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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (6): 721-732.doi: 10.3969/j.issn.1005-3085.2019.06.010

• • 上一篇    

双重介质 Stokes 模型的改进变分时间步格式（英）

侯江勇1,  胡  丹2,  徐金虎2,  何正康3   

  1. 1- 西北大学数学学院，西安  710127
    2- 西安理工大学理学院，西安  710048
    3- 西安交通大学数学与统计学院，西安  710049
  • 收稿日期:2018-12-03 接受日期:2019-03-27 出版日期:2019-12-15 发布日期:2020-02-15
  • 基金资助:
    国家自然科学基金(11701451)；陕西省自然科学基金(2018JQ1077)；陕西省教育厅科研项目(17JK0787)；陕西省大学生科学技术协会青年人才基金(20180504).

Improved Partitioned Time Stepping Scheme for the Dual-porosity-Stokes Model

HOU Jiang-yong1,  HU Dan2,  XU Jin-hu2,  HE Zheng-kang3   

  1. 1- School of Mathematics, Northwest University, Xi'an 710127
    2- School of Sciences, Xi'an University of Technology, Xi'an 710048
    3- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2018-12-03 Accepted:2019-03-27 Online:2019-12-15 Published:2020-02-15
  • Supported by:
    The National Natural Science Foundation of China (11701451); the Natural Science Foundation of Shaanxi Province (2018JQ1077); the Scientific Research Program Funded by Education Department  of Shaanxi Province (17JK0787); the Young Talent Fund of University Association for Science and Technology in Shaanxi (20180504).

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摘要： 在油藏模拟问题的应用中，研究流体相在复杂多孔介质耦合管道系统中的流动规律具有重要意义．最近一种名为双重介质 Stokes 的模型被研究开发，它用来模拟复杂双重介质管道系统，这种系统可以用在如页岩/致密油/气藏等真实问题中．新模型由双重介质模型和 Stokes 方程组成，双重介质模型用来控制多孔介质流，Stokes 方程用来控制自由流，两者通过四个界面条件耦合在一起．这种耦合模型会生成巨大而复杂的系统，因此通常难于求解．本文我们提出一种改进的变分时间步格式，利用它有效且精确地求解由耦合的双重介质 Stokes 模型所导致的大型系统．

关键词: 双重介质模型, Stokes 方程, 有限元方法, 解藕算法

Abstract: In applications of petroleum reservoir problem, it is very important to study the fluid phases within a complicated porous media coupled with conduit systems. Recently, a dual-porosity-Stokes model is developed to simulate the complicated dual-porosity-conduit system which could be used for realistic problems such as shale/tight oil/gas reservoirs. The new model consists of a dual-porosity model to govern the porous media flow and a Stokes equation to control the free flow and coupled via four interface conditions. Such coupled model is usually hard to solve since it will result into a large and complicated system. In this paper, we propose an improved partitioned time stepping scheme to efficiently and accurately solve the large system caused by the coupled dual-porosity-Stokes model.

Key words: dual-porosity model, Stokes equation, finite element method, decoupled algorithm

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