摘要:
运用高分辨率的边界适应网格进行流体动力学数值计算时,如何提高计算稳定性和减少计算量成为数值求解的关键性问题.在非正交的边界适应坐标系中,每个动量方程中同时出现了两个交叉方向的水位偏导数项,给隐式求解带来困难,而显式格式下的时间步长由于受与空间步长有关的Courant-Friedrichs-Lewy条件限制,计算量成倍增加.本文从广义曲线坐标系下浅海动力学方程组出发,导出了流速的逆变张量所满足的动量方程组,使方程中的水位偏导数项变成了沿某一协变基向量方向占优的形式,方便地采用了交替方向隐式差分格式,从而提高了计算稳定性并减小了计算量.本文通过对澳门海域航道和港池中流场的计算,证实了该模式是一种进行高分辩率数值计算的有效方法.
Abstract:
The key problem in the computation of fluid dynamics using fine boundary-fitted grids is how to improve the numerical stability and decrease the calculating quantity.To solve this problem,implicit schemes should be adopted since explicit schemes may bring about a great increase in computation quantity according to the Courant-Friedrichs-Lewy condition.Whereas the adoption of implicit schemes is difficult to be realized because of the existence of two partial derivatives of surface elevations with respect to variables of alternative direction coordinates in each momentum equation in non-rectangular coordinates.With an aim to design an implicit scheme in non-rectangular coordinate,new momentum equations with the contravariant components of velocity vector are derived based on the shallow water dynamic equations in generalized curvilinear coordinates.In each equation the coefficients before the two derivatives of surface elevations have different orders ofmagnitude,i.e.,the derivative with the larger coefficient may play a more important role than that with the smaller one.With this advantage,the ADI scheme can then be easily employed to improve the numerical stability and decrease the calculating quantity.The calculation in a harbour and a channel in Macao nearshore area shows that the implicit model is effective in calculating current fields in small size areas.
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