用双时间推进法求解非定常N-S方程的有关问题讨论

On the Solution of Unsteady Navier-Stokes Equations Using Dual-Time Stepping Method

对于直升机旋翼绕流、飞机机动飞行等非定常问题 ,必须采用相应的非定常运动方程予以求解。而如何提高求解非定常运动方程的计算效率 ,一直是非定常计算中亟待解决的问题。针对这一问题 ,本文简要介绍了旨在提高求解非定常 N- S方程计算效率的双时间推进方法 ,并讨论了在应用双时间推进方法时不同物理时间求导精度、不同内迭代收敛标准、不同物理时间步长对计算结果和计算效率的影响。

The dual time stepping method proposed by A. Jameson [1] shows great advantage over other methods in computation efficiency in unsteady calculations. But the selections of some parameters influence its computation efficiency and accuracy. In this paper, we investigate in detail the influence of the following three parameters: (1) The accuracy order of real time step discretization; (2) The convergent tolerance in inner iterations; (3) The magnitude of real time step. The test case of this paper is the pitching oscillation of NACA 0012 airfoil around the quarter point of the airfoil chord at low angle of attack in transonic flow field. The computation results show: (1) The accuracy of third order real time discretization is higher than the second order one for the lift, and is the same for the drag and pitching moment; (2) The accuracy of the results are not sensitive to the inner iteration tolerance, 10 -2 is enough; (3) The magnitude of real time step can be chosen according to the required accuracy. For lift, 50 real time steps per period is enough to get very good resolution of C l ～ α curve. For drag and pitching moment, 200 real time steps per period is necessary to get good resolution in sharply changing regions of C d ～ α and C m～α curves.