后台阶流动的数值模拟

Numerical simulation of backward facing step flow

简述了大涡模拟的基本思想,指出大涡模拟的效率主要取决于四个因素,即流动中须有大尺度涡存在、合理的计算格式、合适的滤波器和亚格子应力模型。在深入考虑粘性不可压缩流Navier-Stokes方程各个子项作用的基础上,提出二阶全展开Euler-Taylor-Galerkin有限元方法作为大涡模拟的离散格式,并采用Gauss滤波器,对典型算例——后台阶处的流动进行大涡模拟,计算结果与相关文献符合的很好。从计算结果还可以看出大涡模拟与二阶全展开ETG有限元方法的结合在捕捉涡系及反映涡动时变过程方面具有明显的优势,说明大涡模拟适合于边界几何形状复杂区域流动的模拟。同时应用二阶全展开ETG有限元方法对低雷诺数粘性不可压缩后台阶流动进行了计算,得到与相关文献符合良好的计算结果,即该方法也可独立用于对低雷诺数粘性不可压缩流动的计算。

The basic thought of the large eddy simulation (LES) is presented. It is pointed out that the efficiency of LES depends mainly on the four factors - large scale eddies, reasonable calculating scheme, appropriate filter and subgrids stress mode. Based on considering the role of each term of Navier-Stokes equations for the incompressible viscous flow, the second order full expansion Euler-Taylor-Galerkin (ETG) finite element method is deduced and is used as the calculation scheme for LES. Cooperated with the Gauss filter, the large eddy simulation of the flow over a backward-facing step is carried out. The results agree well with that of the given reference. Since the rich eddies are captured and the vortex flow process is shown, LES is applicable to simulate the flow in the domains with complex geometry boundaries. The second order full ETG finite element method is also used to simulate the incompressible viscous flow of low Reynolds number. It is proved that the second order full expansion Euler-Taylor-Galerkin (ETG) finite element method can be used to simulate such a kind of flow independently.