Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction

Santiago Badia, Annalisa Quaini, Alfio Quarteroni

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56 Citations (Scopus)


The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier-Stokes equations with the Biot system. The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier-Stokes/Biot system with the appropriate transmission conditions at the interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it happens in hemodynamics applications.

Original languageEnglish
Pages (from-to)7986-8014
Number of pages29
JournalJournal of Computational Physics
Issue number21
Publication statusPublished - 20 Nov 2009
Externally publishedYes


  • Biot system
  • Darcy's problem
  • Fluid-structure interaction
  • Hemodynamics
  • Poromechanics
  • Stabilized finite elements

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