连续分层海洋中内波传播的一种数值模式  

A NUMERICAL MODEL FOR INTERNAL WAVE PROPAGATION IN CONTINUOUSLY STRATIFIED OCEAN

作　　者：张洪生[1,2] 辜俊波[2,3] 贾海青[1] 古彪 

机构地区：[1]上海海事大学海洋环境与工程学院,上海201306 [2]上海交通大学海洋工程国家重点实验室,上海200240 [3]中国电力工程顾问集团华东电力设计院,上海200063 [4]中国航空工业第六○五研究所,湖北荆门448035

出　　处：《力学学报》2012年第5期896-903,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(51079082);劳氏教育基金会UCL-SJTU-HEU深水工程及水动力学联合研究中心;上海交通大学海洋工程国家重点实验室(GP010818);航空科技创新基金(08A05002)资助项目~~

摘　　要：基于Euler方程,使用有限体积法建立了一种密度为连续分层情况下、适应水深变化的水域中内波传播的数值模式.为了使计算格式能够达到二阶精度,对流项的处理使用了TVD(total variation diminishing)格式.将SIMPLE算法引入连续分层海洋中内波的数值计算,为了简化计算并方便地适应多种TVD格式,在计算预估速度场时采用了显式格式,而没有采用传统的隐式格式;鉴于在原始的SIMPLE算法中没有涉及到由于密度扰动而引起的静水压力场的改变问题,给出了该问题的计算方法.因此改进了SIMPLE算法.出流边界的处理采用阻尼消波和Sommerfeld辐射条件相结合的方式,以使内波得到有效的衰减和释放.将等水深水域的数值解和理论解进行了比较,两者吻合较好;并对存在潜堤时数值计算的不同时刻密度变化的空间分布进行了详细的定性分析.计算结果表明,所建立的数值模式能有效地模拟内波的传播和变形.Based on the Euler equations, the finite volume method is employed to develop a numerical model for the internal wave propagation in continuously stratified ocean with variable water depth. The convection terms are discretized with the total variation diminishing （TVD） scheme to make the numerical scheme accurate up to second order, and the SIMPLE algorithm is used in the present numerical scheme. In order to simplify the calculation process and easily adapt to different TVD schemes, the adopted semi-implicit method for pressure linked equations （SIMPLE） algorithm is modified. The predicted velocity fields are calculated with the explicit scheme, instead of the implicit scheme, which is traditionally adopted in the SIMPLE algorithm. Also, the varieties of the hydrostatic pressure due to the density disturbances are not involved in the original SIMPLE algorithm, but they are involved and resolved in this paper. Thus, the SIMPLE algorithm is further developed. The open boundary at the far end is dealt with a sponge layer combined with the Sommerfield＇s radiation condition. The numerical results with constant depth are compared to the analytical solutions and good agreements are found, and the calculated spatial distributions of the density fields with a submerged dike at different moments are analyzed in details. It is shown that the present numerical model can effectively simulate the propagation of internal wave.

关 键 词：内波 连续分层 有限体积法 数值模拟 SIMPLE算法 

分 类 号：P731.2[天文地球—海洋科学] O353.2[理学—流体力学]