跨音速流场的变域变分间断有限元解法及激波位置的自动捕获

VARIATIONAL PRINCIPLE WITH VARIABLE DOMAIN DISCO-NTINUOUS FINITE ELEMENT METHOD FOR TRANSONICFLOW AND DETERMINING AUTOMATICALLY THEPOSITION AND SHAPE OF THE SHOCK WAVES

一、前言 近年来,刘高联教授提出了利用变域变分法求解含激波的跨声速流场及相应的变分原理。作者根据文献[1]提出的变分原理,在文献[2]的基础上,提出了可移动结点间断有限元模式,以楔形流场为例进行流场的求解。通过计算不仅求出了激波的精确位置,而且激波厚度为零,其解与解析解吻合得较好。

In this paper, the theory of the variational principles with variable domain suggested inref, (1) is applied. The discontinuous finite element modle of moving nodel is made and it can determine automatically and exactly the position and shape of the shock wave in two-dimension trasonic flow pass, and the velocity and density arc jumping on bothsides of shock wave. In the paper, the accurate resultes are obtained and compared satisfy with exact solution for a wedge of inlet Mach number 1. 2.