Geodesic
A second order in time incremental pressure correction finite element method for the Navier-Stokes/Darcy problem
Wang, Yunxia1 ; Li, Shishun2 ; Si, Zhiyong2
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

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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 :
Accepté le :
DOI : 10.1051/m2an/2017049
Classification : 76D05, 35Q30, 65M60, 65N30
Keywords: Navier-Stokes/Darcy equations, projection method, second order in time, incremental pressure correction method, stability analysis, optimal error analysis

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 
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     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},
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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

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