采用近似边界求解壁板颤振的CBS有限元算法

为了简化Euler方程求解壁板颤振问题,将近似边界条件成功地推广到CBS(characteristic-based split)有限元方法求解壁板颤振领域,把运动壁面的影响转化为Euler方程的边界条件,避免了对动网格的处理.通过对近似边界方法、动网格方法以及3阶活塞理论的数值模拟结果进行对比发现:首先,加载近似边界的CBS有限元方法操作非常简便,且模拟结果与动网格方法完全吻合;其次,Euler方程可以准确捕捉到壁板前后两端不光滑尖点所引起的压力突跳,而3阶活塞理论则无法做到;最后,采用近似边界的CBS有限元方法在求解无黏可压缩流动中细长体小变形的流-固耦合问题上具有潜力和优势. 

CBS finite element method with approximate boundary conditions for panel flutter

In order to simplify the solving process of Euler equation for panel flutter, approximate boundary conditions were successfully introduced into CBS (characteristic-based split) finite element method to simulate the panel flutter. The impact of moving boundary was treated as normal boundary conditions for Euler equation. From analysis, it is found that:first, the results by approximate boundary conditions agree very well with those by moving boundary method, and the application of approximate boundary conditions is more convenient; then, Euler equation, rather than 3rd order piston theory is able to capture the pressure jump caused by sharp points at the ends of panels; finally, CBS finite element method with approximate boundary conditions has potentials and advantages in solving the fluid-structure interaction problems of small deformation of slender bodies in inviscid compressible flows.