一般柱形边界区分场的谱方法计算

SPECTRAL METHODS INVOLVING THE GENERAL CYLINDER BOUNDARY

本文设计了一种计算方法,使谱方法可用于一般边界问题,方法分两步:1.用谱方法解具有简单边界的方程;2、修正复杂边界处的解以满足边界条件。算例是孤立波绕椭圆柱的问题,计算结果显示为不同时刻的二维等值线图与三维波动图。

Using the Spectral Method, higher precision derivatives can be calculated in numerical computations. After FFT-code was discovered, this method was used popularly in Computational Fluid Dynamics. But till now, problems that can be studied by this method are limited to such boundaries which are either geometrically simple (rectangular, circular and so on) or periodical. Obviously if we break through this limitation, more and more CFD problems can share the advantage of the Spectral Method. In this paper we design a spliting method with the following two steps in turn:1st step: To integrate the equation with the (pseudo-) Spectral Method without taking care of the boundary conditions.2nd step: To modify the flow parameters near the boundary in order to satisfy the conditions.A demonstration example is the diffraction of a solitary wave by an elliptical cylinder. The whole diffraction process was calculated and displayed by 3-D Graphics.