基于有限体积法的非结构网格大涡模拟离散方法研究

LES Discretization Methods for Unstructured Meshes Based on the Finite Volume Method

非结构网格下的大涡模拟是解决复杂几何体高Reynolds（雷诺）数流动的有效途径.首先,基于有限体积法,研究了对流项和扩散项非结构网格下的离散方法.研究结果表明：基于TVD（total variation diminishing）限制器的限制中心差分格式保证了对流项的二阶精度并抑制了非物理振荡,同时,线性迎风格式虽然稳定,但数值耗散过大,且不能保证有界,中心差分格式引起了周期性非物理振荡;扩散项的超松弛非正交修正减小了网格非正交带来的离散误差,但修正系数须根据网格非正交的程度进行合理选取.为验证所述离散方法对大涡模拟的适用性,数值计算了Re=1.14×10^6下的非定常三维小球绕流,计算方法包括：计算网格用基于Delaunay三角剖分和Netgen前沿推进算法的四面体非结构网格;湍流模型用改进的延迟分离涡大涡模型;在离散格式的选取上,对流项用限制中心差分,扩散项加入非正交修正,插值格式用最小二乘法,时间项用二阶后向差分.计算结果表明,所用离散方法稳定收敛并且与实验数据基本吻合.

The LES of unstructured meshes is an effective way to solve the high Reynolds number flow around complex geometries. Firstly,based on the finite volume method,the discretization methods for the convection term and the diffusion term were analyzed. For the convection term,the central difference scheme with a TVD limiter ensured 2nd-order accuracy and inhibited the nonphysical oscillations. Dissipation of the linear upwind scheme was large and can not guarantee boundedness. The central difference scheme caused a period of nonphysical oscillations. For the diffusion term,the method of over relaxation nonorthogonal correction reduced the discretization error caused by the nonorthogonal mesh. The correction coefficients were chosen according to the nonorthogonal degree of the mesh. Secondly,numerical simulation of unsteady flow around a sphere with high Reynolds number was conducted based on the improved delayed detached eddy simulation（ IDDES） model and the tetrahedral mesh. The limited central difference scheme was used for the convection term,and the over relaxation correction was used for the diffusion term. The least squares method was used for the interpolation scheme. The 2nd-order backward difference scheme was used for the time term. The calculation results show that,the proposed discretization methods are stable and in good agreement with the experimental data.