面向渗流力学应用特征的预条件方法  

Application-oriented Preconditioning of Seepage Mechanics

作　　者：冯春生[1,2] 李仕哲 刘生豪 张晨松 赵梨 FENG Chunsheng;LI Shizhe;LIU Shenghao;ZHANG Chensong;ZHAO Li(School of Mathematics and Computational Science,Xiangtan University,Xiangtan,Hunan 411105,China;National Center for Applied Mathematics in Hunan,Hunan Shaofeng Institute for Applied Mathematics,Xiangtan,Hunan 411105,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭量411105 [2]湖南国家应用数学中心,湖南韶峰应用数学研究院,湖南湘潭量411105 [3]中国科学院数学与系统科学研究院,北京100190

出　　处：《计算物理》2024年第1期98-109,共12页Chinese Journal of Computational Physics

基　　金：科技部国家重点研发计划(2020YFA0711904);国家自然科学基金(11971472);光合基金A类项目(202302011094)资助。

摘　　要：渗流力学模型由多个偏微分方程非线性耦合而成。在不同的应用问题中,渗流力学问题的特性并不完全相同,相应的求解方法也不相同。本文以油气藏开发中的典型数学模型为例,介绍多孔介质中的多相多组分渗流力学方程的数学形式、应用特征以及其离散线性方程组的高效求解方法,特别是一些常用的预条件方法。此外,对标准算例进行适当的修改,对部分预条件方法的共享内存并行效率进行了测试。The seepage mechanics model comprises multiple nonlinearly coupled partial differential equations.In various applications,seepage mechanics problems exhibit distinct characteristics and the corresponding solution methods are also very different.This paper focuses on the representative mathematical models used in oil and gas reservoir development.It introduces the mathematical formulation and application characteristics of multiphase multicomponent seepage mechanics equations within porous media,along with efficient techniques for solving their discretized linear equation systems,including commonly employed preconditioning methods.Additionally,this study appropriately modifies standard test cases and evaluates the shared-memory parallel efficiency of these preconditioning methods.

关 键 词：渗流力学 达西方程 多孔弹性方程 不完全LU分解 代数多重网格法 

分 类 号：O246[理学—计算数学]