【摘要】：本文基于高階間斷有限元法開(kāi)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(nèi)部采用高階多項(xiàng)式表達(dá)流場(chǎng)守恒變量,在單元間采用有限體積法通量解決了間斷問(wèn)題,具有精度高、插值模板小、易于實(shí)現(xiàn)自適應(yīng)以及并行計(jì)算等優(yōu)點(diǎn)而成為計(jì)算流體力學(xué)的研究熱點(diǎn)之一。脫體渦方法(DES)則是平均雷諾應(yīng)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(dòng),在遠(yuǎn)場(chǎng)采用LES方法模擬流動(dòng),在較少網(wǎng)格量下即可對(duì)分離流動(dòng)做到更為精確的模擬。針對(duì)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(wǎng)格彎曲方法,保證了物面真實(shí)形狀的精確表達(dá)。采用了混合網(wǎng)格方法,利用間斷有限元法對(duì)基于SA模型的DES方法進(jìn)行了空間離散,采用隱式雙時(shí)間步方法進(jìn)行時(shí)間推進(jìn),每個(gè)時(shí)間步產(chǎn)生的大型線性系統(tǒng)采用基于ILU預(yù)處理的廣義最小余量法(GMRES)進(jìn)行求解。為了提高計(jì)算速度,根據(jù)間斷有限元法的特點(diǎn),采用了METIS網(wǎng)格分區(qū)技術(shù)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(dòng),驗(yàn)證了二維下對(duì)長(zhǎng)度尺度的修改是成功的,相比SA模型提高了對(duì)分離流動(dòng)的模擬能力。并且借助于高階間斷有限元法,在稀疏網(wǎng)格下即可得到精確的結(jié)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(xué)位授予單位】：南京航空航天大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O35;O241.82

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