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A Cell-Centered Finite Volume Method for the Navier–Stokes/Biot Model

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Part of the Springer Proceedings in Mathematics & Statistics book series (volume 323)

Abstract

We develop a cell-centered finite volume method for the Navier–Stokes/Biot model, based on a fully mixed formulation with weakly symmetric stresses. The multipoint stress mixed finite element method is employed for the Navier–Stokes and elasticity equations, while the multipoint flux mixed finite element method is used for Darcy’s flow. These methods allow for local elimination of the fluid and poroelastic stresses, vorticity, and rotation, resulting in a positive definite finite volume scheme for the fluid and structure velocities and the Darcy pressure, coupled via Lagrange multipliers on the interface to impose the transmission conditions.

Keywords

  • Navier–Stokes/Biot
  • Mixed finite element
  • Multipoint flux
  • Multipoint stress
  • Finite volume method

MSC (2010)

  • 65M08
  • 65M60
  • 74S05
  • 76S05
  • 76D05

S. Caucao is supported in part by BECAS CHILE para postdoctorado en el extranjero (convocatoria 2018). T. Li and I. Yotov are supported in part by NSF grant DMS 1818775.

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  • DOI: 10.1007/978-3-030-43651-3_29
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References

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Correspondence to Ivan Yotov .

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Caucao, S., Li, T., Yotov, I. (2020). A Cell-Centered Finite Volume Method for the Navier–Stokes/Biot Model. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_29

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