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Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2017

Boundary conditions involving pressure for the Stokes problem and applications in computational hemodynamics

Résumé

Pressure driven flows typically occur in hydraulic networks, e.g. oil ducts, water supply, biological flows, microfluidic channels etc. However, Stokes and Navier-Stokes problems are most often studied in a framework where Dirichlet type boundary conditions on the velocity field are imposed, thanks to the simpler settings from the theoretical and numerical points of view. In this work, we propose a novel formulation of the Stokes system with pressure boundary condition, together with no tangential flow, on a part of the boundary in a standard Stokes functional framework using Lagrange multipliers to enforce the latter constraint on velocity. More precisely, we carry out (i) a complete analysis of the formulation from the continuous to discrete level in two and three dimensions (ii) the description of our solution strategy, (iii) a verification of the convergence properties with an analytic solution and finally (iv) three-dimensional simulations of blood ow in the cerebral venous network that are in line with in-vivo measurements and the presentation of some performance metrics with respect to our solution strategy.
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Dates et versions

hal-01420651 , version 1 (27-12-2016)
hal-01420651 , version 2 (10-05-2017)

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Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales

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Silvia Bertoluzza, Vincent Chabannes, Christophe Prud'Homme, Marcela Szopos. Boundary conditions involving pressure for the Stokes problem and applications in computational hemodynamics. Computer Methods in Applied Mechanics and Engineering, 2017, ⟨10.1016/j.cma.2017.04.024⟩. ⟨hal-01420651v2⟩
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