一种适用于三维混合网格的GMRES加速收敛新方法

doi:10.7527/S1000-6893.2016.0038

Abstract

Abstract:

To improve the convergence efficiency of solving the flow field, a parallel implicit time integration method generalized minimal residual (GMRES) is applied to a three-dimentional hybrid grid Navier-Stokes solver. The method is implemented based on a Krylov subspace solver in the scientific computation toolkit portable, extensible toolkit for scientific computation (PETSc). The coefficient matrix of linear system is provided explicitly to stabilize the scheme. In order to accelerate the convergence more specifically, the cell indexes of unstructured grid are reordered such that the system matrix's nonzero elements are clustered close to the main diagonal. The method is applied to simulations of ONERA-M6 wing and AIAA Drag Prediction Workshop model CRM. The results show great agreement with experimental data. Comparisons are made between different implicit schemes. The GMRES method developed in this paper shows more robustness and the residual's convergence has a significant speedup compared with LU-SGS method. Moreover, the method has a faster speed approximating to the steady state of aerodynamic coefficient. It greatly improves the computational efficiency.

Key words: hybrid grid, convergence efficiency, implicit time integration method, GMRES, PETSc, grid reorder

CLC Number:

V211.3
O355

ZHANG Jian, DENG Youqi, LI Bin, ZHANG Yaobing. A new method to accelerate GMRES's convergence applying to three-dimensional hybrid grid[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(11): 3226-3235.

References

[1] JAMESON A, SCHMIDT W, TURKEK E. Numerical solutions of the euler equations by finite volume methods using Runge-Kutta time-stepping schemes:AIAA-1981-1259[R]. Reston:AIAA, 1981.
[2] YOON S, JAMESON A. Lower-upper symmetric gauss-seidel method for the euler and naiver-stokes equations[J]. AIAA Journal, 1988, 26(9):1025-1026.
[3] JAMESON A. Multigrid algorithms for compressible flow calculations, multigrid method II[M]. Berlin:Springer Verlag, 2006:166-201.
[4] SAAD Y, SCHULZ M H. GMRES:A generalized minimum residual algorithm for solving nonsymmetric linear systems[J]. SIAM Journal on Scientific and Statistcal Computing, 1986, 7:856-869.
[5] WIGTON L B, YOUNG D P, YU N J. GMRES acceleration of computational fluid dynamics codes:AIAA-1985-1494[R]. Reston:AIAA, 1985.
[6] KNOLL D A, MCHUGH P R. Inexact Newton's method solutions to the incompressible Navier-Stokes and energy equations using standard and matrix-free implementations:AIAA-1993-3332[R]. Reston:AIAA, 1993.
[7] XIA Y D, LUO H, NOURGALIEV R. An implicit hermite WENO resconstruction-based discontinuous Galerkin method on tetrahedral grids[J]. Computers & Fluids, 2014, 96(5):406-421.
[8] 燕振国, 刘化勇, 毛枚良, 等. 基于高阶耗散紧致格式的GMRES方法收敛特性研究[J]. 航空学报, 2014, 35(5):1181-1192. YAN Z G, LIU H Y, MAO M L, et al. Convergence property investigation of GMRES method based on high-order dissipative compact scheme[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(5):1181-1192(in Chinese).
[9] BALAY S, ABHYANKAR S, ADAMS M, et al. PETSc users manual[EB/OL]. (2014-06-30)[2015-07-01]. http://www.mcs.anl.gov/petsc/documentation/index.html.
[10] ANDERSON W K, GROPP W D, KAUSHIK D K, et al. Achieving high sustained performance in an unstructured mesh CFD application[C]//Proceedings of the 1999 ACM/IEEE Conference of Supercomputing. New York:IEEE, 1999.
[11] 钟英, 张理论, 刘巍. PETSc及典型开源流体力学应用[J]. 计算机应用, 2013, 33(S2):63-66. ZHONG Y, ZHANG L L, LIU W. PETSc and its typical open-source computational fluid dynamics application[J]. Journal of Computer Applications, 2013, 33(S2):63-66(in Chinese).
[12] 屈崑, 李记超, 蔡晋生. CFD数学模型的线性化方法及其应用[J]. 航空学报, 2015, 36(10):3218-3227. QU K, LI J C, CAI J S. Method of linearizing computational fluid dynamics model and its applications[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(10):3218-3227(in Chinese).
[13] 张耀冰, 邓有奇, 吴晓军, 等. DLR-F6翼身组合体数值计算[J]. 空气动力学学报, 2011, 29(2):163-169. ZHANG Y B, DENG Y Q, WU X J, et al. Drag prediction of DLR-F6 using MFlow unstructured mesh solver[J]. Acta Aerodynamica Sinica, 2011, 29(2):163-169(in Chinese).
[14] XIA Y D, LUO H, FRISBEY M, et al. A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids[J]. Computers & Fluids, 2014, 98:134-151.
[15] BLAZEK J. Computational fluid dynamics principles and applications[M]. Oxford:Elsevier Science Ltd., 2001:419-420.
[16] 李劲杰, 王刚, 史爱明, 等. 基于非结构网格流场计算的网格重排序[J]. 航空计算技术, 2005, 35(3):25-28. LI J J, WANG G, SHI A M,et al. Reordering of 3D unstructured grids for computing efficiency improvement[J]. Aeronautical Computer Technique, 2005, 35(3):25-28(in Chinese).
[17] LUO H, BAUM J D, LOHNER R. An improved finite volume scheme for compressible flows on unstructured grids:AIAA-1995-0348[R]. Reston:AIAA, 1995.
[18] SPALART P R, ALLMARAS S R. A one equation turbulence model for aerodynamic flows:AIAA-1992-0439[R]. Reston:AIAA, 1992.
[19] SCHMITT V, CHARPIN F. Pressure distributions on the ONERA-M6 wing at transonic mach numbers, experimental data base for computer program assessment:AGARD AR-138-B1[R].[S.l.]:AGARD, 1979.
[20] 康忠良, 阎超. 适用于混合网格的并行GMRES+LUSGS方法[J]. 空气动力学学报, 2013, 31(2):225-230. KANG Z L, YAN C. Parallel GMRES+LU-SGS method for mixed grids[J]. Acta Aerodynamica Sinica, 2013, 31(2):225-230(in Chinese).
[21] VASSBERG J C, DEHAAN M A, RIVERS S M, et al. Development of a common research model for applied CFD validation studies:AIAA-2008-6919[R]. Reston:AIAA, 2008.
[22] MELISSA B R, ASHLEY D. Experimental Investigation of the NASA common research model in the NASA langley national transonic facility and NASA Ames 11-ft transonic wind tunnel:AIAA-2011-1126[R]. Reston:AIAA, 2011.
[23] LEVY D W, LAFLIN K R, TINOCO E N, et al. Summary of data from fifth AIAA CFD drag prediction workshop:AIAA-2013-0046[R]. Reston:AIAA, 2013.
[24] GONG X, CHEN J, ZHOU N, et al. The effects of turbulence model corrections on drag prediction of NASA common research model:AIAA-2014-3171[R]. Reston:AIAA, 2014.
[25] VASSBERG J, TINOCO E, MANI M, et al. Summary of date from fourth AIAA CFD drag prediction workshop:AIAA-2010-4547[R]. Reston:AIAA, 2010.

