An integrated simulation of a Drosophila wing-body combination in hovering flight has been carried out in order to analyze the Lagrangian and Eulerian coherent structures. A parallel unstructured finite volume method based on an arbitrary Lagrangian-Eulerian (ALE) formulation has been initially validated for a flapping rectangular plate and then employed to solve the incompressible unsteady Navier-Stokes equations around a Drosophila wing-body combination. A robust mesh deformation algorithm based on indirect radial basis function method is utilized at each time level while avoiding remeshing. The time variation of the three-dimensional Eulerian coherent structures around a flapping Drosophila in hovering flight is analyzed in the near wake with lambda 2-criterion. Meanwhile, the Lagrangian coherent structures are investigated using finite-time Lyapunov exponent fields. In addition, the instantaneous velocity vectors and particle traces are presented along with the aerodynamic parameters including the force, moment and power for a wing-body combination. Furthermore, a wing-only configuration is also investigated in order to show the body effects on aerodynamic loads. The numerical simulations are used to gain insight into the near wake topology as well as their correlations with the aerodynamic force generation. The present fully coupled ALE algorithm is shown to be sufficiently robust to deal with large mesh deformations seen in flapping wings and reveals highly detailed near wake topology which is very useful to study physics in biological flights and can also provide an effective tool for designing bio-inspired MAVs and MFIs.