A High-Order Implicit-Explicit Fluid-Structure Interaction Method for Flapping Flight

We present a high-order accurate scheme for fluid-structure interaction (FSI) simulations of flapping flight. The compressible Navier-Stokes equations are discretized using a discontinuous Galerkin arbitrary Lagrangian-Eulerian (DG-ALE) method on an unstructured tetrahedral mesh, and a wing-like structure, represented as a neo-Hookean material, is discretized using standard continuous Galerkin tetrahedral elements. The time integration is performed using a partitioned approach based on an implicit-explicit Runge-Kutta method, with the fluid and structure equations each integrated using the implicit coefficients, and the fluid-to-structure coupling predicted using a combination of the implicit and explicit coefficients. This partitioned approach allows the reuse of existing domain specific efficient parallel solvers. We demonstrate up to fifth order accuracy in time on a non-trivial test problem, showing that subiterations are not required to achieve design accuracy. In addition we show several examples of wing-like structures in both two and three dimensions.