一种能准确模拟波浪复杂演化过程的非静力学数值模型  

A non-hydrostatic model for precise simulation of complex surface wave processes

作　　者：陈善群 吴昊 汤润超 CHEN Shan-qun;WU Hao;TANG Run-chao(College of Architecture Engineering,Anhui Polytechnic University,Wuhu 241000,China)

机构地区：[1]安徽工程大学建筑工程学院,安徽芜湖241000

出　　处：《船舶力学》2018年第11期1342-1353,共12页Journal of Ship Mechanics

基　　金：安徽省高校优秀青年人才支持计划项目(gxyq2017015);安徽工程大学研究生实践与创新基金项目(2017)

摘　　要：选取σ坐标系下的不可压缩Navier-Stokes方程组作为控制方程。将速度变量定义在计算单元的中心位置,同时将非静力学压力定义在计算单元竖直方向界面位置以便于结合Godunov型格式。采用有限体积和有限差分混合方法结合Godunov型格式对控制方程进行空间离散。利用HLL黎曼求解器求解计算单元之间的通量以实现激波捕捉,并采用二阶非线性强稳定性保持龙格库塔(SSP Runge-Kutta)格式进行时间步迭代。基于以上数值方法,文中发展了一种能准确模拟波浪复杂演化过程的非静力学数值模型。将非静力学数值模型用于数值模拟淹没式堤坝上波浪传播、孤立波沿斜坡爬高和海底滑坡诱发海啸三种波浪复杂演化过程,数值计算结果与相应的实验结果较为吻合。The incompressible Navier-Stokes equations in conservative form written inσcoordinates are chosen as the governing equations.In order to apply a Godunov-type scheme,the velocities are defined at cell centers,and the dynamic pressure is defined at vertically facing cell faces.A combined finite-volume and finite-difference scheme with a Godunov-type method is applied to discretize the governing equations.The HLL Riemann approximation is employed to estimate fluxes at cell faces.The nonlinear Strong Stability-Preserving(SSP)Runge-Kutta scheme is adopted for time stepping.Based on above numerical methods,a non-hydrostatic model for precise simulation of complex surface wave processes is developed.The model is validated using three test cases based on experimental data,respectively periodic wave propagation over a submerged bar,solitary wave run-up along a slope beach and tsunami generation by underwater landslides.The numerical results are in good agreement with the corresponding experimental data.

关 键 词：Σ坐标 Godunov型格式 非静力学 HLL黎曼求解器 

分 类 号：TV131.2[水利工程—水力学及河流动力学]