From immersed boundary method to immersed continuum methods

The objective of this paper is to present an overview of the newly proposed immersed contintuum method in conjunction With the traditional treatment of fluid-structure interaction problems, the immersed boundary method, the extended immersed boundary method, the immersed finite element method, and the fictitious domain method. In particular, the key aspects of the immersed continuum method in comparison with the immersed boundary method are discussed. The immersed continuum method retains the same strategies employed in the extended immersed boundary method and the immersed finite element method, namely, the independent solid mesh moves on top of a fixed or prescribed background fluid mesh, and employs fully implicit time integration with a matrix-free combination of Newton-Raphson and GMRES iterative solution procedures. Therefore, the immersed continuum method is capable of handling compressible fluid interacting with a compressible solid. Several numerical examples are also presented to demonstrate that the proposed immersed continuum method is a good candidate for multiscale and multiphysics modeling platforms.