Numerical Solution of Transonic and Supersonic 2D and 3D Fluid–Elastic Structure Interaction Problems

We solve the system of Euler or Navier-Stokes equations in conservative ALE formulation, possibly supplemented by a suitable turbulence model. The structural dynamics is described by the equations of anisotropic elastic continuum with large or small displacements. The problem is closed by suitable interface conditions. We present a cell centered finite volume method with linear least square reconstruction with nonlinear WENO type weights, a cell centered finite volume method with linear reconstruction and Barth’s limiter and a residual distribution scheme to solve the CFD sub-problem. To allow a large time step, all the considered methods use implicit time stepping formulated in dual time. The elastic problem and the mesh motion is solved by a simple finite element method. The whole problem is formulated in dual time and solved by a simple sub-iteration procedure. We present several numerical tests documenting the behavior of the methods. These include 2D transonic turbulent flow past a forced oscillatory pitching NACA0012 airfoil, 2D inviscid supersonic panel flutter and 3D inviscid flow past the elastic AGARD 445.6 wing.