跨音速大迎角Euler方程数值分析

A NUMERICAL SOLUTION OF TRANSONIC EULER EQUATION AT HIGH ANGLES OF ATTACK

应用有限体积法离散三维Euler方程,选用三步显式格式进行时间推进求解;并通过当地时间步长、残值光顺、焓修正等方法加速收敛。对一维波动方程的von Neumann稳定性分析说明这种三步格式的最大Courant数是2。对三角翼跨音速大迎角流动的数值分析表明文中的三步格式及焓修正方法优于人们经常采用的四步、五步格式以及焓阻尼技术。

By finite volume method for spatial discretization and three-stage explicit time-stepping scheme, a numerical solution of three-dimensional Euler equations is presented in this paper. The technique of local time stepping, residual averaging, enthalpy correcting, etc. is used for accelerating convergence. The analysis of von Neumann stability of one-dimensional wave equation indicates that the maximum Courant Number of the above-mentioned three-stage scheme is 2. The calculation of flows around delta wings at high angles of attack shows that the three-stage scheme and enthalpy correction method presented in this paper are better than usually used four or five-stage scheme and enthalpy damping technique. The calculated results show that the numerical method used in this paper can give a good simulation of transonic vortex flow at high angles of attack.