Fractional-step schemes for the coupling of distributed and lumped models in hemodynamics

Cristobal Bertoglio 1 Alfonso Caiazzo 2 Miguel Angel Fernández 1, *
* Corresponding author
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : In three-dimensional (3D) blood flow simulations, lumped parameter models (0D) are often used to model the neglected parts of the downstream circulatory system. We analyze two 3D-0D coupling approaches in which a fractional-step projection scheme is used in the fluid. Our analysis shows that explicit approaches might yield numerical instabilities, particularly in the case of realistic geometries with multiple outlets. We introduce and analyze an implicitly 3D-0D coupled formulation with enhanced stability properties and which requires a negligible additional computational cost. Furthermore, we also address the extension of these methods to fluid-structure interaction problems. The theoretical stability results are confirmed by meaningful numerical experiments in patient specific geometries coming from medical imaging.
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Submitted on : Wednesday, February 6, 2013 - 10:03:26 PM
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Cristobal Bertoglio, Alfonso Caiazzo, Miguel Angel Fernández. Fractional-step schemes for the coupling of distributed and lumped models in hemodynamics. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2013, 35 (3), pp.551-575. ⟨10.1137/120874412⟩. ⟨hal-00690493v2⟩

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