###### Abstract  
An arbitrary Lagrangian-Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with the mode superposition method is proposed in this work and applied to study two- and three-dimensional flutter phenomenon on dynamic unstructured meshes. The ALE-LBFS is applied to predict the flow field by using the vertex-centered finite volume method with an implicit dual time-stepping method. The convective fluxes are evaluated by using lattice Boltzmann solutions of the non-free DIQ4 lattice model and the viscous fluxes are obtained directly. Additional fluxes due to mesh motion are calculated directly by using local conservative variables and mesh velocity. The mode superposition method is used to solve for the dynamic response of solid structures. The exchange of aerodynamic forces and structural motions is achieved through interpolation with the radial basis function. The flow solver and the structural solver are tightly coupled so that the restriction on the physical time step can be removed. In addition, geometric conservation law (GCL) is also applied to guarantee conservation laws. The proposed method is tested through a series of simulations about moving boundaries and fluid-structure interaction problems in 2D and 3D. The present results show good consistency against the experiments and numerical simulations obtained from the literature. It is also shown that the proposed method not only can effectively predict the flutter boundaries in both 2D and 3D cases but can also accurately capture the transonic dip phenomenon. The tight coupling of the ALE-LBFS and the mode superposition method presents an effective and powerful tool for flutter prediction and can be applied to many essential aeronautical problems. title=false, description  
time during the structural deformation, a vital element for accurately obtaining the aerodynamic forces from the surrounding flow field with enhanced resolution near the boundaries. ALE empowers mesh nodes near moving or deforming boundaries to evolve with the structure, while those farther away remain fixed in the Eulerian description. ALE furnishes physical meshes with arbitrary velocities independent of fluid motion, eliminating the need to remap Lagrangian solutions to adjusted meshes. This not only enhances accuracy but also significantly streamlines mesh computations, reducing computational overhead. In terms of solutions on the moving mesh, both Euler equations and Navier-Stokes (NS) equations with suitable turbulence models have worked as fluid solvers. Consequently, the numerical schemes for the discretization of the convective terms should be adapted to the dynamic meshes by considering the local velocity of the grids, which may be not trivial considering the requirement of low dissipation and high stability for transonic and supersonic flows intensive shock waves. [PERSON] and [PERSON] [13; 14] have numerically discovered the transonic dip phenomenon by coupling unsteady Euler and/or Navier-Stokes equations with structural mode equations, separately. Comparing these two solvers, they further present the important role of viscosity in flutter prediction. [PERSON] et al. [15] apply the Roe flux difference splitting scheme to discretize the Euler/NS equations and tightly couple them with structural dynamic equations. By the finite element method, the aircraft wing deforms numerically, governed by the 3D elasticity equations. They succeeded in predicting the aeroelastic instability of the rigid airfoil and elastic AGARD 445.6 wing. For wide engineering applications, the ALE method is adapted and involves new techniques together with various other numerical methodologies for the prediction of flutter, including frequency-domain techniques [16], deep learning [17], and model order reduction [18; 19; 20]. Although some improvements are achieved, most of them still depend on solving the NS equations by evaluating the fluxes in a macroscopic way.