| Issue |
ESAIM: M2AN
Volume 52, Number 4, July-August 2018
|
|
|---|---|---|
| Page(s) | 1477 - 1500 | |
| DOI | https://doi.org/10.1051/m2an/2017049 | |
| Published online | 28 September 2018 | |
A second order in time incremental pressure correction finite element method for the Navier-Stokes/Darcy problem★
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
* Corresponding author: zhiyongsi@gmail.com, sizhiyong@hpu.edu.cn
Received:
25
April
2016
Accepted:
25
September
2017
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.
Mathematics Subject Classification: 76D05 / 35Q30 / 65M60 / 65N30
Key words: Navier-Stokes/Darcy equations / projection method / second order in time / incremental pressure correction method / stability analysis / optimal error analysis
© EDP Sciences, SMAI 2018
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