發(fā)布時(shí)間：2018-05-16 11:49

  本文選題：非定常Euler方程 + 動(dòng)網(wǎng)格方法��； 參考：《南京航空航天大學(xué)》2012年碩士論文

【摘要】：CFD計(jì)算領(lǐng)域中，隨著問(wèn)題的復(fù)雜度和計(jì)算精度要求的提高，計(jì)算耗時(shí)也大大增加，國(guó)外許多學(xué)者已經(jīng)關(guān)注到GPU卓越的計(jì)算性能，并完成了大量基于GPU并行計(jì)算的CFD算法研究，在單塊GPU上取得了數(shù)倍到數(shù)十倍的加速比。本文在介紹GPU計(jì)算軟硬件架構(gòu)的基礎(chǔ)上，基于CUDA Fortran并行環(huán)境，就求解非定常Euler方程涉及的動(dòng)網(wǎng)格及GPU并行算法的實(shí)施等相關(guān)問(wèn)題開(kāi)展了深入的研究。 為了處理動(dòng)網(wǎng)格問(wèn)題，本文首先將Delaunay背景圖方法中采用稀疏背景圖線性插值獲得動(dòng)網(wǎng)格的思想引入到彈簧法中，提出了一種基于非結(jié)構(gòu)背景網(wǎng)格的動(dòng)網(wǎng)格方法。該方法先用少量的物面控制點(diǎn)生成相對(duì)較粗的非結(jié)構(gòu)背景網(wǎng)格，再用彈簧法將動(dòng)邊界的變化量作用到該背景網(wǎng)格，然后利用計(jì)算網(wǎng)格與背景網(wǎng)格的映射關(guān)系插值生成對(duì)應(yīng)的動(dòng)網(wǎng)格，最后對(duì)物面網(wǎng)格點(diǎn)及其附近受影響的密網(wǎng)格點(diǎn)進(jìn)行局部網(wǎng)格修正，獲得最終計(jì)算所需的動(dòng)網(wǎng)格。與直接彈簧法比較，，由于彈簧法作用的背景網(wǎng)格遠(yuǎn)粗于實(shí)際的計(jì)算網(wǎng)格，提高了計(jì)算效率，此外，由于網(wǎng)格的運(yùn)動(dòng)受控于受彈簧法作用的背景網(wǎng)格，邊界變形或運(yùn)動(dòng)能較為均勻地傳遞到內(nèi)部網(wǎng)格上，使網(wǎng)格單元過(guò)渡光滑，提高了動(dòng)網(wǎng)格的質(zhì)量。文中給出了二維和三維動(dòng)網(wǎng)格算例，驗(yàn)證了所提動(dòng)網(wǎng)格方法的可行性和計(jì)算效率。 接著，本文采用格心格式的有限體積法，對(duì)求解非定常Euler方程的GPU并行算法的計(jì)算程序進(jìn)行了開(kāi)發(fā)與研究。算法涉及的空間離散采用具有二階精度的Jameson格式，時(shí)間推進(jìn)采用全隱式的雙時(shí)間推進(jìn)方法，擬時(shí)間步采用三步TVD Runge-Kutta顯式推進(jìn)，同時(shí)還采用當(dāng)?shù)貢r(shí)間步長(zhǎng)、隱式殘值光順等措施加快收斂速度。文中給出了二維NACA0012翼型跨音速非定常繞流和三維M6機(jī)翼定常附著流動(dòng)的算例，并與實(shí)驗(yàn)數(shù)據(jù)及相關(guān)的文獻(xiàn)結(jié)果進(jìn)行了比較與驗(yàn)證。文中最后給出了基于三維M6機(jī)翼扭轉(zhuǎn)變形誘發(fā)的非定常流動(dòng)算例，展示了所提動(dòng)網(wǎng)格技術(shù)及GPU并行計(jì)算的應(yīng)用前景。
[Abstract]:In the field of CFD computing, with the increase of the complexity of the problem and the requirement of computational precision, the computation time is also increased greatly. Many foreign scholars have paid attention to the excellent computing performance of GPU, and have completed a large number of CFD algorithms based on GPU parallel computing. The speedup ratio is several times to dozens times on a single block GPU. Based on the introduction of GPU computing hardware and software architecture and based on the CUDA Fortran parallel environment, this paper makes a deep research on the dynamic grid and the implementation of GPU parallel algorithm for solving unsteady Euler equations. In order to deal with the dynamic grid problem, this paper first introduces the idea of sparse background graph linear interpolation to the spring method, and proposes a dynamic grid method based on unstructured background grid. In this method, a few surface control points are used to generate a relatively coarse unstructured background mesh, and then a spring method is used to influence the dynamic boundary change to the background grid. Then the mapping relationship between computational grid and background grid is used to generate the corresponding moving grid. Finally, the local mesh correction is carried out to obtain the dynamic grid required for the final calculation. Compared with the direct spring method, because the background mesh acting by the spring method is much thicker than the actual computational grid, the computational efficiency is improved. In addition, the movement of the grid is controlled by the background grid acting by the spring method. The boundary deformation or motion can be transferred to the inner mesh uniformly, which makes the mesh transition smooth and improves the quality of the moving mesh. Examples of 2D and 3D moving meshes are given to verify the feasibility and computational efficiency of the proposed method. Then, using the finite volume method of lattice scheme, the program of GPU parallel algorithm for solving unsteady Euler equations is developed and studied. The spatial discretization of the algorithm is based on Jameson scheme with second-order precision, the full implicit dual-time advance method is used for time advance, and the three-step TVD Runge-Kutta explicit method is used for quasi-time step, and the local time step is also used. Implicit residual smoothing and other measures to accelerate the convergence rate. Examples of transonic unsteady flow around two-dimensional NACA0012 airfoil and steady attachment flow of 3D M6 wing are given and compared with experimental data and related literature results. Finally, an example of unsteady flow induced by 3D M6 wing torsional deformation is given, and the application prospect of the proposed moving grid technique and GPU parallel computation is presented.
【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】：2012
【分類(lèi)號(hào)】：O35;TP338.6

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