并行的多重网格方法在离散伴随优化中的应用
收稿日期: 2013-10-18
修回日期: 2014-01-13
网络出版日期: 2014-02-17
Application of Parallel Multigrid Algorithm to Discrete Adjoint Optimization
Received date: 2013-10-18
Revised date: 2014-01-13
Online published: 2014-02-17
伴随优化方法在飞行器气动外形优化设计方面的应用越来越广泛，但以精细减阻等为目标的优化，面对真实飞行器仍然存在计算量大、计算周期长的问题。将多重网格技术结合并行技术运用于基于非结构混合网格、雷诺平均Navier-Stokes方程的离散伴随方程的求解，提高了离散伴随优化系统的整体效率。给出了伴随方程多重网格计算中的延拓和限制算子，采用V循环比较了不同层数的加速效果和粗网格残差计算方法对目标函数梯度敏感导数的影响。结合Metis分区技术，提出了适合伴随方程的数据并行传递简化方式，使伴随方程在300个并行分区计算时加速比仅比理想加速比低13%。采用发展的高效优化系统，选取了112个设计变量，对DLR F6翼身组合体跨声速状态进行减阻优化，使机翼空间激波得到弱化，阻力减小9 counts。模拟验证结果表明，建立的高效的飞行器气动外形优化设计系统在三维真实飞行器外形优化方面，具有良好的应用前景。
李彬 , 唐静 , 邓有奇 , 张耀冰 . 并行的多重网格方法在离散伴随优化中的应用[J]. 航空学报, 2014 , 35(8) : 2091 -2101 . DOI: 10.7527/S1000-6893.2013.0518
The adjoint method is now employed more and more widely for aerodynamic shape optimization. But when used for reducing the drag of a complex aircraft, it still requires a large amount of time-consuming calculation. Based on an unstructured mesh, this paper proposes a parallel multigrid algorithm to solve the discrete adjoint equation for a 3D Reynolds-averaged Navier-Stokes solver, so as to improve the optimization system efficiency. The prolongation operator and the restriction operator are described for the multigrid adjoint solver. By using the V-cycle, the accelerating effect of different layers is compared, and the influence of coarse grid residuals computing methods on the gradient of the objective function is analyzed. Combined with Metis partitioning technology, a simplified parallel-data transfer approach is implemented for the adjoint solver, so that the parallel speedup of the adjoint equation is only 13% lower than the ideal speedup in 300 parallel partitions. The optimization system is successfully demonstrated for a DLR F6 wing-body transonic shape optimization design, in which 112 design variables are selected with the purpose of reducing drag. Shock structure change is presented before and after the optimization, and drag reduction is nine counts. It shows that the efficient optimization system established in this paper has a bright application prospect for three-dimensional complex shape optimization.
[1] Elliott J, Peraire J. Practical three-dimensional aerodynamic design and optimization using unstructured grids[J]. AIAA Journal, 1997, 35(9): 1479-1485.
[2] Nielsen E J, Anderson W K. Recent improvements in aerodynamic design optimization on unstructured meshes[J]. AIAA Journal, 2002, 40(6): 1155-1163.
[3] Brezillon J, Dwight R P. Aerodynamic shape optimization using the discrete adjoint of the Navier-Stokes equations: applications towards complex 3D configurations//KATnet Ⅱ Conference on Key Aerodynamic Technologies. Bremen: machtWissen.de AG, 2009, 36(1): 1-8.
[4] Kim H J, Nakahashi K. Discrete adjoint method for unstructured Navier-Stokes solver, AIAA-2005-0449. Reston: AIAA, 2005.
[5] Nielsen E J, Kleb B. Efficient construction of discrete adjoint operators on unstructured grids by using complex variables, AIAA-2005-0324. Reston: AIAA, 2005.
[6] Lee B J, Kim C. Strategies for robust convergence characteristics of discrete adjoint method[J]. Computational Fluid Dynamics, 2009, 33: 633-639.
[7] Zuo Y T, Gao Z H, He J. Aerodynamic design method based on N-S equations and discrete adjoint approach[J]. Acta Aerodynamica Sinica, 2010, 28(5):509-512. (in Chinese) 左英桃, 高正红, 何俊. 基于N-S 方程和离散共轭方法的气动外形设计[J]. 空气动力学学报, 2010, 28(5):509-512.
