一种中心型有限体积孔隙–裂隙渗流求解方法及其OpenMP并行化

摘要
图/表
参考文献
相关文章 (0)

全文: PDF (658 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要为高效求解单相孔隙–裂隙渗流问题，发展一种基于任意网格的三维中心型有限体积渗流求解算法，并对其进行OpenMP并行化。该算法将压力置于单元中心处；使用串联弹簧模型在空间域离散；使用显式差分格式在时间域离散；使用动态松弛求解技术，逐个单元求解。算例研究表明：该算法与有限元相比具有类似的精度，但求解效率更高。OpenMP并行化使得该算法运算速度在CPU i7–3770上可提高至4.0倍，在CPU i7–4770上可提高至4.2倍；两台机器上的并行效率均高达50%以上。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章

关键词 ：三维中心型有限体积法；单相孔隙&ndash, 裂隙耦合渗流；动态松弛技术；OpenMP并行；离散裂隙网络

Abstract：An efficient three-dimensional cell-centered Finite Volume Method(ccFVM) is developed for single- phase fluid flow in fractured porous media. It works on arbitrary grids and is parallelized through OpenMP. With pressure centered in the cell，the ccFVM employs spring-in-series model for space discretization and explicit difference scheme for time discretization. It uses dynamic relaxation technique for element-by-element iteration. Numerical tests indicate that the ccFVM is as accurate as FEM，but more efficient. The parallel procedure obtains a speedup of 4.0 on CPU i7-3770 and a speedup of 4.2 on CPU i7-4770. High parallel efficiency of over 50% is achieved on both machines.

Key words： three-dimensional cell-centered finite volume method single-phase fluid flow in fractured porous media dynamic relaxation technique OpenMP-based parallelization discrete fracture network

引用本文:

王理想，李世海，马照松，冯春. 一种中心型有限体积孔隙–裂隙渗流求解方法及其OpenMP并行化[J]. 岩石力学与工程学报, 2015, 34(05): 865-875.
WANG Lixiang，LI Shihai，MA Zhaosong，FENG Chun. A CELL-CENTERED FINITE VOLUME METHOD FOR FLUID FLOW IN FRACTURED POROUS MEDIA AND ITS PARALLELIZATION THROUGH OPENMP. , 2015, 34(05): 865-875.

链接本文:

