Implicit Immersed Boundary Methods with Boundary Mass

The immersed boundary method is a general framework used to handle fluid-structure interactions. One computational bottleneck of the immersed boundary methods is that the elastic structures are often very stiff, necessitating the use of a very fine time step. In this talk, we will present an immersed boundary scheme in which the position of the immersed elastic structure is treated implicitly. We show that the resulting implicit method allows much greater time steps to be used compared with an explicit method, and that the computational cost is greatly reduced in certain test situations. We shall also show that the implicit method provides a natural way in which to add addtional mass to the immersed elastic structure.