WANG Qiang, JIANG Peng. A Modified Numerical Method for Arbitrary Mach Number Flows Based on the Preconditioning Technique[J]. Applied Mathematics and Mechanics, 2016, 37(6): 567-573. doi: 10.3879/j.issn.1000-0887.2016.06.002
 Citation: WANG Qiang, JIANG Peng. A Modified Numerical Method for Arbitrary Mach Number Flows Based on the Preconditioning Technique[J]. Applied Mathematics and Mechanics, 2016, 37(6): 567-573.

A Modified Numerical Method for Arbitrary Mach Number Flows Based on the Preconditioning Technique

doi: 10.3879/j.issn.1000-0887.2016.06.002
Funds:  China Postdoctoral Science Foundation（2011M500545）
• Rev Recd Date: 2016-01-13
• Publish Date: 2016-06-15
• The preconditioning technique was applied to modify the existent LU-SGS solver for compressible flows, which was unsuitable for the prediction of low-speed incompressible flows. The preconditioning modification included treatment of the eigen system of the governing equations, improvement of the implicit solving method and discretization of the convection terms with the low-diffusion difference scheme and the AUSM+-up scheme. The modified solver was applied to numerical simulations of inviscid bump flows, lid-driven square cavity viscous flows and Laval nozzle flows. The comparison between the present results and those in the previous literatures proves the feasibility of the preconditioning-modified numerical method in the simulation of arbitrary Mach number flows, including the low-speed, the subsonic, the transonic and the supersonic invicid or viscous flows.
•  [1] Briley W R, Taylor L K, Whitfield D L. High-resolution viscous flow simulations at arbitrary Mach number[J]. Journal of Computational Physics,2003,184(1): 79-105. [2] 廖守亿, 王正华, 王承尧. 预处理方法在低速粘性流动中的应用[J]. 国防科学技术大学学报, 2000,22(1): 89-93.(LIAO Shou-yi, WANG Zheng-hua, WANG Cheng-yao. The application of preconditioning in viscous flow at low speeds[J]. Journal of National University of Defense Technology,2000,22(1): 89-93.(in Chinese)) [3] Choi Y H, Merkle C L. The application of preconditioning in viscous flows[J]. Journal of Computational Physics,1993,105(2): 207-223. [4] Turkel E, Radespiel R, Kroll N. Assessment of preconditioning methods for multidimensional aerodynamics[J]. Computer & Fluids,1997,26(6): 613-634. [5] Weiss J M, Smith W A. Preconditioning applied to variable and constant density flows[J]. AIAA Journal,1995,33(11): 2050-2057. [6] Liou M S. A sequel to AUSM—part Ⅱ: AUSM+-up for all speeds[J]. Journal of Computational Physics,2006,214(11): 137-170. [7] Coakley T J. Turbulence modeling methods for the compressible Navier-Stokes equations[C]// AIAA 16th Fluid and Plasmadynamics Conference.Danvers, Massachusetts, 1983. [8] Eidelman S, Colella P, Shreeve R P. Application of the Godunov method and its second-order extension to cascade flow modeling[J]. AIAA Journal,1984,22(11): 1609-1615. [9] Edwards J R, Liou M S. Low-diffusion flux splitting methods for flows at all speeds[J]. AIAA Journal,1998,36(9): 1610-1617. [10] 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.

Catalog

通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

/