http://www.rockmech.org/CN/Y2015/V34/I05/865

[35]	Wikipedia. OpenMP[EB/OL]. http：//zh.wikipedia.org/wiki/OpenMP. 2014. " target="_blank">
[7]	GRANT M. Geothermal reservoir engineering[M]. Elsevier，2013. " target="_blank">
[3]	刘洋，李世海，刘晓宇. 基于连续介质离散元的双重介质渗流应力耦合模型[J]. 岩石力学与工程学报，2011，30(5)：951-959.(LIU Yang，LI Shihai，LIU Xiaoyu，Coupled fluid flow and stress computation model of dual media based on continuum-medium distinct element method[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(5)：951-959.(in Chinese))
[2]	CIPOLLA C L，LOLON E P，ERDLE J C，et al. Reservoir modeling in shale-gas reservoirs[J]. SPE Reservoir Evaluation & Engineering，2010，13(4)：638-653. " target="_blank">
[14]	张丽，刘晓宇，李世海. 裂隙岩体稳定/非稳定渗流数值模拟[J]. 岩石力学与工程学报，2009，28(增2)：3 409-3 416.(ZHANG Li，LIU Xiaoyu，LI Shihai. Numerical simulation of steady/unsteady flow in fractured rock masses[J]. Chinese Journal of Rock Mechanics and Engineering，2009，28(Supp.2)：3 409-3 416.(in Chinese)) " target="_blank">
[17]	张社荣，杨璐玲，钟登华. 裂隙岩体渗流场分析及其三维有限元程序设计[J]. 岩土力学，2005，26(1)：46-49.(ZHANG Sherong，YANG Luling，ZHONG Denghua. Analysis of the seepage field in fractured rocks and the design of 3-D finite element analyzing program[J]. Rock and Soil Mechanics，2005，26(1)：46-49.(in Chinese)) " target="_blank">
[21]	NICK H M，MATTHÄI S K. Comparison of three FE-FV numerical schemes for single- and two-phase flow simulation of fractured porous media[J]. Transport in Porous Media，2011，90(2)：421-444.
[25]	KARIMI-FARD M，DURLOFSKY L J，AZIZ K. An efficient discrete-fracture model applicable for general-purpose reservoir simulators[J]. SPE Journal，2004，9(2)：227-236. " target="_blank">
[30]	LIU J T，MA Z S，LI S H，et al. A GPU accelerated red-black SOR algorithm for computational fluid dynamics problems[J]. Advanced Materials Research，2011，320：335-340. " target="_blank">
[5]	BLESSENT D，THERRIEN R，GABLE C W. Large-scale numerical simulation of groundwater flow and solute transport in discretely- fractured crystalline bedrock[J]. Advances in Water Resources，2011，34(12)：1 539-1 552. " target="_blank">
[1]	KAZEMI H，MERRILL L S，PORTERFIELD K L，et al. Numerical simulation of water-oil flow in naturally fractured reservoirs[J]. SPE Journal，1976，16(6)：317-326. " target="_blank">
[4]	SHEN B，STEPHANSSON O，RINNE M，et al. A fracture propagation code and its applications to nuclear waste disposal[J]. International Journal of Rock Mechanics and Mining Sciences，2004，41：472-477. " target="_blank">
[6]	李世海，周东，王杰，等. 水电能源开发中的关键工程地质体力学问题[J]. 中国科学：物理学力学天文学，2013，43(12)：1 602-1 616.(LI Shihai，ZHOU Dong，WANG Jie，et al. Key problem of engineering geomechanics in hydroelectric energy exploitation[J]. Scientia Sinica Physica，Mechanica and Astronomica，2013，43(12)：1 602-1 616.(in Chinese)) " target="_blank">
[8]	BARENBLATT G I，ZHELTOV I P，KOCHINA I N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks[J]. Journal of Applied Mathematics and Mechanics，1960，24(5)：852-864. " target="_blank">
[10]	LONG J C S，REMER J S，WILSON C R，et al. Porous media equivalents for networks of discontinuous fractures[J]. Water Resources Research，1982，18(3)：645-658. " target="_blank">
[11]	DVERSTORP B，ANDERSSON J，NORDQVIST W. Discrete fracture network interpretation of field tracer migration in sparsely fractured rock[J]. Water Resources Research，1992，28(9)：2 327-2 343. " target="_blank">
[28]	ZHANG L，ZHANG G X，WANG L X，et al. A comparative study on different parallel solvers for nonlinear analysis of complex structures[J]. Mathematical Problems in Engineering，2013，2013：764237. " target="_blank">
[34]	仵彦卿，张倬元. 岩体水力学导论[M]. 成都：西南交通大学出版社，1995：45-48.(WU Yanqing，ZHANG Zhuoyuan. An introduction to rock mass hydraulics[M]. Chengdu：Southwest Jiaotong University Press，1995：45-48.(in Chinese)) " target="_blank">
[38]	LEI Z，ROUGIER E，KNIGHT E E，et al. A framework for grand scale parallelization of the combined finite discrete element method in 2d[J]. Computational Particle Mechanics，2014，1(3)：307-319. " target="_blank">
[9]	SAMARDZIOSKA T，POPOV V. Numerical comparison of the equivalent continuum，non-homogeneous and dual porosity models for flow and transport in fractured porous media[J]. Advances in Water Resources，2005，28(3)：235-255.
