一种高效的隐式间断Galerkin方法研究
A high efficient implicit discontinuous Galerkin method
-
摘要: 基于线性化处理，在时间方向上对间断Galerkin方程进行了隐式离散，从整体上对迭代过程进行了合理的优化，并以此求解了计算流体力学中的二维Euler方程。其中，LUSGS方法得到了进一步的推广，被用来高效求解隐式格式对应的大型稀疏线性系统。数值实验表明，无论对于亚声速问题还是跨声速问题，该格式都是无条件稳定的；与显式的RungeKutta间断Galerkin格式相比，当残值下降到相同量级时，隐式格式所需的迭代步数和CPU时间均在很大程度上得到了减少。
-
关键词:
- 间断Galerkin /
- 隐式格式 /
- 优化 /
- 无条件稳定 /
- CPU时间
Abstract: In the introduction of the full paper, we point that, in our opinion, Cuckborn and Shu's Runge-Kutta discontinuous Galerkin method is good in calculation precision, but its slow convergence puts severe limits on its application to engineering problems. Therefore, we propose our efficient implicit scheme for accelerating convergence. In the iterative process, some important amendments are in application, which improve the efficiency significantly. At the same time, LU-SGS method is used to solve the large sparse linear system. By this means, subsonic and transonic flow over the airfoil is computed. It is found that this implicit scheme keeps unconditional stable for the subsonic and transonic flow. These results show preliminarily that, compared with the explicit scheme, our novel solver delivers a convergence rate that is approximately one order higher and much of the CPU time is saved.-
Keywords:
- discontinuous Galerkin /
- implicit scheme /
- improve /
- unconditional stable /
- CPU time
-
-
[1] COCKBURN B, SHU C W. TVD Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: General Framework[J].Math.Comp,1989, (52):411-435. [2] PATRICK RASETARINERA, HUSSAINI M Y. An efficient implicit discontinuous spectral Galerkin method[J]. Journal of Computational Physics, 2001(172): 718-738. [3] 王烈衡, 许学军. 有限元方法的数学基础[M]. 北京: 科学出版社, 2004. [4] ROE P L. Approximate Riemann solver,parameter vectors and different schemes [J]. Journal of Computational Physics, 1981, 43: 357-372. [5] 奥特加 J M, 莱因博尔特 W C. 多元非线性方程组迭代解法[M]. 北京: 科学出版社, 1983. [6] JAMESON A, TURKEL E. Implicit scheme and LUdecompositions[J]. Math. Comput.,1981, 37:385-397.
计量
- 文章访问数: 1210
- HTML全文浏览量: 7
- PDF下载量: 1135
下载:
