Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation

Yassine Mabrouki; Jamil Satouri

Applications of Mathematics (2022)

  • Volume: 67, Issue: 4, page 445-470
  • ISSN: 0862-7940

Abstract

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We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis.

How to cite

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Mabrouki, Yassine, and Satouri, Jamil. "Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation." Applications of Mathematics 67.4 (2022): 445-470. <http://eudml.org/doc/298313>.

@article{Mabrouki2022,
abstract = {We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis.},
author = {Mabrouki, Yassine, Satouri, Jamil},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equation; Darcy equation; spectral element},
language = {eng},
number = {4},
pages = {445-470},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation},
url = {http://eudml.org/doc/298313},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Mabrouki, Yassine
AU - Satouri, Jamil
TI - Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 445
EP - 470
AB - We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis.
LA - eng
KW - Navier-Stokes equation; Darcy equation; spectral element
UR - http://eudml.org/doc/298313
ER -

References

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