A modified leapfrog scheme for shallow water equations

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 heights in the pressure gradient force in the momentum equations. The stability analysis shows that the new scheme is neutr...

Full description

Saved in:
Bibliographic Details
Main Authors Sun, Wen-Yih, Sun, Oliver M. T
Format Publication
LanguageEnglish
Published 25.01.2011
Subjects
Courant number
Eigenvalue
Finite-volume
Leapfrog scheme
Semi-implicit
Shallow Water Equations
Stability
Online AccessGet more information

Cover

More Information
Summary: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 heights 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. Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Computers & Fluids 52 (2011): 69-72, doi:10.1016/j.compfluid.2011.08.019.