.1016/j.compfluid.2011.08.019
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In the 1D linearized shallow water equations, the Courant number should be <0.5 for stability in the original Leapfrog (LF) scheme. Here, we propose using the time-averaged height in the pressure gradient force in the momentum equations. The stability analysis shows that the new scheme is neutral when Courant number <1. The scheme is 2nd order accurate in both time and space. It does not require iterations and can be easily applied in 2D or 3D wave equations. The numerical simulations for 2-D linearized shallow water equations are consistent with those obtained from a 2-time-step semi-implicit scheme. The time filter can also be easily applied to this modified LF scheme. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：69 / 72
页数：4
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