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该文针对复杂地形条件下浅水流动数值模拟在干、湿边界附近面临计算失稳和格式和谐性差等难题,建立了非统一结构网格下二维浅水方程的高精度、高分辨率的有限体积模型。以基于水位的改进浅水方程为水流控制方程,采用能够有效捕获激波的HLLC近似黎曼算子计算界面通量;采用MUSCL-Hancock预测-校正法获得了在空间和时间上都具有二阶精度的Godunov格式;通过构造底坡修正项,保证了计算格式的和谐性;采用改进的半隐式格式解决摩阻项可能引起的刚性问题,提高了格式的稳定性。并通过算例研究,结果表明,该模型具有很好的和谐性与稳定性,适应干、湿界面计算,能有效模拟复杂地形条件下的水流运动。
In this paper, the numerical simulation of shallow water flow under complex terrain conditions is faced with the problems of instability and poor format harmony near the dry and wet boundary. The finite volume model of high precision and high resolution for two-dimensional shallow water equations under non-uniform structure grid is established . Based on the improved shallow water equation based on water level, the HLLC approximate Riemannian operator was used to calculate the interface flux. The MUSCL-Hancock prediction-correction method was used to obtain the second-order accuracy in space and time Godunov format. By constructing the bottom slope correction term, the harmony of the calculation format is guaranteed. The improved semi-implicit format is used to solve the rigid problem that the friction resistance may cause and the stability of the format is improved. The results show that the model has good harmony and stability and can adapt to the calculation of dry and wet interfaces, which can effectively simulate water flow under complicated terrain conditions.