[8] Ma X Y, Fan Z L, Wu W H, et al. Aerodynamic shape optimization for wing based on NURBS[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(9): 1616-1621. (in Chinese) 马晓永, 范召林, 吴文华, 等. 基于NURBS方法的机翼气动外形优化[J]. 航空学报, 2011, 32(9): 1616-1621.
[9] Li B, Deng Y Q, Tang J, et al. Discrete adjoint method for 3D unstructured grid[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(3): 674-686. (in Chinese) 李彬, 邓有奇, 唐静, 等. 基于三维非结构混合网格的离散伴随优化方法[J]. 航空学报, 2014, 35(3): 674-686.
[10] Mavriplis D J. Formulation and multigrid solution of the discrete adjoint for optimization problems on unstructured meshes, AIAA-2005-0319. Reston: AIAA, 2005.
[11] Mavriplis D J. A discrete adjoint-based approach for optimization problems on three-dimensional unstructured meshes, AIAA-2006-0050. Reston: AIAA, 2006.
[12] Nielsen E J, Anderson W K. Implementation of a parallel framework for aerodynamic design optimization on unstructured meshes[M]//Keyes D, Periaux J, Ecer A, et al. Paraller Computational Fluid Dynamics 1999. Williamsburg: Elsevier, 1999: 313-320.
[13] Qin N, Wong W S, Moigne A L. Adjoint-based optimisation of a Blended Wing Body aircraft with shock control bumps, AIAA-2007-0057. Reston: AIAA, 2007.
[14] Xiong J T, Qiao Z D, Yang X D, et al. Optimum aerodynamic design of transonic wing based on viscous adjoint method[J]. Acta Aeronautica et Astronautica Sinica, 2007, 28(2): 281-285. (in Chinese) 熊俊涛, 乔志德, 杨旭东, 等. 基于黏性伴随方法的跨声速机翼气动优化设计[J]. 航空学报, 2007, 28(2): 281-285.
[15] Sharov D, Nakahashi K. Reordering of 3D hybrid unstrucrured grids for vectorized LU-SGS Navier-Stokes computations, AIAA-1998-0614. Reston: AIAA, 1998.
[16] Venkatakrishnan V. On the accuracy of limiters and convergence to steady state solutions, AIAA-1993-0880. Reston: AIAA, 1993.
[17] VanLeer B. Flux vector splitting for the Euler equations[J]. Lecture Notes in Physics, 1982, 170: 507-512.
[18] Spalart P R, Allmaras S R. A one-equation turbulence model for aerodynamic flows, AIAA-1992-0439. Reston: AIAA, 1992.
[19] James L, Nishikawa H. A critical study of agglomerated multigrid methods for diffusion on highly stretched grids[J]. Comput Fluids, 2011, 41(1): 82-93.
[20] Daniel G, Sreenivas K. Parallel FAS multigrid for arbitrary Mach number, high Reynolds number unstructured flow solver, AIAA-2006-2821. Reston: AIAA, 2006.
[21] Zhang L P, Zhao Z, Chang X H, et al. A 3D hybrid grid generation technique and a multigrid/parallel algorithm based on anisotropic agglomeration approach[J]. Chinese Journal of Aeronautics, 2013, 26(1): 47-62.
[22] Mavriplis D J, Pirzadeh S. Large-scale parallel unstructred mesh computations for 3D high-lift analysis, AIAA-1999-0537. Reston: AIAA, 1999.
[23] Li Q, Guo Z D, Deng Y J, et al. CFD high performance computing in aeronautics[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2011, 39(SupⅠ): 79-82. (in Chinese) 李权, 郭兆电, 邓一菊, 等. 航空CFD高性能计算应用研究[J]. 华中科技大学学报(自然科学版), 2011, 39(SupⅠ): 79-82.
[24] Karypis G, Kumar V. A fast and high quality multilevel scheme for partitioning irregular graphs[J]. SIAM Journal of Scientific Computing, 1998, 20(1): 359-392.
[25] Amoiralis E I, Nikolos I K. Freeform deformation versus B-spline representation in inverse airfoil design[J]. Journal of Computing and Information Science in Engineering, 2008, 8(2): 13.
[26] Lamousin H J, Waggenspack W N. NURBS-based free-form deformations[J]. Computer Graphics and Applications, 1994, 14(6): 59-65.
/
| 〈 |
|
〉 |
CJA