对一类广义对称正则长波(generalized symmetrical regularized long wave,GSRLW)方程的初边值问题进行了数值研究,提出了一个三层有限差分格式,并利用离散泛函分析方法分析了该格式的二阶收敛性与无条件稳定性,格式合理地模拟了初边值问题的守恒性质.数值结果表明,本文的三层格式具有二阶收敛性;与两层的守恒格式相比计算精度有了进一步的提高.
Much effort has been devoted to researching the common Rosenau equation, but the numerical method of it has not been studied. In this paper, a conservative Crank-Nicolson difference scheme for an initial-boundary value problem of the generalized Rosenau equation is proposed. Existence and uniqueness of numerical solutions are derived. By method of discrete energy, the second order convergence and stability are discussed. Numerical examples demonstrate the theoretical results.
A characteristic rainfall is introduced to overcome the difficulties encountered in determining a critical rainfall value for triggering debris flow.The characteristic value is defined as the rainfall at which debris-flow occurrence probability shows a rapid increase,and can be used as a warning rainfall threshold for debris flows.Investigation of recorded debris flows and 24-hour rainfall data at Jiangjia basin,Yunnan Province,in southwestern China,demonstrates the existence of such a characteristic rainfall.It was found that the characteristic rainfall corresponds to the daily rainfall of 90% cumulative probability by analyzing the basin's daily rainfall histogram.The result provides a simple and useful method for estimating a debris-flow warning rainfall threshold from the daily rainfall distribution.It was applied to estimate the debris-flow warning rainfall threshold for the Subaohe basin,a watershed in the 2008 Wenchuan earthquake zone with many physical characteristics similar to those of the Jiangjia basin.
HU KaihengCui PengWang ChuanchangLi YongLu Xiaobing
