The main idea of the Eulerian fluid-structure interaction (FSI) model is derived from the idea of the multi-phase analysis on fixed Cartesian mesh. The volume fraction data is used to distinguish the fluid and structure regions, and the mixed stress on an Eulerian element is calculated with each volume fraction. In order to describe the structure deformation, which relates to the elastic stress, the left Cauchy-Green deformation tensor is introduced in a hyper-elastic material. In this paper, further development for the numerical approach is proposed such as the advection scheme of the volume data and implicit treatment for the elastic stress. The simple validation problems will be shown, and a pressure-driving capillary flow involving several biconcave materials will be also investigated.
