预处理算法在非定常流动计算中的应用

Preconditioning algorithm in unsteady flow simulations

介绍了一种可应用于全速度范围的非定常N-S方程数值求解方法,并全面考核该方法的适用性。该方法通过引进伪时间导数项,对伪时间导数进行预处理以解决低速时方程系数矩阵刚性过大的问题;同时用双时间步推进算法保证时间精度,将该方法推广应用到非定常问题的求解。文中给出了若干算例,覆盖了从极低马赫数到超音速、无粘/层流/湍流、二维/三维、定常/非定常情况。算例结果表明,该方法在较宽的使用范围内均能得到理想的计算结果。

This paper describes a numerical method for solving the unsteady N-S equations at any speed. Preconditioning pseudo-time derivatives alleviate the numerical stiffness encountered in low-speed flow calculations and a dual-time stepping approach extended the algorithm to high-speed unsteady-flows. Numerical tests, including low Mach number/ transonic/ supersonic, inviscid/ laminar/ turbulent, 2-D/3-D, and steady/unsteady problems, showed that this method effectively could lower the numerical stiffness and provide satisfactory results for a large range of flow problems.