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In this paper, we analyse a Vector Penalty Projection Scheme (see [1]) to treat the displacement of a moving body in incompressible viscous flows in the case where the interaction of the fluid on the body can be neglected. The presence of the obstacle inside the computational domain is treated with a penalization method introducing a parameter η to enforce the velocity on the solid boundary. The incompressibility constraint is approached using a Vector Projection method which introduces a relaxation parameter ε. We show the stability of the scheme and that the pressure and velocity converge towards a limit when the relaxation parameter ε and the time step δt tend to zero with a proportionality constraint ε = λδt. Finally, when η goes to 0, we show that the problem admits a weak limit which is a weak solution of the Navier-Stokes equations with no-slip condition on the solid boundary.
Bruneau, Vincent 1 ; Doradoux, Adrien 2 ; Fabrie, Pierre 2
@article{M2AN_2018__52_4_1417_0,
author = {Bruneau, Vincent and Doradoux, Adrien and Fabrie, Pierre},
title = {Convergence of a vector penalty projection scheme for the {Navier} {Stokes} equations with moving body},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1417--1436},
publisher = {EDP-Sciences},
volume = {52},
number = {4},
year = {2018},
doi = {10.1051/m2an/2017016},
mrnumber = {3875291},
zbl = {1406.35220},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017016/}
}
TY - JOUR AU - Bruneau, Vincent AU - Doradoux, Adrien AU - Fabrie, Pierre TI - Convergence of a vector penalty projection scheme for the Navier Stokes equations with moving body JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1417 EP - 1436 VL - 52 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017016/ DO - 10.1051/m2an/2017016 LA - en ID - M2AN_2018__52_4_1417_0 ER -
%0 Journal Article %A Bruneau, Vincent %A Doradoux, Adrien %A Fabrie, Pierre %T Convergence of a vector penalty projection scheme for the Navier Stokes equations with moving body %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1417-1436 %V 52 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017016/ %R 10.1051/m2an/2017016 %G en %F M2AN_2018__52_4_1417_0
Bruneau, Vincent; Doradoux, Adrien; Fabrie, Pierre. Convergence of a vector penalty projection scheme for the Navier Stokes equations with moving body. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1417-1436. doi: 10.1051/m2an/2017016
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