用AF方法生成贴体坐标系的研究

On Generation of Boundary-Fitted Curvilinear Coordinate System with AF Method

本文从理论上讨论了近似因子方法(Approximate FactorizationMethod,简称AF方法)生成二维贴体曲线坐标系的稳定性,给出了分解参数、松弛参数与加速参数选取的理论依据,通过实际计算考证了AF方法生成贴体坐标系的可行性及求解无粘性不可压流场之压力分布的正确性。理论分析与实际计算表明:对于贴体曲线坐标系的生成及无粘性不可压流场流函数的计算,AF方法的特定格式均能够提供简单、迅速的算法及可靠的收敛结果。

In numerical solution of partial differential equation, Thompson et al proposed the theory of boundary-fitted coordinate system [1-3] in order to satisfy fully boundary condi- tions. But, somewhat too much computer time is needed for generating this coordinate sys- tem with SOR method[2]. In this paper, AF(approximate factorization) method, a fast algorithm frequently em- ployed in aerodynamic computations[4-6], is used for generating two-dimensional bound- ary-fitted coordinate system. The correctness of the coordinate system so generated is checked against well known numerical results of non-viscous incompressible flows. On the basis of the authors theoretical analysis and actual computatons, the follow- ing findings are abtained: (1) For factorization scheme I (eq. 7.a in full paper), the program design of AF algorithm is simple and the convergence rate is much more rapid than that of the SOR method. (2) Convergence rate is greatly influenced by the selection of approximate factorization. Factorization schemes Ⅱ(eq. 7.b) Ⅲ(eq. 7.c) Ⅳeq. (7.d) give poor convergence rates or instability. (3) Once boundary-fitted coordinate system is generated and basic flows are computed, numerical values of pressure can be computed for different angles of attack by suitable superposition of basic flows. The authors theoretical analycis will now be brifly sketched. The authors are believed to be the First to use Von Neumann's method to analyze the stability conditions of AF forms used in generating boundary-fitted coordinate system. Using the principle of mini- mum modulus of amplification, the authors select proper values of resolution parameter and relaxation parameter in order to accelerate convergence. At the same time, the authors also show how the acceleration parameter should be selected so as to make the errors of high frequency or low frcuqency a minimum.