一种提高河道演算稳定性及计算效率的TVD格式的研究及应用  

Research and Application of a Total Variation Diminishing Scheme to Improve the Stability and Efficiency of Channel Routing

作　　者：臧帅宏 李致家[1] 杜若愚 ZANG Shuaihong;LI Zhijia;DU Ruoyu(College of Hydrology and Water Resources,Hohai University,Nanjing 210098,China)

机构地区：[1]河海大学水文水资源学院,江苏南京210098

出　　处：《水文》2023年第3期40-44,59,共6页Journal of China Hydrology

基　　金：国家自然科学基金(52079035);中央高校基本科研业务费;江苏省研究生科研与实践创新计划项目(KYCX21_0509)。

摘　　要：在洪水演算中,使用Muskingum-Cunge-Todini(MCT)方法进行差分求解时通常会出现非物理的振荡、负流或突变式增长等现象,将一个TVD(Total Variation Diminishig)限制器引入到MCT方法中,来保证其数值解的“总变差减小”,从而提高MCT方法的稳定性。将TVD格式以及一阶精度的MCT方法用到了XAJ-DCH模型中,相比于模型中原有的二阶精度的MCT方法,引入了TVD格式以及一阶精度的MCT方法之后出现不稳定的场次洪水明显减少,且能达到与二阶精度的MCT方法相似的模拟效果。另外,原有模型在1996060100号洪水需要时间步长为200 s才能保持稳定,由于引入TVD限制器和一阶精度的MCT方法以后,可以使用3600 s作为河道演算时间步长,而场次洪水的模拟时间可以由原来的3 min左右缩短为1 min左右,模型的模拟效率得到明显提高。Non-physical oscillation,negative flow or overshoot often occur when using some river flood routing methods due to the rapid change of flood wave in a short time.This study introduced a TVD limiter into Muskingum-Cunge-Todini(MCT)method,to guarantee the“total variation diminishing”(TVD)of the numerical solution,so as to improve the robustness of MCT method.The TVD,first-order versions and second-order versions of MCT were implemented in the XAJ-DCH model and applied in Tunxi catchments.Compared with the second-order version of MCT,the TVD and first-order versions of MCT are more robust and can achieve the similar simulation accuracy with the second-order version of MCT.In addition,the original model needs 200s as the time step of channel routing to remain numerical stability in flood No.1996060100,after the introduction of TVD and first-order versions of MCT method,the time step of river routing can be extended to 3600s.Therefore,its run time can be shortened from about 3min to about 1min.

关 键 词：TVD格式 河道洪水演进 MCT方法 XAJ-DCH模型 

分 类 号：P333.2[天文地球—水文科学] TV122[水利工程—水文学及水资源]