弯曲网格上的间断有限元湍流数值解法研究

摘要

Discontinuous Galerkin (DG)finite element method was adopted for the numerical approxima-tion of the Reynolds-averaged Navier-Stokes(RANS)equations with the Spalart-Allmaras turbulence model. In order to make the solver robust,the original turbulence model equation were modified accordingly.Fur-thermore,high order approximation of the real solid boundary was used and several layers of curved meshes were constructed to avoid inconsistent mesh cross-overs.For the computation of the distance of each quadra-ture point to the nearest curved wall boundaries,a fast straightforward numerical method was proposed.The DG discretization of the RANS equations were demonstrated for turbulent flows past a NACA0012 airfoil and RAE airfoil based on hybrid mesh.Numerical results indicate that highly accurate solutions can be obtained with the modified turbulent equation on coarse curved hybrid mesh.%采用间断有限元方法对雷诺平均 Navier-Stokes（RANS）方程进行了数值求解，对 Spalart-Allmaras 单方程湍流模型进行了部分修正，使得求解器更加鲁棒。构造了分段高次多项式来逼近真实物面，同时物面附近采用多层弯曲网格来避免网格交叉，此外提出了一种快速计算积分点的曲面物面距的方法。采用混合网格对 NACA0012翼型以及 RAE 翼型进行了数值计算，并与实验数据以及前人数据进行了对比。计算结果表明，采用物面弯曲网格结合修正的湍流模型方法在相对稀疏的网格上就能得到比较好的数值解。