Analysis of a Coupled Fluid-Structure Model with Applications to Hemodynamics

Abstract : We propose and analyze a simplified fluid-structure coupled model for flows with compliant walls. As in [F. Nobile and C. Vergara, SIAM J. Sci. Comput., 30 (2008), pp. 731--763], the wall reaction to the fluid is modeled by a small displacement viscoelastic shell where the tangential stress components and displacements are neglected. We show that within this small displacement approximation a transpiration condition can be used which does not require an update of the geometry at each time step, for pipe flow at least. Such simplifications lead to a model which is well posed and for which a semi-implicit time discretization can be shown to converge. We present some numerical results and a comparison with a standard test case taken from hemodynamics. The model is more stable and less computer demanding than full models with moving mesh. We apply the model to a three-dimensional arterial flow with a stent.
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SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2016, SIAM Journal on Numerical Analysis, 54 (2), pp.994 - 1019. 〈http://epubs.siam.org/doi/abs/10.1137/140991509〉. 〈10.1137/140991509〉
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T. Chacón Rebollo, V. Girault, F. Murat, O. Pironneau. Analysis of a Coupled Fluid-Structure Model with Applications to Hemodynamics. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2016, SIAM Journal on Numerical Analysis, 54 (2), pp.994 - 1019. 〈http://epubs.siam.org/doi/abs/10.1137/140991509〉. 〈10.1137/140991509〉. 〈hal-01003208v3〉

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