TY - JOUR
T1 - 隐式超松弛LU-SGS间断Galerkin算法
AU - Duan, Zhi Jian
AU - Xie, Gong Nan
AU - Zhang, Ying Chun
N1 - Publisher Copyright:
© 2019, Editorial Department of Journal of Beijing University of Posts and Telecommunications. All right reserved.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - 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.
AB - 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.
KW - Discontinuous Galerkin finite element method
KW - Euler equation
KW - Implicit time discrete algorithm
KW - Lower upper-symmetric Gauss-Seidel scheme
UR - http://www.scopus.com/inward/record.url?scp=85086180777&partnerID=8YFLogxK
U2 - 10.13190/j.jbupt.2019-023
DO - 10.13190/j.jbupt.2019-023
M3 - 文章
AN - SCOPUS:85086180777
SN - 1007-5321
VL - 42
SP - 8
EP - 14
JO - Beijing Youdian Daxue Xuebao/Journal of Beijing University of Posts and Telecommunications
JF - Beijing Youdian Daxue Xuebao/Journal of Beijing University of Posts and Telecommunications
IS - 5
ER -