扩展型Boussinesq水波方程的一种改进有限体积/有限差分混合算法  

A modified hybrid finite-volume/finite-difference scheme for extended Boussinesq-type model

作　　者：岳良毅 汪学锋[1,2] 尤云祥[1,2] 

机构地区：[1]上海交通大学海洋工程国家重点实验室,上海200240 [2]高新船舶与深海开发装备协同创新中心,上海200240

出　　处：《水动力学研究与进展（A辑）》2015年第5期477-484,共8页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金项目(11372184);国家重点基础研究发展计划(973计划;2013CB036163)~~

摘　　要：为高效数值求解扩展型Boussinesq水波方程,采用一种近似变换方法,将动量方程中的混合导数项变换为纯空间导数项,建立了一种基于原始变量的新的守恒形式方程。对守恒形式方程中的通量项采用基于二阶迎风TVD格式的有限体积方法进行求解,时间导数项采用具有TVD性质的三阶龙格-库塔多步积分方法进行时间积分,剩余项采用中心差分方法进行计算,发展了扩展型Boussinesq水波方程的一种简单高效的混合有限体积/有限差分求解方法。该方法具有数值格式构造过程简单、无需可调参数、数值稳定性强等优点。利用典型波浪传播算例对数值模型进行了验证,计算结果与文献实验数据吻合良好。For efficiently solving the extended Boussinesq-type model, a new conservative form based on primitive variables is proposed by using an approximate transformation method where the mixed partial derivative terms in the momentum equation are replaced by pure spatial ones. On this basis, a simple and efficient hybrid finite-volume/finite-difference scheme is presented, where the second-order upwinding total variation diminishing （TVD） technique is applied for solving the flux terms, and the third-order TVD Runge-Kutta method is used for solving the time integral terms, while the center difference scheme is utilized for solving the rest terms. The advantages of the proposed numerical scheme are its simplicity, strong stability and no need of adjustable parameters. Two typical numerical tests are conducted for model validation, while the calculated results are in good agreement with experimental data.

关 键 词：Boussinesq水波方程 守恒形式 混合格式 波浪传播 

分 类 号：TV139.2[水利工程—水力学及河流动力学]