论文部分内容阅读
该文基于浅水方程(SWE)和扩展的Boussinesq方程建立了一维溃坝波演变及波浪爬坡显格式数学模型,该模型能够计算不同时刻及不同地段洪水在波浪演进过程中的水深和流速等。模型采用有限体积法离散方程和应用带有四阶精度的HLL格式的近似Riemann解计算界面的通量,且能够精确的捕捉干湿界面的动边界问题,在计算中静水压力被放入源项中,摩阻项和植物拖曳力项采用隐式离散的方法来增加计算的稳定性。采用建立的数学模型对溃坝波越过三角障碍物、溃坝波爬坡及无植物和带有植物的孤立波爬坡等典型算例进行模拟,结果显示该模型具备较好的精度、守恒性、捕捉间断和模拟动边界的能力,故该模型对于溃坝水流的预测以及海岸带岸坡的设计和防护等方面具有重要的应用价值。
Based on the shallow water equation (SWE) and the extended Boussinesq equation, an explicit mathematic model of one-dimensional dam-break wave evolution and wavy hill-climbing is established. The model can calculate the depth and velocity of flood during different waveforms . The model uses the finite volume method and the approximate Riemann solution of the HLL scheme with fourth-order accuracy to calculate the interface flux and accurately captures the dynamic boundary conditions of the wet-dry interface. Hydrostatic pressure is put into the source term In the friction resistance and plant drag forces using implicit discrete method to increase the stability of the calculation. The mathematical model is established to simulate typical examples such as dam-break waves crossing triangular obstacles, dam-break waves and isolated vegetation with plants and isolated waves. The results show that the model has better accuracy and conservation So as to capture the capability of discontinuities and simulations of moving boundaries. Therefore, this model is of great value in predicting dam-break flow and in the design and protection of coastal slope.