基于Newton/Gauss-Seidel迭代的DGM隐式方法

刘伟; 张来平; 赫新; 贺立新; 张涵信

doi:10.6052/0459-1879-11-352

基于Newton/Gauss-Seidel迭代的DGM隐式方法

doi: 10.6052/0459-1879-11-352

1.
中国空气动力研究与发展中心空气动力学国家重点实验室, 绵阳 621000
2. 中国空气动力研究与发展中心计算空气动力学研究所, 绵阳 621000

基金项目: 国家重点基础研究发展计划(2009CB723802);国家自然科学基金(11028205,91016011,91130029)和空气动力学国家重点实验室基金(JBKY11010913)资助项目.

详细信息

中图分类号: V211.3
计量
- 文章访问数: 2519
- HTML全文浏览量: 53
- PDF下载量: 1503
- 被引次数: 0
出版历程
- 收稿日期: 2011-11-30
- 修回日期: 2012-02-10
- 刊出日期: 2012-07-18

AN IMPLICIT ALGORITHM FOR DISCONTINUOUS GALERKIN METHOD BASED ON NEWTON/GAUSS-SEIDEL ITERATIONS

1.
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
2. Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China

Funds: The project was supported by the National Basic Research Program of China (2009CB723802); the National Natural Science Foundation of China (11028205, 91016011, 91130029) and Science Foundation of SKLA(JBKY11010913).

摘要

摘要: 在Newton迭代方法的基础上,对高阶精度间断Galerkin有限元方法(DGM)的时间隐式格式进行了研究. Newton迭代法的优势在于收敛效率高效,并且定常和非定常问题能够统一处理,对于非定常问题无需引入双时间步策略. 为了避免大型矩阵的求逆,采用一步Gauss-Seidel迭代和Matrix-free技术消去残值Jacobi矩阵的上、下三角矩阵,从而只需计算和存储对角(块)矩阵. 对角(块)矩阵采用数值方法计算. 空间离散采用Taylor基,其优势在于对于任意形状的网格,基函数的形式是一致的,有利于在混合网格上推广. 利用该方法,数值模拟了Bump绕流和NACA0012翼型绕流. 计算结果表明,与显式的Runge-Kutta时间格式相比,隐式格式所需的迭代步数和CPU时间均在很大程度上得到减少,计算效率能够提高1～ 2个量级.
- 间断Galerkin有限元 /
- Taylor基函数 /
- Newton迭代 /
- Gauss-Seidel迭代 /
- 时间隐式方法
Abstract: An efficient implicit algorithm was developed for high-order discontinuous Galerkin (DGM) based on Newton/Gauss-Seidel iteration approach. The second-order to the forth order DGMs based on Taylor basis functions were employed to carry out the spatial discretization. Newton iteration scheme was used to solve the nonlinear system, and the linear system was solved with one-step Gauss-Seidel iteration. In addition, the effects of several parameters in the implicit scheme, such as the CFL number, the Newton sub-iteration steps, and the update frequency of mass-matrix, have been investigated for two-dimensional Euler equations. Two typical cases, including subsonic flows over a bump and a NACA0012 airfoil, were simulated, and compared with the traditional explicit Runge-Kutta scheme. The numerical results demonstrate that the present implicit scheme can accelerate the convergence history evidently.
- implicit algorithm /
- discontinuous Galerkin method /
- taylor basis /
- Newton iteration /
- Gauss-Seidel iteration

HTML全文

参考文献(8)

Reed WH, Hill TR. Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Lab., 1973

Cockburn B, Shu CW. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math Comp, 1989, 52: 411-435

Wang L, Mavriplis DJ. Implicit solution of the unsteady Euler equation for high-order accurate discontinuous Galerkin discretizations. J Comput Phys, 2007, 225: 1994-2005

Saad Y, Schultz MH. GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems. SIAM J Sci Stat Comput, 1986, 7: 865-884

Rasetarinera P, Hussaini MY. An efficient implicit discontinuous Galerkin method. J Comput Phys, 2001, 172: 718-738

Sharov D, Nakahashi K. Low speed preconditioning and LUSGS scheme for 3D viscous flow computations on unstructured grids. AIAA 98-0614, 1998

Hong L, Baum JD, Lohner R. A discountinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids. J Comput Phys, 2008, 227: 8875-8893

http://www.public.iastate.edu/～ zjw/hiocfd.html

施引文献

资源附件(0)

访问统计