Journal of Scientific Computing

, Volume 79, Issue 1, pp 389–413 | Cite as

Partitioned Time Stepping Method for a Dual-Porosity-Stokes Model

  • Li Shan
  • Jiangyong HouEmail author
  • Wenjing Yan
  • Jie Chen


In this report, we study a partitioned time stepping algorithm for a dual-porosity-Stokes model, which consists of dual-porosity media and macrofractures/conduits in the coupled system. More specifically, the dual-porosity-Stokes model uses two pressures, the matrix pressure and the fracture pressure, to couple with the Stokes equations. There are four physically valid interface conditions to couple the two models on the interface, including a no-exchange condition, a mass balance condition, a force balance condition, and the Beavers–Joseph condition. To decouple the complex model into three simple sub-problems and solve them separately, we propose a partitioned time stepping method. It solves one, uncoupled matrix pressure equation, microfracture pressure equation and Stokes equation per time step. Under a modest time step restriction of the form \(\triangle t\le C\)(depending on physical parameters) , we prove the stability of the method. We also derive its optimal error estimates. Numerical tests verify the theoretical results.


Dual-porosity-Stokes model Partitioned time stepping method Beavers–Joseph interface condition Error estimate 


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Authors and Affiliations

  1. 1.College of ScienceLiaoning Technical UniversityFu XinPeople’s Republic of China
  2. 2.School of MathematicsNorthwest UniversityXi’anPeople’s Republic of China
  3. 3.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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