计算机翼跨音速绕流的加罚Galerkin有限元法

1.引言 全速位Galerkin有限元法是跨音速有限元法中重要方法之一。处理超临界流时,为了自动捕捉到激波,通常采用上风技术,但因此导致了质量守恒条件得不到完全满足。文献1]从Bateman变分原理出发,应用加罚函数方法,找出了强制满足质量守恒条件在Galerkin有限元方程中所应加入的附加项。本文将文献1]的方法应用到超临界跨音速绕机翼流动,克服了一般Galerkin有限元法中由于采用上风技术而出现的激波不够陡和位

A PENALTY-GALERKIN FINITE ELEMENT METHOD FOR CALCULATING TRANSONIC FLOW OVER WINGS

An upwind technique is usually used in order to capture the shocks in the (Jalerkm full potential finite element method for calculating supercritical transonic flows. But it leads to the vibration of the equation of mass conservation. The present formulation extends the Galerkin finite element method by modifying it with penalty function to enforce the conservation of mass across the element interfaces, while allowing sudden changes in velocities and densities in 2-D transonic flows over airfoils. The algorithm is then extended to over three-dimentional wings.