处理二维浅水流动中动边界问题的淹没节点法

针对浅水流动中的动边界问题，本文设计一种淹没节点方法，根据网格单元各节点的被淹没情况，即单元水面高程和各节点高程的差值，对单元平均水深和单元界面处平均水深进行修正，运用高精度无振荡的FDS格式和有限体积法求解含有动边界的二维浅水方程。除对单元水深和界面水深进行修正外，离散方程形式与传统方法相同，实现过程简单。应用该方法对两个典型算例进行了数值模拟，模拟结果分别与其他学者的模拟结果和精确解高度吻合。表明本文方法精度较高、实现过程简单、可以有效解决浅水方程的间断、动边界和河床起伏问题。

The submerged-node method for treatment of moving boundary in 2D shallow-water flows

To deal with the problems concerning moving boundary in 2D shallow-water flow simulation,a novel scheme called the submerged-node method(SNM) has been developed.In contrast to conventional methods which judge whether a cell is submerged or not by its cell average water depth and calculate the flux at a cell interface based on the water depth at the interface midpoint,water depth modified according to the signed vertical distance from bed level at each cell node to the cell water level is chosen as the criterion of being submerged and to calculate the flux at cell faces.This method incorporated with high-resolution FDS scheme in finite volumes is applied to solve 2D shallow-water flows with moving boundary and bed level changes.The accuracy of the scheme has been verified by recourse to two typical problems concerning discontinuity,moving boundary and bed level changes.Excellent agreement has been obtained between our numerical simulations and other researchers' or the analytical solution.The results indicate that the new scheme is accurate,simple and efficient.