New Central-Upwind Scheme for Shallow Water Equations
Liu Caixia(1),Feng Jianhu(2),Zheng Supei(3)
(1 School of Science, Henan University of Technology，Zhengzhou 450052, China)
(2 School of Science，Chang'an University Xi'an 710064, China)
(3 School of Science, Northwest Polynomial University，Xi'an 710072, China)

Abstract: A new semi-discrete central-upwind scheme for shallow water equa tions was presented. The interface value is used instead of the cell-averages for the source terms to obtain a well-balanced scheme to capture the steady solution. The second-order version ensuring the non-negativity of water height is also proved, which allows one to deal with the problems including dry zones. Compared with the staggered central scheme, the proposed scheme can be efficiently used with timesteps as small as the requirement of numerical stability.
Keywords: shallow water equation, semi-discrete central-upwinds-  cheme,hyperb olic conservation laws.