A Computational Method for the Navier-Stokes Equations at All Speeds
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摘要: 为了在低马赫数到高马赫数范围内求解可压缩Navier-Stokes方程,给出了基于预处理算法的PLU-SGS方法.将高分辨率AUSMPW格式与三阶MUSCL格式融合,将其扩展到三阶精度,并采用特征边界条件.为了验证该方法的有效性,通过求解曲线坐标系可压缩Navier-Stokes方程,对几个典型流动问题进行了数值计算.计算结果与文献计算结果或实验数据比较表明,该方法对不同马赫数Navier-Stokes方程的计算,具有较高的计算精度和收敛速度以及良好的稳定性.Abstract: A PLU-SGS method based on a time-derivative preconditioning algorithm and LU-SGS method is developed in order to calculate the Navier-Stokes equations at all speeds. The equations were discretized using AUSMPW scheme in conjunction with the third-order MUSCL scheme with Van Leer limiter. The present method was applied to solve the multidimensional compressible Navier-Stokes equations in curvilinear coordinates. Characteristic boundary conditions based on the eigensystem of the preconditioned equations were employed. In order to examine the performance of present method, driven-cavity flow at various Reynolds numbers and viscous flow through a convergent-divergent nozzle at supersonic were selected to test this method. The computed results were compared with the experimental data or the other numerical results available in literature and good agreements between them are obtained. The results show that the present method is accurate, self-adaptive and stable for a wide range of flow conditions from low speed to supersonic flows.
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[1] Choi Y H,Merkle C L.The application of perconditioning in viscous flows[J].Journal of Computational Physics,1993,105(2):207-233. [2] Turkel E,Radespiel R,Kroll N.Assessment of preconditioning methods for multidimensional aerodynamic[J].Computers & Fluids,1997,26(6):613-634. [3] Edwards J K,Roy C.Preconditioned multigrid methods for two-dimensional combustion calculations at all speeds[J].AIAA Journal,1998,36(2):185-192. [4] Liou M-S,Steffen C J.A new flux splitting scheme[J].Journal of Computational Physics,1993,107(1):23-39. [5] Liou M-S.A sequel to AUSM:AUSM+[J].Journal of Computational Physics,1996,129(2):364-382. [6] Kim K H,Kim G C,Rho O H.An improvement of AUSM schemes by introducing the pressure-based weight functions[J].Computers & Fluids,1998,27(2):311-346. [7] Anderson W K,Thomas J L,Van Leer B.Comparison of finite volume flux vector splitting for the Euler equations[J].AIAA Journal,1986,24(9):1453-1460. [8] Yoon S,Jameson A.Lower-Upper Symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations[J].AIAA Journal,1988,26(9):1061-1069. [9] Ghia U,Ghia K N,Shin C T.High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method[J].Journal of Computational Physics,1982,48(3):387-411. [10] Mason M L,Putnam L E,Re J.The effect of throat contouring on two-dimensional converging-diverging nozzle at static condition[R].NASA TN-1704,1980.
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