Implicit second-order immersed boundary methods with boundary mass

The immersed boundary method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. Immersed boundary computations typically evaluate the elastic forces explicitly in the configuration of the immersed elastic structure. In many applications this results in a severe restriction on the time step. We present a semi-implicit and a fully implicit secondorder accurate immersed boundary method. The methods provide a natural way to handle mass on the immersed elastic structures. We demonstrate their performance for a prototypical fluid–structure interaction problem. The methods are shown to possess superior stability properties that significantly alleviate the typically severe time step restriction of explicit computations. 2007 Elsevier B.V. All rights reserved.