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Convergence analysis for a class of splitting schemes in incompressible fluid-structure interaction

Miguel Angel Fernández 1, * Jimmy Mullaert 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 : This paper is devoted to the convergence analysis of the generalized Robin-Neumann schemes introduced in [C. R. Math. Acad. Sci. Paris, 349(17-18):1011--1015, 2011; Internat. J. Numer. Methods Engrg., 101(3):199--229, 2015] for the coupling of a viscous incompressible fluid with a thick-walled elastic structure. The methods are formulated within a class of operator splitting schemes which treat implicitly the coupling between the fluid and the solid inertia contributions. This guarantees energy stability. A priori error estimates are derived for all the explicit and semi-implicit variants. The analysis predicts a non-uniformity in space of the splitting error, hence confirming the numerical evidence reported in [Internat. J. Numer. Methods Engrg., 101(3):199--229, 2015] for the explicit variants. Besides, the analysis demonstrates that the genesis of this accuracy loss is the spatial non-uniformity of the discrete visco-elastic solid operator. The theoretical findings are illustrated via a numerical study which shows, in particular, that alternative splitting schemes recently reported in the literature also suffer from these accuracy issues.
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https://hal.inria.fr/hal-01102975
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Submitted on : Tuesday, January 13, 2015 - 5:22:42 PM
Last modification on : Monday, December 14, 2020 - 5:00:02 PM
Long-term archiving on: : Friday, September 11, 2015 - 6:41:44 AM

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  • HAL Id : hal-01102975, version 1

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Miguel Angel Fernández, Jimmy Mullaert. Convergence analysis for a class of splitting schemes in incompressible fluid-structure interaction. [Research Report] RR-8670, Inria. 2015. ⟨hal-01102975v1⟩

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