Explicit strategies for incompressible fluid-structure interaction problems: Nitsche type mortaring versus Robin-Robin coupling

Erik Burman 1 Miguel Angel Fernández 2
2 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : We discuss explicit coupling schemes for fluid-structure interaction problems where the added mass effect is important. In this paper we show the close relation between coupling schemes using Nitsche's method and a Robin-Robin type coupling. In the latter case the method may be implemented either using boundary integrals of the stresses or the more conventional discrete lifting operators. Recalling the explicit method proposed in Comput. Methods Appl. Mech. Engrg. 198(5-8):766-784, 2009 we make the observation that this scheme is stable under a hyperbolic type CFL condition, but that optimal accuracy imposes a parabolic type CFL conditions due to the splitting error. Two strategies to enhance the accuracy of the coupling scheme under the hyperbolic CFL-condition are suggested, one using extrapolation and defect-correction and one using a penalty-free non-symmetric Nitsche method. Finally we illustrate the performance of the proposed schemes on some numerical examples in two and three space dimensions.
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International Journal for Numerical Methods in Engineering, Wiley, 2014, 97 (10), pp.739--758. 〈10.1002/nme.4607〉
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Erik Burman, Miguel Angel Fernández. Explicit strategies for incompressible fluid-structure interaction problems: Nitsche type mortaring versus Robin-Robin coupling. International Journal for Numerical Methods in Engineering, Wiley, 2014, 97 (10), pp.739--758. 〈10.1002/nme.4607〉. 〈hal-00819948v2〉

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