基于TVD框架的Godunov格式水锤求解模型  

Godunov scheme water hammer solution model based on TVD framework

作　　者：莫铁祥 李国栋[1] 杨振东 张巧玲[1] Tie-xiang Mo;Guo-dong Li;Zhen-dong Yang;Qiao-ling Zhang(State Key Laboratory of Eco-hydraulics in North Arid Region,Xi’an University of Technology,Xi'an 710048,China)

机构地区：[1]西安理工大学省部共建西北旱区生态水利国家重点实验室,西安710048

出　　处：《水动力学研究与进展（A辑）》2022年第3期326-334,共9页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金(52079107)。

摘　　要：求解有压管道系统水锤波时,传统特征线法及有限差分法受Courant数约束,会导致计算速度低,且因多波插值,存在插值误差问题。该文通过搭构TVD框架、分析并选取最优限制函数以及优化管网分叉口处理方法的方式,提出了一种基于Godunov格式的两阶有限体积格式管网水锤计算模型,并通过管网算例对模型计算效率进行了对比。结果表明:有限体积法在低Courant数时能得到最佳的计算结果,与特征线法及Sweby TVD差分法相比,计算耗时分别节省了28.6%及85.3%;模型选取Van Leer限制器,Courant数值范围为0.2≤Cr≤0.5;模型在网格划分上更为灵活,可根据实际需求选取满足Courant数范围的任意网格间距,实现对变空间步长管网系统瞬变流的高效计算。When solving the water hammer wave in pressurized pipeline systems,the traditional Method of Characteristics and the finite difference method are constrained by the Courant number,resulting in low computational speed and interpolation errors due to multi-wave interpolation.In this paper,by constructing a TVD framework,analyzing and selecting the optimal restriction function and optimizing the bifurcation processing method of the pipe network,a two-order finite volume scheme pipe network water hammer calculation model based on the Godunov scheme is proposed,and the efficiency of the model is compared through a pipe network calculation example.The results show that:the finite volume method can obtain the best calculation results at low Courant number,and the calculation time can be saved by 28.6%and 85.3%respectively compared with the Method of Characteristics and the Sweby TVD difference method.The model selects the Van Leer limiter,and the Courant value range is 0.2≤Cr≤0.5;the model is more flexible in grid division,and any grid spacing that meets the range of Courant numbers can be selected according to actual needs to achieve efficient c alculation of transient flow in variable space step pipe network systems.

关 键 词：水锤 Godunov格式 变步长 有限体积法 TVD框架 

分 类 号：TV134[水利工程—水力学及河流动力学]