求解二维Navier-Stokes方程的谱元法

A Spectral Element Method for Solution of 2-D Navier-Stokes Equation

本文研究了谱元法的插值函数选取和谱元法的离散,给出离散方程的一般形式,分析了误差和收敛速度,并采用时间分裂格式的谱元法求解Navier-Stokes方程,计算表明结果是令人满意的,方法不仅具有良好的稳定性而且具有较高的精度,易于推广到三维及湍流的直接数值模拟中去。

The selection of interpolating function for spectral method and the description ofspectral method are considered in this paper. The general form of the discrete equation is giv-en. The error and the velocity of convergence of the method is analysed. Navier-Stokes equa-tion has been solved numerically by a time splitting scheme. The computational results are sat-isfactory. The method given here is stable and it presents a higher accuracy. The extension ofthe method is easy to do for solving 3-D Problems and can be adopted for direct numerital sim-ulation of turbulent flow.