摘要
本文改进了基于MUSCL方法求解一维浅水波方程组的中心迎风格式.利用MUSCL-Hancock方法在每个时间步的中间时刻求解Riemann问题,并分别在t_(n)时刻和t_(n+12)时刻对自由面的斜率进行了修正,得到了MUSCL-Hancock中心迎风格式.在合理的CFL条件下,我们证明了该格式的平衡性与保正性.数值结果表明,与MUSCL格式相比,本文格式能有效减少计算量并具有更高的分辨率.
In this paper,we improve the central-upwind scheme for solving one-dimensional shallow water wave equations based on MUSCL method.This method adopted MUSCL-Hacock method to solve the Riemann problem at the middle of each time step,and correct the slope of the free surface at t_(n) and t_(n+1/2) respectively,which is called MUSCL-Hancock central-upwaind scheme.Under the reasonable CFL condition,we prove that the new scheme is well-balanced and preserves non-negativity of the water height.Compared with MUSCL scheme,numerical examples show that the method can effectively reduce computation and has higher resolution.
作者
王静舟
童帷
闫瑞芳
陈国贤
WANG Jing-zhou;TONG Wei;YAN Rui-fang;CHEN Guo-xian(School of Mathmatics and Statistics Wuhan University,Hubei Key Laboratory of Computational Science(Wuhan University),Wuhan 430072,China)
出处
《数学杂志》
2021年第4期329-341,共13页
Journal of Mathematics
基金
国家自然科学基金资助(11371023).
