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Rapport (Rapport De Recherche) Année : 2015

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

Résumé

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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Dates et versions

hal-01102975 , version 1 (13-01-2015)
hal-01102975 , version 2 (14-01-2015)
hal-01102975 , version 3 (23-10-2015)

Identifiants

  • HAL Id : hal-01102975 , version 1

Citer

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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