A benchmark proposal for contactless rebounds of elastic solids in fluids

The paper deals with the rebound of an elastic solid off a rigid wall of a container filled with an incompressible Newtonian fluid. Accordingly, a new fluid-structure interaction benchmark is introduced. We show that the benchmark captures a rebound without the solid touching the wall, hence omitting any artificial bouncing law. An adaptive numerical scheme that reconstructs the rebound for very small viscosities is introduced. As the viscosity decreases, the solution converges to the free rebound in a vacuum. The scheme is based on a Glowinski time scheme and a localized arbitrary Lagrangian-Eulerian map on finite elements in space. The absence of topological contact requires that very thin liquid channels are solved with sufficient accuracy. This is done by newly developed geometrically driven adaptive strategies. A rebound is simulated in the absence of topological contacts. The benchmark is further tested by a here-introduced adaptive purely Eulerian level-set method, which produces the same dynamics but with a much higher computational cost. The experiments allow for a better understanding of the effect of fluids on the dynamics of elastic objects. Several observations are discussed, such as the amount of elastic and/or kinetic energy loss or the precise connection between the fluid pressure and the rebound of the solid.