V. Pasquariello, G. Hammerl, F. Örley, S. Hickel, C. Danowski, A. Popp, W.A. Wall, N.A. Adams (2016) 
Journal of Computational Physics 307: 670-695. doi: 10.1016/

We present a loosely coupled approach for the solution of fluid–structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet–Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface.

The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid–structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.


Interpolation of state variables. (a) FVM: constant value per cell, (b) FEM: linear Lagrange polynomials.


Schematic of the staggered time integration of the coupled system.


Qualitative comparison between simulation (left) and experiment (right) for 50 mm panel length by means of schlieren images for selected time instances.


Contours of density gradient magnitude in the fluid domain and magnitude of the Cauchy stress tensor in the solid domain at four different simulation times.