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 引用本文: 刘双兵 刘海湖. 亚网格尺度稳定化有限元求解不可压黏性流动[J]. 力学学报, 2011, 43(6): 1083-1090.
Shuangbing Liu Haihu Liu. Subgrid scale stabilized finite element for solution of incompressible viscous flows[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(6): 1083-1090.
 Citation: Shuangbing Liu Haihu Liu. Subgrid scale stabilized finite element for solution of incompressible viscous flows[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(6): 1083-1090.

## Subgrid scale stabilized finite element for solution of incompressible viscous flows

• 摘要: 从亚网格尺度稳定化方法的基本原理出发, 提出了适合时间推进求解非定常Navier-Stokes方程获得定常解的SGS稳定化方法. 基于一定程度的近似和简化, 获得了与时间步长相关的稳定化参数, 从而排除了传统SGS稳定化方法在求解高Re数、小时间步长问题时所引发的数值不稳定性. 把SGS稳定化方法应用于求解不可压湍流, 结合标准k-\varepsilon湍流模型和壁面函数法估计湍流黏性系数, 详细讨论了壁面函数法的实施、湍流输运方程的求解和保证湍流变量非负性的限制策略, 发展了时间推进求解不可压湍流的分离式算法. 二维外掠后台阶层流和湍流计算结果表明,该方法求解不可压黏性流动是可行的, 并且具有稳定性好、计算精度高的特点.

Abstract: Started with the concept and fundamental of Subgrid Scalestabilized (SGS) method, an improved SSS finite element formulation isproposed to obtain time independent solutions by solving the unsteadyincompressible Navier-Stokes equations. Based on some rational approximationand simplification, a new stabilization parameter which has relation withthe selective time step size is deduced. As a result, the numericalinstability resulting from high Reynolds and/or small time step size iseliminated. Combined with standard k-\varepsilon turbulence model andwall function method to estimate turbulent viscosity, the improved SGS method is applied to solve incompressible turbulent flows. Thefinite element implementation of wall function along with solution ofturbulence transport equations is discussed in detail and the positivitypreserving limiter for turbulence variables is introduced. A segregatedalgorithm for time stepping to solve incompressible turbulent flows isdeveloped. The numerical examples of laminar and turbulent flows over abackward facing step are presented in order to show the possibility,stability and high accuracy of the proposed approach for simulating steadyincompressible viscous flows.

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