###### Abstract
In fact, with the rising tendency of complex flow environments and novel materials for aircraft manufacturing, it is feasible and superior to obtain the macroscopic equations of fluid mechanics from the mesoscopic point of view. In the merit of simple implementation and parallelism, the lattice Boltzmann method (LBM) [21; 22; 23] turns out to be a good choice in the domains of multiphase flow [24], microscale flow [25], thermal flow [26], and turbulence [27]. The LBM is established on the kinetic theory and describes the flow as discrete particle distribution functions associated with a set of discrete velocities statistically. The particles propagate over time and tend to relax toward a local equilibrium state. The density distribution of discrete particles evolves on simple rules of the collision and the subsequent streaming. Its simplicity and efficiency make it an attractive alternative to traditional CFD methods [28; 29; 30; 31]. [PERSON] et al. [29] couple the LBM with the immersed boundary method for moving objects. The shear layer and near-wall effects are both predicted in the high Reynolds number flow. [PERSON] et al. [22] apply the ALE approach to the LBM to simulate the flow-structure interactions. Validated by a moving square cylinder in a Poiseuille flow, it is confirmed that the ALE-LBM framework succeeds in capturing the flow phenomena. For robustness, [PERSON] et al. [19] introduce a two-population lattice Boltzmann formulation to describe the complex flows. Under the ALE scheme, they accurately capture the dynamic behavior of multiple cylinders and simulate transonic flutter over an airfoil. Coincidentally, [PERSON] et al. [21] investigate the unsteady flows over forced pitching airfoils in transonic regions and even at high speeds. The moving boundary is described by the ALE technique. Stemming from lattice Boltzmann equations, a lattice Boltzmann flux solver (LBFS) [32; 33; 34] has been proposed by [PERSON] and his colleagues recently. The LBFS abandons the restriction on the uniform meshes and endows itself with a flexible alternative for problems with complex geometries, no matter structured or unstructured meshes [35; 36; 37; 38]. Moreover, within the framework of LBFS, the boundary and initial conditions are treated in a manner identical to finite-volume NS solvers. Thanks to these aforementioned advantages, the applications of lattice Boltzmann flux solver with various lattice Boltzmann models have been accessible for multiphase flow [39], thermal flow [40], and compressible flow [41; 42]. The LBFScoupled with the immersed boundary method has also been extended for the study of fluid-structure interaction problems with large deformation on the simple Cartesian mesh. For example, [PERSON] et al. apply IBM-LBFS to simulate the flow-induced vibration of single and multiple hyperelastic beams behind a cylinder [43] and falling freely solid objects [44; 45]. [PERSON] et al. [46] solve 3D FSI problems of complex multiple flexible structures. However, it is rare to combine the LBFS with the ALE technique on unstructured dynamic meshes for fluid-structure interactions in aeronautical applications, such as airfoil and wing flutter in compressible flows, which motivates the present work. In this study, an ALE-LBFS coupled with the mode superposition method is developed and applied to study both 2D and 3D transonic flutter phenomenon on dynamic unstructured meshes. To simulate the transonic flow field on the dynamic meshes, the vertex-centered ALE-LBFS with the non-free parameter lattice model DIQ4 [47] is presented. With the aid of reconstructed variables, the lattice Boltzmann solutions are obtained locally and then employed to evaluate the fluxes across the interfaces. As the general application of ALE to other problems, an additional velocity accounting for mesh motion and morph is involved in the convective term of the governing equations. The mode superposition method is applied to solve for the structural motion caused by the action of the aerodynamic, structural, and inertial forces.