二维非定常欧拉方程的有限元解法

本文通过求解时间相关的欧拉方程，对振荡翼型的非定常二维无粘可压缩绕流作了数值模拟。求解方程时采用了有限体积积分的方法，并用ＶａｎＬｅｅｒ逆风通量分裂格式来计算控制体通量。隐式格式的采用，大大提高了计算效率；同时，通过插值使得空间离散达到了二阶精度。另外，本文采用基于非结构三角形网格的动态网格来处理刚性物体的移动，从而顺利地解决了复杂几何外形物体的非定常绕流的问题。文章最后给出了ＮＡＣＡ００１２翼型绕四分之一弦线作简谐俯仰振动的计算结果。一个周期内的瞬时压强分布以及升力和力矩系数都与实验结果吻合良好，

A Finite Element Method for Solving Two Dimensional Unsteady Euler Equations

The present paper describes the numerical simulation of unsteady two-dimensional invisid Compressible flow around an oscillating airfoil, by solving the time-dependent Euler equations. A finite-volume integration method is implemented, together with an upwind-biased fluxvector splitting of Van Leer. The temporal discretization involves an implicit time- integration scheme, which is computationally efficient.Second order spatial accuracy is achived by interpolation. Dynamic mesh algorithm based on unstructured triangular grid is used to handle the moving solid body, which can easily treat the most complex of geometric configurations .The unsteady results are obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment cofficents during a cycle of motion compare well with experimental data.