AF-2格式的加速收敛参数研究

 一、引言 Ballhaus等人提出的求解跨音速定常流动的隐式近似因式分解法（AF-2）具有收敛快速,占计算机存储少等优点。文献1,2]分别对于完全小扰动方程和全位势方程的计算给出了很好的例证。文献3]表明上述结论对于横向小扰动位势方程也是成立的。AF-2格式的快速收敛主要是通过加速收敛参数的循环取值来实现的。因此,合理正确地选取加速收敛参数序列对AF-2格式至关重要。

AF-2 ITERATION COMPUTATIONS FOR PLANE STEADY TRANSONIC POTENTIAL FLOWS OVER AIRFOILS WITH CHORD-WISE LARGE DISTURBANCE

Implicit approximate-factorization scheme 2（AF-2）is applied for solving the plane steady transonic potential equation with large disturbance in the x-direction and small disturbance in the y-direction for flow over NACA0012 transonic airfoil. Von-Neumann analysis of the stability for AF-2 scheme is carried out. Acceleration parameters are investigated via Von-Neumann stability analysis and numerical experiments. The convergence characteristics of the AF-2 and SLOR Schemes are compared by computations.The considered free stream Mach numbers are 0.8, 0.85 and 0.9. The angles of attack are 0°, 1°, 2° and 4°.The solutions are obtained on a variably spaced grid with 39×31 points on x-y plane with 22 points along the chord. The x-mesh extends about ten times of the chord ahead and behind the airfoil. The y-mesh extends about ten times the chord above and below the airfoil. The computations are started from uniform flow （ = 0）.Von-Neumann stability analysis for AF-2 indicates that when 0< < 2 , the low-frequency error components do not increase at supersonic points. The linearized stability condition derived for subsonic points is given by formula（16）. Uon-Neumann stability analysis and the computational practice indicate that the acceleration parameter sequence （23） is better than the sequence （24） for the convergence. Convergenc can be improved by increasing H and lowering L. appropriately in the neighborhood of the airfoil boundry. The comparisons between the convergence characteristics of the AF-2 and SLOR schemes are given in Table 1. The results indicate that AF-2 is about thirteen times faster than SLOR.