交错网格下的Boussinesq水波数值模型  

Boussinesq Wave-model in Staggered Difference Scheme

作　　者：刘忠波[1,2] 孙昭晨[1] 

机构地区：[1]大连理工大学海岸及近海工程国家重点实验室,辽宁大连116024 [2]大连海事大学交通与物流工程学院,辽宁大连116026

出　　处：《海洋科学进展》2011年第1期10-15,共6页Advances in Marine Science

基　　金：国家自然科学基金--三维波浪不稳定性研究(50779004)

摘　　要：针对一组近似到二阶完全非线性、四阶色散的Boussinesq方程,在交错网格下建立了数学模型。计算中时间层不交错,模型的求解利用混合四阶Adams-Bashforth-Moulton格式的有限差分法。数值模拟了波浪在潜堤上的演化过程,再现了波浪的浅化、反射以及非线性波能量传递等现象。对数值计算结果采用Friouer变换可分析出波浪的各次谐波幅值,并与实验数据进行了比较,二者有较好的吻合,这说明基于交错网格求解Boussinesq方程求解是有效的,该方法可为同类方程的数值求解提供参考。Fully nonlinear and 4th order dispersive Boussinesq eqnations with their 2nd order approximation are used to set up a numerical model in the staggered difference scheme.In the numerical modeling,the composite 4th-order Adams-Bashforth-Moulton scheme are used with all the variables keeping their simultaneity in the time integration.By means of the model,the wave evolution over a submerged sill is simulated to describe the phenomena such as wave shoaling,reflection,and nonlinear energy trarsferring,The ampitudes of the harmonic wave components can be derived from the numerical calculation results by means of Foruier transform.It is learnt from the comparison between the calculated results and the experimental data that the both are consistent with each other.Therefore it is evidenced that the staggered difference scheme is effective to solve Boussinesou equations.This expounded method can be used as a reference for solving similar equations.

关 键 词：交错网格 BOUSSINESQ方程 四阶色散 波浪 

分 类 号：P76[天文地球—海洋科学]