摘要
本文用有限元与三次样条结合,数值模拟近海水域的流场。推导方程时,为更具一般性,考虑了水平粘性项。作为对模式的检验,分别计算了矩形区域的风生流和扇形区域的潮流,均得到了满意的结果。本文还给出了伶仃洋海域流态的计算结果,此结果比通常二维模式得到的要更为合理。
3-D tidal flow and wind-induced flow have numerically been simulated for over ten years. To simulate, velocity distributions in vertical direction on fluid field, Heaps gave the method using eigenfunction. On the basis of Heaps' work, Divies et al. gave method of B-spline function expansion, method of orthogonal function expansion and method of Galerkin-Eigen function expansion respectively. These methods have a general character, that is, the velocity distributions in vertical direction are continuous. Some other methods, for example, stratified modelling given by Leendertse, FEM used by Koutitas, and O'Connor and method of fixed-net difference in σ-coordinates adopted by Davies and Stephen, give discrete distributions of the velocity.In this paper, a mathematical method is presented for solving the three dimensional nonlinear hydrodynamic equations by using the finite element in the horizontal and the cubic spline in the vertical.Discretization in the horizontal domain is accomplished by using the nine-node isoparametric quadratic finite element and Galerkin method is applied over the horizontal domain. In vertical direction, discretization for nonliniar terms is accomplished by using cubic spline.Numerical results are presented for the three dimensional wind-induced flow in a closed rectangular basin, the tidal flow in an annular section and the tidal flow of Ling-Ding Yang area near South China Sea of Guangdong, Province.For the wind-induced flow, the numerical results show excellent agreement with the analytic solutions. For the tidal flow of Ling-Ding Yang area, the result is more reasonable than by using 2-d methods.
出处
《海洋与湖沼》
CAS
CSCD
北大核心
1990年第3期225-235,共11页
Oceanologia Et Limnologia Sinica
基金
国家自然科学基金