A new method to accelerate GMRES's convergence applying to three-dimensional hybrid grid

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	ZHANG Peihong, ZHANG Yaobing, ZHOU Guiyu, CHEN Jiangtao, DENG Youqi. Entropy correction method for high accuracy drag prediction with mixed grids [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(9): 122019-122030.
[2]	ZHANG Peihong, ZHANG Yaobing, ZHOU Guiyu, CHEN Jiangtao, DENG Youqi. Gradient calculation method of unstructured mixed grids for improving drag prediction accuracy [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(1): 121415-121415.
[3]	SUN Junlei, WANG Heping, ZHOU Zhou, LEI Shan. Effects of propeller slipstream on aerodynamic performance of diamond joined-wing configuration UAV [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(1): 121431-121431.
[4]	GONG Yiming, LIU Zhanhe, LIU Yilang, ZHANG Weiwei. Efficient GMRES algorithm in time spectral method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(7): 120894-120894.
[5]	WANG Kelei, ZHU Xiaoping, ZHOU Zhou, WANG Hongbo. Distributed electric propulsion slipstream aerodynamic effects at low Reynolds number [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(9): 2669-2678.
[6]	ZHANG Yang, ZHANG Laiping, HE Xin, DENG Xiaogang. Detached eddy simulation based on adaptive hybrid grids [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(12): 3605-3614.
[7]	ZHANG Yang, ZHANG Laiping, HE Xin, DENG Xiaogang. Detached-eddy simulation based on unstructured and hybrid grid [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(9): 2900-2910.
[8]	YAN Zhenguo, LIU Huayong, MAO Meiliang, DENG Xiaogang, ZHU Huajun. Convergence Property Investigation of GMRES Method Based on High-order Dissipative Compact Scheme [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(5): 1181-1192.
[9]	LU Tianyu, WU Xiaosheng. Numerical Calculation Effects of Deforming Leading Edge on Airfoil Dynamic Stall Control [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(4): 986-994.
[10]	Lu Hongqiang;Wu Yizhao;Zhou Chunhua;Tian Shuling. High Resolution of Subsonic Flows on Coarse Grids [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2009, 30(2): 200-204.
[11]	Liu Zhou;Zhou Weijiang. Adaptive Viscous Cartesian Grid Generation and Application [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2009, 30(12): 2280-2287.
[12]	CHEN De-hua;WU Wen-hua;WANG Jin-jun. Numerical Simulation Research of the Fighter Ejection Escape System [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2006, 27(5): 778-783.
[13]	LIU Xue-qiang;WU Yi-zhao. The Computation of the Lateral Jet Turbulence Flow Using DES Method [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2004, 25(3): 209-213.
[14]	WANG Ping;ZHU Zi-qiang;TUO Shuang-fen;YIN Xing-yu. 2D HYBRID STRUCTURED-UNSTRUCTURED GRID GENERATION AND FLOW SIMULATION [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2001, 22(6): 536-538.
[15]	Wang Renpeng;Zhang Xiaosong;Ye Tianqi. A NEW METHOD FOR PARALLEL BOUNDARY ELEMENT COMPUTATION [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1997, 18(2): 139-145.