[12]	于青春，刘丰收，大西有三. 岩体非连续裂隙网络三维面状渗流模型[J]. 岩石力学与工程学报，2005，24(4)：662-668.(YU Qingchun，LIU Fengshou，OHNISHI Yuzo. Three-dimensional planar model for fluid flow in discrete fracture network of rock masses[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(4)：662-668.(in Chinese))
[13]	李新强，杨松青，汪小刚. 岩体随机结构面三维网络的生成和可视化技术[J]. 岩石力学与工程学报，2007，26(12)：2 564-2 569.(LI Xinqiang，YANG Songqing，WANG Xiaogang. Generation and visualization technologies of three-dimensional network of rock mass stochastic structural plane[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(12)：2 564-2 569.(in Chinese)) " target="_blank">
[19]	吕心瑞，姚军，黄朝琴，等. 基于有限体积法的离散裂缝模型两相流动模拟[J]. 西南石油大学学报(自然科学版)，2012，34(6)：123-130.(LÜ Xinrui，YAO Jun，HUANG Zhaoqin，et al. Study on discrete fracture model two-phase flow simulation based on finite volume method[J]. Journal of Southwest Petroleum University：Science & Technology Edition，2012，34(6)：123-130.(in Chinese))
[23]	CAILLABET Y，FABRIE P，LASSEUX D，et al. Computation of large-scale parameters for dispersion in fissured porous medium using finite-volume method[J]. Computational Geosciences，2001，5(2)：121-150.
[27]	刘耀儒，杨强，覃振朝. 基于统计模型的裂隙岩体渗流场的并行数值模拟[J]. 岩石力学与工程学报，2008，27(4)：736-742.(LIU Yaoru，YANG Qiang，QIN Zhenchao. Parallel numerical simulation of in fractured rock mass based on statistic model[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(4)：736-742.(in Chinese))
[29]	MA Z S，FENG C，LIU T P，et al. A GPU accelerated continuous- based discrete element method for elastodynamics analysis[J]. Advanced Materials Research，2011，320：329-334. " target="_blank">
[36]	何杨，柴军瑞，唐志立，等. 三维裂隙网络非稳定渗流数值分析[J]. 水动力学研究与进展(A辑)，2007，22(3)：338-344.(HE Yang，CHAI Junrui，TANG Zhili，et al. Numerical analysis of 3D unsteady seepage through fracture network in rock mass[J]. Journal of Hydrodynamics (Ser. A)，2007，22(3)：338-344.(in Chinese)). " target="_blank">
[15]	张奇华，邬爱清. 三维任意裂隙网络渗流模型及其解法[J]. 岩石力学与工程学报，2010，29(4)：720-730.(ZHANG Qihua，WU Aiqing. Three-dimensional arbitrary fracture network seepage model and its solution[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(4)：720-730.(in Chinese))
[18]	刘洋，李世海，刘继棠. 裂隙岩体非稳态渗流数值模型及其应用[J]. 力学与实践，2011，33(6)：23-29.(LIU Yang，LI Shihai，LIU Jitang. Numerical model of unsteady fluid flow in fractured rock and its application[J]. Mechanics and Engineering，2011，33(6)：23-29.(in Chinese))
[22]	CAILLABET Y，FABRIE P，LANDEREAU P，et al. Implementation of a finite-volume method for the determination of effective parameters in fissured porous media[J]. Numerical Methods for Partial Differential Equations，2000，16(2)：237-263 " target="_blank">
[26]	刘耀儒，杨强，黄岩松，等. 基于双重孔隙介质模型的渗流-应力耦合并行数值分析[J]. 岩石力学与工程学报，2007，26(4)：705-711.(LIU Yaoru，YANG Qiang，HUANG Yansong，et al. Parallel numerical analysis of coupled fluid flow and stress based on dual porosity media model[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(4)：705-711.(in Chinese))
[31]	WANG L X，LI S H，ZHANG G X，et al. A GPU-based parallel procedure for nonlinear analysis of complex structures using a coupled FEM/DEM approach[J]. Mathematical Problems in Engineering，2013，2013：618980. " target="_blank">
[32]	TAKAHASHI T，HAMADA T. GPU-accelerated boundary element method for Helmholtz’ equation in three dimensions[J]. International Journal for Numerical Methods in Engineering，2009，80(10)：1 295- 1 321. " target="_blank">
[37]	TATOMIR A. Numerical investigations of flow through fractured porous media[D]. University of Stuttgart，Stuttgart，Germany，2007. " target="_blank">
[16]	KIM J G，DEO M D. Finite element，discrete-fracture model for multiphase flow in porous media[J]. AIChE Journal，2000，46(6)： 1 120-1 130. " target="_blank">
[20]	宋晓晨，徐卫亚. 裂隙岩体渗流模拟的三维离散裂隙网络数值模型(II)：裂隙网络的随机生成[J]. 岩石力学与工程学报，2004，23(12)：2 021-2 026.(SONG Xiaochen，XU Weiya. Numerical model of three-dimensional discrete fracture network for seepage in fractured rocks(II)：computation of steady flow[J]. Chinese Journal of Rock Mechanics and Engineering，2004，23(12)：2 021-2 026.(in Chinese)) " target="_blank">
[24]	GRANET S，FABRIE P，LEMONNIER P，et al. A two-phase flow simulation of a fractured reservoir using a new fissure element method[J]. Journal of Petroleum Science and Engineering，2001，32(1)：35-52. " target="_blank">
[33]	SNOW D T. A parallel plate model of fractured permeable media[D]. University of California，Berkeley，USA，1965. " target="_blank">