面向渗流力学应用特征的预条件方法

doi:10.19596/j.cnki.1001-246x.8791

摘要/Abstract

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。

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

Abstract:

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.

Key words: seepage mechanics, Darcy equation, poroelasticity equation, incomplete LU decomposition, algebraic multigrid method

中图分类号:

O246

冯春生, 李仕哲, 刘生豪, 张晨松, 赵梨. 面向渗流力学应用特征的预条件方法[J]. 计算物理, 2024, 41(1): 98-109.

Chunsheng FENG, Shizhe LI, Shenghao LIU, Chensong ZHANG, Li ZHAO. Application-oriented Preconditioning of Seepage Mechanics[J]. Chinese Journal of Computational Physics, 2024, 41(1): 98-109.

图/表 7

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解法器	CPR-FGMRES(30)
线程数	1	2	4	8	16
时间步数	53	53	53	53	53
牛顿迭代次数	214	214	214	214	214
线性迭代次数	5 322	5 322	5 322	5 322	5 322
解法器时间/s	5 738.62	3 125.07	1 795.88	1 140.44	935.73
并行加速比	1.00	1.84	3.20	5.03	6.13

解法器	CPR-FGMRES(30)
线程数	1	2	4	8	16
时间步数	53	53	53	53	53
牛顿迭代次数	214	214	214	214	214
线性迭代次数	5 322	5 322	5 322	5 322	5 322
解法器时间/s	5 738.62	3 125.07	1 795.88	1 140.44	935.73
并行加速比	1.00	1.84	3.20	5.03	6.13

解法器	CPR-FGMRES(30)
线程数	1	2	4	8	16
时间步数	267	267	267	267	267
牛顿迭代次数	1 083	1 083	1 083	1 083	1 083
线性迭代次数	16 389	16 393	16 390	16 389	16 388
解法器时间/s	5 605.10	3 067.03	1 801.19	1 177.64	915.39
并行加速比	1.00	1.83	3.11	4.76	6.12

解法器	CPR-FGMRES(30)
线程数	1	2	4	8	16
时间步数	267	267	267	267	267
牛顿迭代次数	1 083	1 083	1 083	1 083	1 083
线性迭代次数	16 389	16 393	16 390	16 389	16 388
解法器时间/s	5 605.10	3 067.03	1 801.19	1 177.64	915.39
并行加速比	1.00	1.83	3.11	4.76	6.12

解法器	CPR-FGMRES(30)
线程数	1	2	4	8	16
时间步数	147	147	147	147	147
牛顿迭代次数	362	362	362	362	362
线性迭代次数	3 741	3 737	3 735	3 736	3 741
解法器时间/s	2 685.36	1519.28	931.29	637.65	512.10
并行加速比	1.00	1.77	2.88	4.21	5.24