A simple, rigorous benchmark for fully coupled flow--structure interaction algorithms.

We report (semi-)analytical solutions of a benchmark problem for rigorously testing coupled incompressible fluid--elastic solid interaction algorithms. The problem involves a visco-hyperelastic solid material layer sandwiched between two fluid layers, in turn confined by two long planar walls. The walls undergo oscillatory motion which drive a characteristic system response. The governing equations in this setting reduce to one-dimension and admit (semi-)analytical solutions, whose form depends on fluid viscosity and solid elasticity. Using these solutions, we highlight specific parameter settings that serve as rigorous, challenging long-time benchmarks for validating multiphase solvers, in the context of FSI simulations.