In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid-structure interaction problems. We will use the immersed boundary method to model the fluid-structure interaction, while the fluid flow is governed by the incompressible Navier-Stokes equations. The immersed boundary method is proven to be a successful scheme to model fluid-structure interactions. To ensure mass conservation, we will use the staggered discontinuous Galerkin method to discretize the incompressible Navier-Stokes equations. The staggered discontinuous Galerkin method is able to preserve the skew-symmetry of the convection term. In addition, by using a local postprocessing technique, the weakly divergence free velocity can be used to compute a new postprocessed velocity, which is exactly divergence free and has a superconvergence property. This strongly divergence free velocity field is the key to the mass conservation. Furthermore, energy stability is improved by the skew-symmetric discretization of the convection term. We will present several numerical results to show the performance of the method.
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