Saint-Venant方程组全隐式标量耗散有限体积法  

Full implicit solution with scalar-dissipation finite-volume approach for Saint-Venant equations

作　　者：夏庆福[1] 余弘婧[1] 朱锐[2] 章少辉[1] 郭新蕾[1] XIA Qingfu1, YU Hongjing1, ZHU Rui2, ZHANG Shaohui1, GUO Xinle1(1. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China; 2. Construction Supervision Center of the South to North Water Diversion Project, Beijing 100038, Chin)

机构地区：[1]流域水循环模拟与调控国家重点实验室中国水利水电科学研究院,北京100038 [2]南水北调工程建设监管中心,北京100038

出　　处：《中国水利水电科学研究院学报》2018年第1期23-28,共6页Journal of China Institute of Water Resources and Hydropower Research

基　　金：国家重点基础研究发展规划"973"项目(2013CB036405)

摘　　要：基于Saint-Venant方程组的守恒形式,重构了各物理变量在单元格边界的黎曼状态值,实现了各变量在计算区域内的二阶精度分布。在此基础上,构造了对流通量项的具有标量耗散特征的有限体积法,并在地表水位相对高程梯度离散式中引入额外空间离散项,该项在有水区域为零,并在无水区域能与地表水位相对高程梯度项相互抵消,从而正确描述地表水位相对高程梯度的真实作用。采用双时间步法对Saint-Venant方程组的空间离散式进行全隐式离散,实现了无条件稳定求解。选取了2个典型算例,采用数量呈倍数递减的3种时间步长进行数值模拟,通过与解析解和实测结果进行对比,验证了数值解法的模拟效果和收敛性。结果表明,建立的数值解法能以优良的拟合度模拟不同断面几何约束下的溃坝过程,模拟结果表现出了良好的收敛性。Based on the conservative form of Saint-Venant equations, the Riemann state value of eachphysical variable in the cell boundary was reconstructed,and the two order accuracy distribution of eachvariable in the computational domain was realized. On this basis,the finite-volume scheme with scalar dis-sipation is constructed for the convective fluxes. In order to describe the real physical impact of the rela-tive elevation gradient of water level,extra space discretization is added in the discrete term of relative ele-vation gradient of water level. This term is equal to zero at the wetted region,and can be counteracted bythe term of relative elevation gradient of water level at the dry area. Dural time-step algorithm is used forthe fully implicit discretization the time terms in Saint-Venant equations. Therefore,the unconditional stabil-ity of solution is achieved. Finally,two typical examples are given to verify the stability and convergenceof this new numerical solution.

关 键 词：非恒定流 全隐式 标量耗散 有限体积法 

分 类 号：TV131[水利工程—水力学及河流动力学]