Numerical Solution of Transonic and Supersonic 2D and 3D Fluid–Elastic Structure Interaction Problems J. Dobeˇ s, J. F ¨ urst, H. Deconinck, and J. Foˇ rt Abstract We solve the system of Euler or Navier-Stokes equations in conserva- tive 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 con- ditions. 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 in- viscid supersonic panel flutter and 3D inviscid flow past the elastic AGARD 445.6 wing. 1 Introduction Consideration of problems of interaction between fluids and structural bodies is an important part of the design process. Despite a large progress in the improvement of Jiˇ r´ ı Dobeˇ s,Jiˇr´ ı F¨ urst, and Jaroslav Foˇ rt Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical Uni- versity, Karlovo N´ amˇ est´ ı 13, Prague, CZ-121 35 Czech Republic, e-mail: {Jiri.Dobes, Jiri.Furst, Jaroslav.Fort}@fs.cvut.cz Herman Deconinck Von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, B-1640 Sint-Genesius-Rode, Belgium, e-mail: Deconinck@vki.ac.be 539