并行的多重网格方法在离散伴随优化中的应用

doi:10.7527/S1000-6893.2013.0518

Abstract

Abstract:

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.

Key words: unstructured grid, shape optimization, discrete adjoint, multigrid, parallel computing

CLC Number:

V211.3

LI Bin, TANG Jing, DENG Youqi, ZHANG Yaobing. Application of Parallel Multigrid Algorithm to Discrete Adjoint Optimization[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(8): 2091-2101.

References

[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.

Application of Parallel Multigrid Algorithm to Discrete Adjoint Optimization

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