李群法在二维深水进行波计算中的应用  

Applications of Lie Groups to Two Dimensional Wave in Deep Water

作　　者：曹雪玲[1] 刘洋[1] 

机构地区：[1]广州航海学院船舶与海洋工程学院,广东广州510725

出　　处：《广州航海学院学报》2017年第1期19-21,共3页Journal of Guangzhou Maritime University

基　　金：广州航海学院创新强校平台项目(B510624);广州航海学院高层次人才引进项目(B330501)

摘　　要：复杂的海洋环境使海洋能研究在数值计算方面必然面对三重障碍:非线性问题、无限问题、随机问题.虽然现有数值方法在这些问题上的研究已取得成绩,但因各自的局限性,无法同时解决这三重障碍,且计算精度较低.本文引入李群法求解二维水波问题中Laplace方程,将原问题逐次降维,得到该Laplace方程的无限李群通解,考虑二维深水情形下的边界条件,得出其解析解,证明了该方法的可行性.鉴于该方法的工作原理,李群法有望发展成为求解非线性随机水波问题的数学工具.The current numerical methods of wave energy faces three obstacles ： nonlinear, infinite and stochastic problems. Although the existing numerical methods have made a lot of achievements in the research, they can not solve these three obstacles at the same time,and the calculation accuracy is relatively low. This paper has completed the derivations and the calculations, including the general solution of Laplace equation and the particular solution of a specified boundary condition using Lie Group. It has proved the feasibility of this method. In view of the theory of Lie Group,it is expected to be a mathematical tool for solving nonlinear, stochastic wave problems.

关 键 词：李群 深水进行波 海洋能 LAPLACE方程 

分 类 号：O353.2[理学—流体力学]