当地DFD方法向LES湍流模拟推广的研究

Extension of the Local Domain-Free Discretization Method to Large Eddy Simulation of Turbulent Flows

为有效地降低近壁面网格分辨率的要求,将一种被称为当地自由域离散化(domain-free discretization,DFD)方法的浸没边界法(immersed boundary method,IB)与大涡模拟(large eddy simulation,LES)相结合模拟湍流。偏微分方程在解域内节点上的离散形式可能包含解域之外的节点,外部相关点处的流动变量通过沿垂直于壁面方向的线性外推进行估算。引入基于湍流边界层方程的平衡型壁面模型,壁面模型产生的壁面剪应力和无穿透条件在浸没边界处强制执行,以计算外部相关节点处的速度分量。对于湍流闭合,采用动态亚网格尺度(subgridscale,SGS)模型,并使用拉格朗日平均法计算模型系数。外部相关节点处的SGS涡流黏度为外层处的涡流黏度。为验证当前LES-DFD方法的能力,在相对粗的网格上进行了后台阶绕流的数值实验。计算结果与已发表的实验或数值结果非常吻合。

To alleviate the requirement of mesh resolution in the near-wall region,an immersed boundary method,called the local domain-free discretization(DFD)method,is extended to large eddy simulation(LES)of turbulent flows.The discrete form of partial differential equations at an interior node may involve some nodes outside the solution domain.The flow variables at these exterior dependent nodes are evaluated via linear extrapolation along the direction normal to the wall.A wall model based on the turbulence boundary layer equations is introduced.The wall shear stress yielded by the wall model and the no-penetration condition are enforced at the immersed boundary to evaluate the velocity components at an exterior dependent node.For turbulence closure,a dynamic subgrid scale(SGS)model is adopted and the Lagrangian averaging procedure is used to compute the model coefficient.The SGS eddy viscosity at an exterior dependent node is set to be equal to that at the outer layer.Numerical experiments of backward-facing step flow on relatively coarse meshes have been conducted to verify the ability of the present LES-DFD method.The predicted results agree well with the published experimental or numerical data.