基于预处理GMRES算法的油藏数值模拟研究
Research on Numerical Reservoir Simulation Based on Preprocessing GMRES Algorithm
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- 引用格式:
-
刘,刚,李治平,冯,彬,王,宇.基于预处理GMRES算法的油藏数值模拟研究[J].天然气与石油,2011,29(5):0.doi:
.Research on Numerical Reservoir Simulation Based on Preprocessing GMRES Algorithm[J].Natural Gas and Oil,2011,29(5):0.doi:
- DOI:
- 作者:
- 刘 刚 李治平 冯 彬 王 宇
- 作者单位:
- 中国地质大学（北京）
- 关键词:
- 油藏数值模拟；大型线性方程组；GMRES算法；矩阵预处理
Numerical reservoir simulation；Large?鄄scale linear equations；GMRES algorithm；
- 摘要:
- 随着油藏数值模拟技术的不断发展，研究的油藏类型越来越复杂，相应的大型线性方程组的求解难度也不断增大。从油藏数值模拟中大型线性方程组的求解入手，引入了广义极小残差算法（GMRES），通过对算法迭代原理的讨论，采用不完全LU分解方法对方程组矩阵进行预处理，使病态矩阵得以改善。由实际油井数值模拟表明，相对于传统的Gauss-Seidel迭代方法，广义极小残差算法在运算速度上表现出极大的优越性，而矩阵预处理则使运算速度至少提高了1倍。
：With continuous development of numerical reservoir simulation，the researched reservoir types are more and more complex，accordingly，solving large?鄄scale linear equations is much more difficult. Based on solving large?鄄scale linear equations in numerical reservoir simulation，introduced is the generalized minimal residual algorithm（GMRES）. Discussed is the iterative principle of GMRES，conducted is matrix preconditioning of the equations by using incomplete LU resolution method，thereby，ill?鄄conditioned matrix can be improved. Practical reservoir simulation results show that the generalized minimal residual algorithm has demonstrated much more significant superior in arithmetic speed than the traditional method of Gauss?鄄Seidel iteration and the arithmetic speed can be doubled by the matrix preconditioning.
