求解三维裂缝型多孔介质流体的场分裂预条件子研究  

Field-Split Preconditioners for Solving Three-dimensional Reservoir Flows in Fractured Porous Media

作　　者：杨念 杨海建[1,2] 邵柏强 Yang Nian;Yang Hajian;Shao Baiqiang(Chongqing Research Institute,Hunan University,Chongqing 401120,China;School of Mathematics,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学重庆研究院,重庆401120 [2]湖南大学数学学院,长沙410082

出　　处：《数学理论与应用》2023年第4期123-137,共15页Mathematical Theory and Applications

基　　金：重庆市自然科学基金项目(No.cstc2021jcyj-msxmX0227)资助。

摘　　要：随着Newton-Krylov方法在求解大型稀疏非线性方程组中的逐步应用,线性预条件子的设计对整个求解器起着至关重要的作用.本文研究基于物理和区域分解方法的不同组合的场分裂(Field-Split,FS)预条件子,并应用于裂缝型多孔介质的非定常流动问题.在区域分解的框架下,考虑几种新的FS预条件子:加性FS预条件子、乘性FS预条件子、舒尔补FS预条件子和约束压力残差(Constrained Pressure Residual,CPR)预条件子,对相应的子系统采用限制加性Schwarz算法(Restricted additive Schwarz algorithm,RAS)进行近似求解.为了进一步提高场分裂预条件子的数值性能,提出并构建两水平的场分裂预条件子.最后在天河二号超算平台上进行数值实验,结果显示所提出的预条件子具有良好的鲁棒性和并行可扩展性.With the applications of Newton-Krylov method in solving large sparse nonlinear equations,the design of linear preconditioners plays a vital role in the whole solver.In this paper,we study the application of different combinations of field-split(FS)preconditioners based on physical and domain decomposition methods to the unsteady flow problem of fractured porous media.Under the framework of domain decomposition technology,several new FS preconditioners are considered:the additive FS preconditioner,the multiplicative FS preconditioner,the Schur-complement FS preconditioner and the constrained pressure residual(CPR)preconditioner.The corresponding subsystems are approximately solved by the restricted additive Schwarz(RAS)algorithm.In order to further improve the performance of the FS preconditioner,we designe a two-level FS preconditioner.Numerical experiments on Tianhe-2 supercomputer show that the proposed preconditioner has a good robustness and parallel scalability.

关 键 词：油藏模拟 限制加性Schwarz算法 场分裂预条件子 并行计算 

分 类 号：O241.82[理学—计算数学]