A Numerical Model of Nonlinear Wave Propagation in Curvilinear Coordinates  

作　　者：周华伟 张洪生 

机构地区：[1]State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University

出　　处：《China Ocean Engineering》2010年第4期597-610,共14页中国海洋工程（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos .51079082 and 40676053);State Key Laboratory of Ocean Engineering ( Grant Nos . GKZD010012, GP010818 and GKZD010024)

摘　　要：For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries, a numerical model is developed in curvilinear coordinates. In the model, the Boussinesq-type equations including the dissipation terms are em- ployed as the governing equations. In the present model, the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables, instead of the usual primitive velocity variables. The introduction of utility velocity variables which are the products of the contravariant components of the velocity vector and the Jacobi ma- trix can make the transformed equations relatively concise, the treatment of lateral boundary conditions easier and the de- velopment of the program simpler. The predictor-corrector method and five-point finite-difference scheme are employed to discretize the time derivatives and the spatial ones, respectively. The numerical model is tested for three cases. It is found that the numerical results are in good agreement with the analytical results and experimental data.For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries, a numerical model is developed in curvilinear coordinates. In the model, the Boussinesq-type equations including the dissipation terms are em- ployed as the governing equations. In the present model, the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables, instead of the usual primitive velocity variables. The introduction of utility velocity variables which are the products of the contravariant components of the velocity vector and the Jacobi ma- trix can make the transformed equations relatively concise, the treatment of lateral boundary conditions easier and the de- velopment of the program simpler. The predictor-corrector method and five-point finite-difference scheme are employed to discretize the time derivatives and the spatial ones, respectively. The numerical model is tested for three cases. It is found that the numerical results are in good agreement with the analytical results and experimental data.

关 键 词：numerictd model generalized curvilinear coordinates Boussinesq equations corrtravariant velocity 

分 类 号：O186.11[理学—数学]