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Boundary update via resolvent for fluid–structure interaction

Martina Bukač and Catalin Trenchea

Abstract

We propose a BOundary Update using Resolvent (BOUR) partitioned method, second-order accurate in time, unconditionally stable, for the interaction between a viscous incompressible fluid and a thin structure. The method is algorithmically similar to the sequential Backward Euler — Forward Euler implementation of the midpoint quadrature rule. (i) The structure and fluid sub-problems are first solved using a Backward Euler scheme, (ii) the velocities of fluid and structure are updated on the boundary via a second-order consistent resolvent operator, and then (iii) the structure and fluid sub-problems are solved again, using a Forward Euler scheme. The stability analysis based on energy estimates shows that the scheme is unconditionally stable. Error analysis of the semi-discrete problem yields second-order convergence in time. The two numerical examples confirm theoretical convergence analysis results and show an excellent agreement between the proposed partitioned scheme and the monolithic scheme.

JEL Classification: 65M12

Funding statement: The work of the first author was partially supported by the NSF under grants DMS 1912908, DMS 1619993, and DCSD 1934300. The work of the second author was partially supported by the AFOSR under grant FA 9550-16-1-0355 and the NSF under grant DMS 1522574.

Acknowledgment

We would like to thank Fasma Diele (Italian National Research Council, Bari) for helpful discussions on symplectic and geometric integration.

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Published Online: 2020-06-30
Published in Print: 2021-03-26

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