Figure 4:

The coupling for the compressible structure combines (a) the partitioned formulation and (b) immersed FSI formulations to create (c) the penalty-ILE coupling. The fluid-structure interface representation in this case (determined by $\mathit{\chi }$) conforms to the inner boundary of the structure (determined by $\mathit{\xi }$) in an approximate sense. The displacement between the two representations is exaggerated here for illustration purposes.