An unfitted mesh semi-implicit coupling scheme for fluid-structure interaction with immersed solids

Unfitted mesh finite element approximations of immersed incompressible fluid-structure interaction problems which efficiently avoid strong coupling without compromising stability and accuracy are rare in the literature. Moreover, most of the existing approaches introduce additional unknowns or are limited by penalty terms which yield ill-conditioning issues. In this paper, we introduce a new unfitted mesh semi-implicit coupling scheme which avoids these issues. To this purpose, we provide a consistent generalization of the projection based semi-implicit coupling paradigm of (Int. J. Num. Meth. Engg., 69(4):794-821, 2007) to the unfitted mesh Nitsche-extended-FEM framework.