具有捕捉激波能力的一维溃坝波及孤立波爬坡数学模型  

One dimensional numerical model for dam break wave and solitary wave runup with shock capturing capacity

作　　者：张明亮[1] 时锋[2] 郝子宁 

机构地区：[1]大连海洋大学海洋科技与环境学院,大连116023 [2]大连理工大学海岸近海工程国家重点实验室,大连116025

出　　处：《水动力学研究与进展（A辑）》2012年第6期687-695,共9页Chinese Journal of Hydrodynamics

基　　金：大连海洋大学人才引进科研启动项目(SYYJ2011004);辽宁省首批博士后集聚工程项目(2011921018);国家自然科学基金(50839001)资助~~

摘　　要：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。An explicit one dimensional numerical model for dam breok and wave run-up is set up to calculate the water depth and water level for the flooding processes and wave propagation based on the shallow water equations and extended Boussinesq equations. The finite volume method is used to discretize all equations in this model. The interface flux is computedby the HLL approximate Riemann solver with four order accuracy, which can calculate the moving boundary line between dry and wet bed. The static pressure is put into source terms; the implicit scheme is used to calculate the terms of vegetation effect and bed shear stress in order to increase the stability of this model. This model is used to simulate dam break flows over sloping bed, dam break flow over a triangular obstacle, solitary wave run-up at sloping bed with vegetation and non-vegetation. The calculated results show that this model provides the capability with high calculation accuracy, good conservation and shock capturing which can simulate the moving boundary line. This model has important application value for forecast of dam break flow and protection and design of coastal bank.

关 键 词：有限体积法 Godunov格式 溃坝 孤立波 植物作用 

分 类 号：TV142[水利工程—水力学及河流动力学]