Implicit Overrelaxation LU-SGS Discontinuous Galerkin Finite Element Algorithm

doi:10.13190/j.jbupt.2019-023

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2019, Vol. 42 ›› Issue (5): 8-14.doi: 10.13190/j.jbupt.2019-023

Previous Articles Next Articles

Implicit Overrelaxation LU-SGS Discontinuous Galerkin Finite Element Algorithm

DUAN Zhi-jian^1,2, XIE Gong-nan³, ZHANG Ying-chun¹

1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China;
2. School of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, China;
3. School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China

Received:2019-03-01 Online:2019-10-28 Published:2019-11-25

Abstract

Abstract: In order to improve the computational efficiency of solving Euler equation and Navier-Stokes equation, the discontinuous Galerkin finite element method was investigated by combining with the implicit time discrete scheme. The lower upper-symmetric Gauss-Seidel(LU-SGS) scheme was improved through retaining the round-off error item, and an overrelaxation interior iteration LU-SGS discrete scheme was constructed to realize the calculation of unsteady compressible flow fields. The reliability and accuracy of the algorithm were verified by solving the Sod shock tube problem and the two-dimensional pipeline problem. The transonic compressible flows around RAE2822 airfoil and ONERA M6 wing were numerically calculated, and the results were compared with that of the multistep Runge-Kutta(RK) algorithm, LU-SGS algorithm and generalized minimal residual algorithms(GMRES). The results show that the presented algorithm has good stability and efficiency, and its computational efficiency is 2.35~3.1 times that of LU-SGS scheme and 5.4 times that of RK scheme.

Key words: implicit time discrete algorithm, Euler equation, lower upper-symmetric Gauss-Seidel scheme, discontinuous Galerkin finite element method

CLC Number:

TP399

DUAN Zhi-jian, XIE Gong-nan, ZHANG Ying-chun. Implicit Overrelaxation LU-SGS Discontinuous Galerkin Finite Element Algorithm[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2019, 42(5): 8-14.

References

[1] Reed W H, Hill T R. Triangular Mesh methods for the neutron transport equation:LA-UR-73-479[R]. Ann Arbor:Los Alamos Scientific Laboratory Report, 1973.
[2] Cockburn B, Shu C W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II:general frame work[J]. Mathematics of Computation, 1989, 52(186):411-435.
[3] Cockburn B, Shu C W. The Runge-Kutta discontinuous Galerkin method for conservation laws V:multidimensional systems[J]. Journal of Computational Physics, 1998, 141(2):199-224.
[4] Rhebergen S, Wells G N. A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field[J]. Journal of Scientific Computing, 2017, 76(3):1484-1501.
[5] 张来平, 李明, 刘伟等. 基于非结构/混合网格的高阶精度DG/FV混合方法研究进展[J]. 空气动力学学报, 2014, 32(6):717-726. Zhang Laiping, Li Ming, Liu Wei, et al. Recent development of high order DG/FV hybrid methods[J]. Acta Aerodynamica Sinica, 2014, 32(6):717-726.
[6] Filbet F, Tao X. A hybrid discontinuous Galerkin scheme for multi-scale kinetic equations[J]. Journal of Computational Physics, 2018(372):841-863.
[7] Luo H, Luo L, Nourgaliev R. A reconstructed discontinuous Galerkin method for the Euler equations on arbitrary grids[J]. Communications in Computational Physics, 2012, 12(5):1495-1519.
[8] Lou J, Li L, Luo H, et al. Reconstructed discontinuous Galerkin methods for linear advection-diffusion equations based on first-order hyperbolic system[J]. Journal of Computational Physics, 2018(369):103-124.
[9] 康忠良, 阎超. 适用于混合网格的并行GMRES+LU-SGS方法[J]. 空气动力学学报, 2013, 31(2):225-230. Kang Zhongliang, Yan Chao. Parallel GMRES+LU-SGS method for mixed grids[J]. Acta Aerodynamica Sinica, 2013, 31(2):225-230.
[10] 蒋跃文, 叶正寅, 王刚. 基于非结构网格的高效求解方法研究[J]. 计算力学学报, 2012, 29(2):217-223. Jiang Yuewen, Ye Zhengyin, Wang Gang. Efficient solution of Euler/N-S equations on unstructured grids[J]. Chinese Journal of Computational Mechanics, 2012, 29(2):217-223.
[11] 党亚斌, 刘凯礼, 孙一峰, 等. 用隐式高精度间断伽辽金方法模拟可压层流和湍流[J]. 空气动力学学报, 2018, 36(3):535-541. Dang Yabin, Liu Kaili, Sun Yifeng, et al. Implicit high order discontinuous Galerkin method for compressible laminar turbulent flow simulation[J]. Acta Aerodynamica Sinica, 2018, 36(3):535-541.
[12] Schmitt V, Charpin F. Pressure distributions on the ONERA-M6-wing at transonic Mach numbers[EB/OL]. (1979-05-01)[2019-01-12] http://cf13d.larc.nasa.gov/TestCases/ONERAM6Wing(steady)/exp.dat.
[13] Zhou Y, He F Z, Qiu Y M. Optimization of parallel iterated local search algorithms on graphics processing unit[J]. Journal of Supercomputing, 2016, 72(6):2394-2416.
[14] Zhou Y, He F Z, Qiu Y M. Accelerating image convolution filtering algorithms on integrated CPU-GPU architectures[J]. Journal of Electronic Imaging, 2018, 27(3):033002.
[15] Yan X H, He F Z, Chen Y L. A novel hardware/software partitioning method based on position disturbed particle swarm optimization with invasive weed optimization[J]. Journal of Computer Science and Technology, 2017, 32(2):340-355.
[16] Hou N, He F Z, Chen Y L, et al. An adaptive neighborhood taboo search on GPU for hardware/software co-design[C]//2016 IEEE 20^th International Conference on Computer Supported Cooperative Work in Design (CSCWD). Nanchang:[s.n.], 2016:239-244.

