摘要
将Jin's的界面方法应用到求解双曲守恒型方程的半离散中心迎风方法中,给出了一种新的求解浅水波方程的半离散中心迎风差分方法。对于源项,不是采用传统的单元均值而是采用单元界面处的值来近似,使所得格式对稳定态的求解是均衡的。且已证明所给的二阶精度的求解格式保持水深的非负性,这一特性使其能够较好的处理干河床问题。使用该方法产生的数值粘性(与O(Δ2r-1)同阶)要比交错的中心格式小(与O(Δx2r/Δt)同阶),而且由于数值粘性与时间步长无关,从而时间步长可根据稳定性需要尽可能的小,因此适用于稳定态的求解。
A new semi-discrete central-upwind scheme for shallow water equations 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.
出处
《应用力学学报》
EI
CAS
CSCD
北大核心
2006年第2期246-249,共4页
Chinese Journal of Applied Mechanics
关键词
浅水波方程
半离散中心迎风格式
双曲守恒律方程
shallow water equation,semi-discrete central-upwind scheme,hyperbolic conservation laws.
