DGFEM for dynamical systems describing interaction of compressible fluid and structures

The paper is concerned with the numerical solution of flow-induced vibrations of elastic structures. The dependence on time of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian–Eulerian) formulation of the compressible Navier–Stokes equations. The deformation of the elastic body, caused by aeroelastic forces, is described by the linear dynamical elasticity equations. These two systems are coupled by transmission conditions. The flow problem is discretized by the discontinuous Galerkin finite element method (DGFEM) in space and by the backward difference formula (BDF) in time. The structural problem is discretized by conforming finite elements and the Newmark method. The fluid–structure interaction is realized via weak or strong coupling algorithms. The developed technique is tested by numerical experiments and applied to the simulation of vibrations of vocal folds during phonation onset.