任意马赫数非定常流动数值模拟的统一算法

发展适用于从低速到高速任意马赫数非定常流动数值模拟的统一算法.通过引入一个伪时间导数项和一个新的预处理矩阵,得到双时间非定常预处理可压缩Navier-Stokes方程.方程的对流项采用三阶Roe通量近似差分格式离散,粘性项采用二阶中心差分格式离散.基于数值通量的线性化技术,实现伪时间步的隐式ADI-LU格式迭代,进而获得物理时间步的二阶推进精度.重点以低马赫数流动为例,求解了圆柱绕流和NACA0015翼型等速上仰动态失速问题.计算结果表明该统一算法能够较好地模拟低马赫数乃至任意马赫数非定常流动.

A Uniform Method for Unsteady Flows at Arbitrary Mach Number

A uniform method for unsteady flows at arbitrary Mach number is developed.The preconditioned dual-time compressible Navier-Stokes equations for unsteady flows are obtained by incorporating a pseudo-time derivative term and preconditioning.The inviscid flux vectors and the viscous flux vectors are differentiated by a Roe-scheme of three-order and a general central difference scheme,respectively.A pseudo-time subiteration with an implicit ADI-LU scheme is implemented based on state-vector flux linearization.A two-order precision for physical-time step is achieved.Taking low speed flows as examples,the flow over a circular cylinder and the dynamic stall of the NACA0015 airfoil with identical pitching rate are simulated.Computed results agree with published results.It shows that the method simulates unsteady flows at arbitrary Mach number well.