A second order in time incremental pressure correction finite element method for the Navier-Stokes/Darcy problem

Wang, Yunxia; Li, Shishun; Si, Zhiyong

doi:10.1051/m2an/2017049

Wang, Yunxia ¹ ; Li, Shishun ² ; Si, Zhiyong ²

¹ School of Materials Science and Engineering, Henan Polytechnic University, 454003, Jiaozuo, P.R. China
² School of Mathematics and Information Science, Henan Polytechnic University, 454003, Jiaozuo, P.R. China

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1477-1500.

Résumé

In this paper, we give a second order in time incremental pressure correction finite element method for the Navier-Stokes/Darcy problem. In this method, the Navier-Stokes/Darcy problem is solved in three steps: a convection-diffusion step, a projection correction (incremental pressure correction) step and a Darcy step. In this way, the Navier-Stokes/Darcy equation is solved in a fractional step way, which is a decoupled method. In order to decouple the equation, we use the numerical solutions at the last time level to give the interface conditions. The stability analysis shows that the second order in time incremental pressure correction finite element method is unconditionally stable. The optimal error estimate is also given. Finally, we present some numerical results to show the efficiency of the method.

Reçu le : 2016-04-25
Accepté le : 2017-09-25

MR Zbl

DOI : 10.1051/m2an/2017049

Classification : 76D05, 35Q30, 65M60, 65N30
Mots-clés : Navier-Stokes/Darcy equations, projection method, second order in time, incremental pressure correction method, stability analysis, optimal error analysis

Affiliations des auteurs :

Wang, Yunxia ¹ ; Li, Shishun ² ; Si, Zhiyong ²

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     author = {Wang, Yunxia and Li, Shishun and Si, Zhiyong},
     title = {A second order in time incremental pressure correction finite element method for the {Navier-Stokes/Darcy} problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1477--1500},
     publisher = {EDP-Sciences},
     volume = {52},
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     year = {2018},
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     mrnumber = {3875294},
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     url = {http://www.numdam.org/articles/10.1051/m2an/2017049/}
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Wang, Yunxia; Li, Shishun; Si, Zhiyong. A second order in time incremental pressure correction finite element method for the Navier-Stokes/Darcy problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1477-1500. doi : 10.1051/m2an/2017049. http://www.numdam.org/articles/10.1051/m2an/2017049/

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