Geodesic
Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation
Applications of Mathematics, Tome 67 (2022) no. 4, pp. 445-470.

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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.
DOI : 10.21136/AM.2022.0372-20
Classification : 35Q30, 65F08, 65N30, 65N55, 76S05
Keywords: Navier-Stokes equation; Darcy equation; spectral element 
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     title = {Spectral discretization of {Darcy} equations coupled with {Navier-Stokes} equations by vorticity-velocity-pressure formulation},
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Mabrouki, Yassine; Satouri, Jamil. Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation. Applications of Mathematics, Tome 67 (2022) no. 4, pp. 445-470. doi : 10.21136/AM.2022.0372-20. http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0372-20/

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