A decoupled scheme with leap-frog multi-time step for non-stationary Stokes–Darcy system

ABSTRACT

In this paper, a multiple-time-step decoupled algorithm for a non-stationary Stokes–Darcy problem is proposed and investigated. Under a modest time step restriction of physical parameters and the time step proportion, we give the stability analysis and convergence analysis of the decoupled scheme with different time step in fluid and porous subregions. Finally, a series of numerical experiments are provided to illustrate the accuracy, efficiency, and stability of the presented method for the coupled problem with the Beavers–Joseph–Saffman–Jones interface conditions.

Keywords:

• Coupled Stokes–Darcy flow
• different time step
• partitioned methods
• backward Euler-leap frog scheme
• finite element method

2010 Mathematics Subject Classifications:

• 65M12
• 76S05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China under the contract No. 11401467, China Postdoctoral Science Foundation Funded Project under the contract No. 2013M542334 and No. 2015T81012, Natural Science Foundation of Shaanxi Province under the contract No. 2015JQ1012, Fundamental Research Funds for the Central Universities under the contract No. xjj2014011, and Foundation CMG in Xi'an Jiaotong University.