基于高階間斷有限元法的非定常流場數值模擬
發(fā)布時間：2018-09-17 12:22
【摘要】：本文基于高階間斷有限元法開展了二維脫體渦方法的模擬。間斷有限元法是有限體積法和有限單元法的混合方法,在單元內部采用高階多項式表達流場守恒變量,在單元間采用有限體積法通量解決了間斷問題,具有精度高、插值模板小、易于實現自適應以及并行計算等優(yōu)點而成為計算流體力學的研究熱點之一。脫體渦方法(DES)則是平均雷諾應力方程(RANS)方法和大渦模擬(LES)方法的混合方法,其在物面附近采用RANS方程模擬流動,在遠場采用LES方法模擬流動,在較少網格量下即可對分離流動做到更為精確的模擬。針對間斷有限元方法,本文首先發(fā)展了適用于間斷有限元法的網格彎曲方法,保證了物面真實形狀的精確表達。采用了混合網格方法,利用間斷有限元法對基于SA模型的DES方法進行了空間離散,采用隱式雙時間步方法進行時間推進,每個時間步產生的大型線性系統(tǒng)采用基于ILU預處理的廣義最小余量法(GMRES)進行求解。為了提高計算速度,根據間斷有限元法的特點,采用了METIS網格分區(qū)技術以及MPICH并行策略。利用圓柱繞流、單翼型分離和多段翼型的縫翼非定常流動,驗證了二維下對長度尺度的修改是成功的,相比SA模型提高了對分離流動的模擬能力。并且借助于高階間斷有限元法,在稀疏網格下即可得到精確的結果。
[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.
【學位授予單位】：南京航空航天大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O35;O241.82
本文編號：2245905
[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.
【學位授予單位】：南京航空航天大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O35;O241.82
【參考文獻】
相關期刊論文 前7條
1 李明;劉偉;張來平;張涵信;;高階精度DG/FV混合方法在二維粘性流動模擬中的推廣[J];空氣動力學學報;2015年01期
2 秦望龍;呂宏強;伍貽兆;;彎曲網格上的間斷有限元湍流數值解法研究[J];空氣動力學學報;2014年05期
3 王翔宇;李棟;;SST-DES在小分離流動數值模擬中的改進[J];北京航空航天大學學報;2014年09期
4 夏軼棟;伍貽兆;呂宏強;宋江勇;;高階間斷有限元法的并行計算研究[J];空氣動力學學報;2011年05期
5 閻超;于劍;徐晶磊;范晶晶;高瑞澤;姜振華;;CFD模擬方法的發(fā)展成就與展望[J];力學進展;2011年05期
6 蔚喜軍,周鐵;流體力學方程的間斷有限元方法[J];計算物理;2005年02期
7 劉學強,伍貽兆;用DES數值模擬具有橫向噴流的紊流流場[J];航空學報;2004年03期
相關博士學位論文 前1條
1 陳龍;基于CFD/CSD耦合的旋翼氣動彈性數值模擬[D];南京航空航天大學;2011年
相關碩士學位論文 前1條
1 黃華;基于前緣射流的縫翼噪聲控制研究[D];上海交通大學;2013年
，本文編號：2245905
本文鏈接：http://sikaile.net/kejilunwen/yysx/2245905.html
