Fig. 17.

Illustration of the fluid-structure system. Ω denotes the entire domain with its boundary denoted as ∂Ω. Ω^s(t) denotes the immersed structure domain with its boundary (also the fluid-structure interface) denoted as ∂Ω^s(t). ε_a is a small portion of ∂Ω^s(t). Across ε_a, a small control volume with an infinitesimal width h is picked. The volume of the small control volume is denoted as ε_v. The faces of the small control volume in the fluid domain and the structure domain are denoted as ε_af and ε_as, respectively. The Cauchy stress in the fluid domain and the structure domain is denoted by σ^f and σ^s, respectively. σ^s can be split into two parts: the fluid-like stress σ^f and the additional stress, Δσ.