摘要
基于混合通量分裂的思想,通过应用Gauss-Seidel迭代求解差分方程,构造了一种时空二阶精度、无条件稳定的隐式迭代NND算法,并讨论了时间精度与稳定性,亚迭代收敛判则,几何守恒律的应用以及动壁边界条件等相关问题。通过引入一种简便易行的加权函数来综合刚性动网格生成技术和超限插值生成动网格这两种方法的优点,发展了一种计算量小、比较实用的加权动网格生成技术。作为应用实例,本文给出了多个动态物体绕流的数值模拟算例,计算结果表明了本文数值方法的成功。
An implicit unconditionally stable subiteration NND scheme of second order accurate in time and space employing Gauss-Seidel subiteration method and mixed-flux-splitting is developed. Some key issues for numerical simulation unsteady flows such as the time accuracy and stability, subiteration convergence tolerance, the application of the geometry conservation law, the moving wall boundary conditions are discussed. A simple dynamic grid generation method is introduced by weighted method to colligate the merits of the rigid dynamic grid generation method and the trans-infinite interpolation method. As the tests, the unsteady inviscid flows around airfoil in forced pitching, the unsteady viscous seperation flows around NACA0015 airfoil in forced pitching up, the Hopf bifurcation for the PAPA flutter model applying to NACA64A006 airfoil in pitching and plunge, the viscous supersonic unsteady flows around the rolling missile, are simunated by the present method, The numerical results show the success of the unsteady numerical methods developed by this paper. For comparison, the author also compute the same two dimensional cases by the famous dual time step and single time step Newton-like subiteration methods. In conclusion, temporal accuracy of conventional implicit schemes such as LU-SGS and AF-ADI is improved by all three different subiteration methods, In practice the present scheme is more efficient than the other two schemes at the same conditions, but the added benefits have been found for the single time-step and the dual time-step subiteration scheme with eliminating the error introduced by simplifications and more robust implied larger physical time step without degrading temporal accuracy.
出处
《空气动力学学报》
CSCD
北大核心
2004年第4期432-437,共6页
Acta Aerodynamica Sinica
