Boussinesq水波方程新型数值解法  

Novel numerical solution to Boussinesq wave equations

作　　者：房克照[1,2] 孙家文[2] 刘忠波[1] 尹晶[2] 张哲[1] 

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024 [2]国家海洋环境监测中心,辽宁大连116023

出　　处：《海洋工程》2014年第2期97-103,共7页The Ocean Engineering

基　　金：国家自然科学基金资助项目(51009018);国家海洋局海域管理技术重点实验室资助项目(201206)

摘　　要：为建立高效的Boussinesq类水波数值模型,提出了一种新型的、基于有限差分和有限体积方法的混合数值格式。针对守恒形式的一维控制方程,在等间距矩形控制体内对其进行积分并离散,采用有限体积方法计算界面数值通量,剩余源项采用有限差分方法计算。其中,采用MUSTA格式并结合高精度状态插值方法计算控制体界面数值通量。时间积分则采用具有TVD性质的三阶龙格-库塔多步积分法进行。除验证模型外,重点对MUSTA格式和广泛使用的HLL格式进行了比较。结果表明,MUSTA格式可用于Boussinesq类水波方程数值求解,综合考虑数值精度、计算效率、程序编制和实际应用这几个方面,其较HLL格式更具有优势。To develop an efficient Boussinesq type wave model, a novel hybrid finite-difference/finite-volume scheme is proposed in this paper. Finite volume method is used to evaluate the flux terms in the conservative form of equations while higher-accuracy finite difference method is used to approximate the rest terms. MUSTA scheme, in conjunction with higher accuracy MUSCL method for variable reconstruction, is adopted to compute the interface flux. The third order Runge-Kutta method with TVD property is adopted to perform time marching. In addition to model validation, we focus on comparing the numerical performance between MUSTA scheme and widely used HLL scheme. The numerical tests demonstrate that one-stage MUSTA scheme is overall superior to the HLL scheme, in terms of numerical accuracy, computation cost, program coding and practical implementation.

关 键 词：Boussinesq水波方程 混合格式 MUSTA HLL 

分 类 号：O353.2[理学—流体力学]