Implicit Overrelaxation LU-SGS Discontinuous Galerkin Finite Element Algorithm

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 9

Recommended Articles

Metrics

Comments

[1]	Lü Xin-chen, ZHANG Chen-yu. Edge Intelligence Multi-Source Data Processing for Autonomous Driving in Internet of Vehicles [J]. Journal of Beijing University of Posts and Telecommunications, 2021, 44(2): 102-108.
[2]	XU Tao, ZHANG Ji-shui, LU Min. A Probabilistic Model for Discovering Potential High-Value Passengers Based on Trip Purposes Mining [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2019, 42(1): 81-86.
[3]	PENG Hui-bo, ZHOU Ya-jian. Data Pricing Mechanism Status and Development Trends [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2019, 42(1): 120-125.
[4]	FENG Jun, LIU Fei-hong, LI Pan, BU Qi-rong, WANG Hong-yu. Multi-Object Segmentation for Abdominal CT Images Based on Gestalt Cognitive Framework [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2016, 39(5): 51-55.
[5]	ZHANG Wei-yu, WU Bin, LIU Yang. Integrating Multi-Feature for Link Sign Prediction in Signed Networks [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2014, 37(5): 80-84.
[6]	LI Jian, LIU Peng, LIU Wei. Recommendation Model for Fully Combining Review Features Based on Dual Attention [J]. Journal of Beijing University of Posts and Telecommunications, 2021, 44(4): 115-120.
[7]	SU An-yang. Bargaining Exploration in Electronic Business [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2003, 26(S1): 95-98.
[8]	YAN Yi-fei, WANG Zhi-li, QIU Xue-song, WANG Jia-lu. A Shuffle Partition Optimization Scheme Based on Data Skew Model in Spark [J]. Journal of Beijing University of Posts and Telecommunications, 2020, 43(2): 116-121.
[9]	WANG Xiao-yu, FENG Yang. An Algorithm for Differential Gene Analysis of Breast Cancer Based on PPI Network [J]. Journal of Beijing University of Posts and Telecommunications, 2020, 43(4): 76-82.