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We present a strongly-coupled immersed-boundary method for flow-structureinteraction problems involving thin deforming bodies. The method is stable forarbitrary choices of solid-to-fluid mass ratios and for large body motions. Aswith many strongly-coupled immersed-boundary methods, our method requires thesolution of a nonlinear algebraic system at each time step. The system issolved through iteration, where the iterates are obtained by linearizing thesystem and performing a block LU factorization. This restricts all iterationsto small-dimensional subsystems that scale with the number of discretizationpoints on the immersed surface, rather than on the entire flow domain.Moreover, the iteration procedure we propose does not involve heuristicregularization parameters, and has converged in a small number of iterationsfor all problems we have considered. We derive our method for general deformingsurfaces, and verify the method with two-dimensional test problems ofgeometrically nonlinear beams undergoing large amplitude flapping behavior.

A strongly-coupled immersed-boundary formulation for thin deforming surfaces, with application to elastic beams