基于GPU并行计算的非定常Euler方程算法研究

发布时间：2018-05-16 11:49

本文选题：非定常Euler方程 + 动网格方法　；参考：《南京航空航天大学》2012年硕士论文

【摘要】：CFD计算领域中，随着问题的复杂度和计算精度要求的提高，计算耗时也大大增加，国外许多学者已经关注到GPU卓越的计算性能，并完成了大量基于GPU并行计算的CFD算法研究，在单块GPU上取得了数倍到数十倍的加速比。本文在介绍GPU计算软硬件架构的基础上，基于CUDA Fortran并行环境，就求解非定常Euler方程涉及的动网格及GPU并行算法的实施等相关问题开展了深入的研究。为了处理动网格问题，本文首先将Delaunay背景图方法中采用稀疏背景图线性插值获得动网格的思想引入到弹簧法中，提出了一种基于非结构背景网格的动网格方法。该方法先用少量的物面控制点生成相对较粗的非结构背景网格，再用弹簧法将动边界的变化量作用到该背景网格，然后利用计算网格与背景网格的映射关系插值生成对应的动网格，最后对物面网格点及其附近受影响的密网格点进行局部网格修正，获得最终计算所需的动网格。与直接弹簧法比较，，由于弹簧法作用的背景网格远粗于实际的计算网格，提高了计算效率，此外，由于网格的运动受控于受弹簧法作用的背景网格，边界变形或运动能较为均匀地传递到内部网格上，使网格单元过渡光滑，提高了动网格的质量。文中给出了二维和三维动网格算例，验证了所提动网格方法的可行性和计算效率。接着，本文采用格心格式的有限体积法，对求解非定常Euler方程的GPU并行算法的计算程序进行了开发与研究。算法涉及的空间离散采用具有二阶精度的Jameson格式，时间推进采用全隐式的双时间推进方法，拟时间步采用三步TVD Runge-Kutta显式推进，同时还采用当地时间步长、隐式残值光顺等措施加快收敛速度。文中给出了二维NACA0012翼型跨音速非定常绕流和三维M6机翼定常附着流动的算例，并与实验数据及相关的文献结果进行了比较与验证。文中最后给出了基于三维M6机翼扭转变形诱发的非定常流动算例，展示了所提动网格技术及GPU并行计算的应用前景。
[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.
【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】：2012
【分类号】：O35;TP338.6

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