A semi-implicit level set method for multiphase flows and fluid-structure interaction problems

In this paper we present a novel semi-implicit time-discretization of the level set method introduced in [8] for fluid-structure interaction problems. The idea stems form a linear stability analysis derived on a simplified one-dimensional problem. The semi-implicit scheme relies on a simple filter operating as a post-processing on the level set function. It applies to multiphase flows driven by surface tension as well as to fluid-structure interaction problems. The semi-implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost. It is validated through comparisons with the original explicit scheme and refinement studies on two and three-dimensional membranes.