Flying insects flap their wings in the air, induce air flows, and generate the aerodynamic force and torque as the reactions of the induced flow, indicating that the flapping flight of insects is a typical example of moving boundary flows. Among a lot of species of insects, butterflies have unique features in terms of flight dynamics, i.e., butterflies flap their wings downward to generate lift force and flap backward to generate thrust force, by changing the stroke plane. To change the stroke plane, butterflies should control their thorax-pitch angle by the aerodynamic and inertial torques. However, the control mechanisms for the thorax-pitch angle have not been clarified.
Our research group has been studying the butterfly flight through numerical simulations using the immersed boundary–lattice Boltzmann method (IB-LBM). The numerical model of a butterfly is represented as an arrangement of boundary Lagrangian points, and the position and velocity of these points are updated by solving the equations of motion of the butterfly model. The fluid flows around the butterfly model are computed by the single-relaxation-time lattice Boltzmann method, and the no-slip boundary condition at the boundary Lagrangian points is satisfied by the multi-direct-forcing immersed boundary method.
In my presentation, I will present some results of butterfly flight simulations in a “bottom-up” approach. The bottom-up butterfly model develops from the minimal configuration with the square wings, rod-shaped body, and simplified wing motion and incorporates individual factors (e.g., wing mass, wing shape, and wing flexibility) to reproduce more realistic butterfly aerodynamics and flight dynamics. Our first results using the minimal butterfly model showed that the model can support an actual butterfly's weight in free flight, but it generates the nose-up torque and consequently gets off-balance. Then, a more sophisticated model with the body composed of thorax and abdomen parts showed that the thorax-pitch angle can be perfectly controlled by abdomen undulation, but the amplitude and phase of the abdominal angle are still unrealistic. Finally, the model with the lead–lag motion (the motion inclining the wings forward or backward) showed the possibility of the thorax-pitch control keeping the abdominal angle in a realistic range.

Lattice Boltzmann method,Immersed boundary method,Flapping flight