Alternating lower-upper splitting iterative method and its application in CFD
-
摘要: 在CFD(Computational Fluid Dynamics)时间相关算法中,为了保证计算的稳定性,时间步长的取值通常会很小,这将导致计算过程收敛缓慢.针对这一问题,提出了一种新的迭代算法—交替LU分裂(ALUS,Alternating Lower-Upper Splitting)算法,可以有效加速收敛,提高计算效率.ALUS算法将系数矩阵分裂成上、下三角矩阵,因此仅需要利用追赶法求解两个三角矩阵,计算量较小,容易实现.给出了ALUS算法收敛的定理,并且通过线性问题以及CFD圆柱绕流的数值模拟对ALUS算法进行了检验.理论分析和数值实验的结果均表明:ALUS算法计算量小,大大节省了计算时间,而且该算法是鲁棒的.因此ALUS算法是高效的、稳定的算法,适用于CFD数值模拟.Abstract: Small time step is used to ensure convergence in the time-dependent method in computational fluid dynamics(CFD). An improved iteration method termed as the alternating lower-upper splitting (ALUS) iterative method was proposed to address the problem, in which the coefficient matrix was split into a lower and an upper triangular matrix. In each inner step, only two triangular matrices were solved by Thom asalgorithm, therefore the ALUS method is simple. Theorems were listed to ensure the ALUS method convergence.A linear equation problem and flow around the cylinder were used to illustrate the characteristic of the ALUS method.Theoretical analysis and numerical results both demonstrate the new method performs well for positive definite matrices. Withless amount of computational work, the CPU time can be greatlydiminished. Thus the new ALUS method is efficient and robust and it is applicable in CFD numerical simulation.
-
Key words:
- numerical simulation /
- large scale linear systems /
- positive definite matrix /
- robustness
-
[1] 李良.大型线性方程组求解技术及在计算电磁学中的应用研究.成都:电子科技大学数学科学学院,2009
Li Liang.Study of solutions to large linear systems with applications in computational electromagnetic.Chengdu:School of Mathematical,University of Electronic Science and Technology,Jr of China,2009(in Chinese)[2] Peaceman D W,Rachford H H,Jr.The numerical solution of parabolic and elliptic differential equations[J].J Soc Indust and Appl Math,1955,3(1): 28-41 [3] Bai Z Z,Golub G H,Nq M K.Hermitian andskew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J].J Matrix Anal and Appl,2003,24(3): 603-626 [4] Bai Z Z,Golub G H,Lu L Z,et al.Block triangular and skew-Hermitian splitting methods forpositive-definite linear systems [J].J Sci Comput,2006,26(3): 844-863 [5] 蒋尔雄.矩阵计算[M].北京:科学出版社,2008:104-120 Jiang Erxiong.Matrix computations[M].Beijing: Science Press,2008: 104-120(in Chinesec) [6] Jiang Erxiong.Algorithm for solving a shifted skew-symmetric linear system [J].Front Math China,2007,2(2): 227-242 [7] Benzi M,Guo X P.A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations[J].Applied Numerical Mathematics,2011,61(1): 66-76 [8] Bai Z Z,Benzi M,Chen F.On preconditioned MHSS iteration methods forcomplex symmetric linear systems [J].Numer Algorithms,2011,56(2): 297-317 -
点击查看大图
计量
- 文章访问数: 2900
- HTML全文浏览量: 260
- PDF下载量: 514
- 被引次数: 0
下载:
