Towards to the direct numerical simulation of insect flight

The parallel large-scale unstructured finite volume method based on an Arbitrary Lagrangian-Eulerian (ALE) formulation has been employed in order to investigate the near wake structure of Drosophila in hover and forward flight. The numerical algorithm is based on side-centered finite volume method where the velocity vector components are defined at the mid-point of each cell face while the pressure is defined at the element centroid. DISTENE MeshGems-Hexa algorithm based on the octree method is used to generate the all hexahedral mesh for the wing-body combination. The mesh deformation algorithm is based on the indirect radial basis function (RBF) method at each time level while avoiding remeshing in order to enhance numerical robustness. For the algebraic solution of the resulting large-scale equations, a matrix factorization is introduced similar to that of the projection method for the whole coupled system and we use two-cycle of Boomer AMG solver for the scaled discrete Laplacian provided by the HYPRE library, a high performance preconditioning package developed at Lawrence Livermore National Laboratory, which we access through the PETSc library. The present numerical algorithm is applied to the numerical simulation of flow field around a flapping Drosophila in hover and forward flight. The time variation of the Eulerian coherent structures in the near wake is analyzed with the lambda-2 criterion. In addition, the Lagrangian coherent structures is also investigated using finite-time Lyapunov exponents (FTLE) fields. For the symmetrical wing rotation with respect to stroke reversal, the flapping frequency is determined to balance the weight of the Drosophila. The body effect on the Drosophila flight is investigated by comparing the numerical results for the wing-body combination and no-body configuration. The visualization results indicate that the both cases are very similar to each other. Two different wing kinematic are applied for the Drosophila in forward flight in order to balance drag force due to forward motion. In the first case, the wing tip-path plane is tilted forward to generate forward force (as in helicopter rotor). In the second case, paddling wing motion is used to generate the forward force. The Eulerian coherent structures are analyzed with the lambda-2 criterion. In addition, a new monolithic approach is proposed to solve the fluid-structure interaction (FSI) problem with Lagrange multipliers in order to model free swimming/flying. The solid domain is modeled by the constitutive laws for the nonlinear Saint Venant-Kirchhoff material and the classical Galerkin finite element method is used to discretize the governing equations in a Lagrangian frame. In order to impose the body motion/deformation, the distance between each pair of nodes is imposed using the Lagrange multiplier approach, which is independent from the frame of reference. The resulting algebraic linear equations are solved in a fully coupled manner using a dual approach (null space method). The present numerical algorithm is validated for the two-dimensional three-link swimmer proposed by Eldredge (2008). In the future, the present method will be applied to Drosophila in free flight in three-dimensions.