Application-oriented Preconditioning of Seepage Mechanics

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

Abstract

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

CLC Number:

O246

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.

Figures/Tables 7

References 37

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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