基于高阶间断有限元法的非定常流场数值模拟

发布时间：2018-09-17 12:22

【摘要】：本文基于高阶间断有限元法开展了二维脱体涡方法的模拟。间断有限元法是有限体积法和有限单元法的混合方法,在单元内部采用高阶多项式表达流场守恒变量,在单元间采用有限体积法通量解决了间断问题,具有精度高、插值模板小、易于实现自适应以及并行计算等优点而成为计算流体力学的研究热点之一。脱体涡方法(DES)则是平均雷诺应力方程(RANS)方法和大涡模拟(LES)方法的混合方法,其在物面附近采用RANS方程模拟流动,在远场采用LES方法模拟流动,在较少网格量下即可对分离流动做到更为精确的模拟。针对间断有限元方法,本文首先发展了适用于间断有限元法的网格弯曲方法,保证了物面真实形状的精确表达。采用了混合网格方法,利用间断有限元法对基于SA模型的DES方法进行了空间离散,采用隐式双时间步方法进行时间推进,每个时间步产生的大型线性系统采用基于ILU预处理的广义最小余量法(GMRES)进行求解。为了提高计算速度,根据间断有限元法的特点,采用了METIS网格分区技术以及MPICH并行策略。利用圆柱绕流、单翼型分离和多段翼型的缝翼非定常流动,验证了二维下对长度尺度的修改是成功的,相比SA模型提高了对分离流动的模拟能力。并且借助于高阶间断有限元法,在稀疏网格下即可得到精确的结果。
[Abstract]:Based on the high order discontinuous finite element method, the two-dimensional detached vortex method is simulated in this paper. The discontinuous finite element method is a hybrid method of finite volume method and finite element method. The high order polynomial is used to express the conserved variables of the flow field in the element, and the flux of finite volume method is used among the elements to solve the discontinuous problem with high accuracy. Interpolation template is small, easy to realize adaptive and parallel computing, so it has become one of the research hotspots in computational fluid dynamics. The (DES) method is a hybrid method of the (RANS) method of the mean Reynolds stress equation and the (LES) method of large eddy simulation. The RANS equation is used to simulate the flow near the body surface and the LES method is used to simulate the flow in the far field. A more accurate simulation of the separated flow can be achieved with less mesh. For the discontinuous finite element method, the mesh bending method which is suitable for the discontinuous finite element method is developed in this paper, which ensures the accurate expression of the real shape of the object surface. The hybrid mesh method is used to discretize the DES method based on SA model by discontinuous finite element method, and the implicit dual time step method is used to advance the time. The large linear systems generated by each time step are solved by the generalized minimum margin method (GMRES) based on ILU preprocessing. In order to improve the computing speed, according to the characteristics of discontinuous finite element method, METIS mesh partitioning technique and MPICH parallel strategy are adopted. By using the flow around a cylinder, the separation of single airfoil and the unsteady flow of multiple airfoils, it is verified that the modification of the length scale in two dimensions is successful, and the simulation ability of the separated flow is improved compared with the SA model. With the help of high order discontinuous finite element method, the exact results can be obtained under sparse meshes.
【学位授予单位】：南京航空航天大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O35;O241.82

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