Three-dimensional real-life simulations are generally unsteady and involve moving geometries. Industry is currently very far from performing such body-fitted simulations on a daily basis, mainly due to the robustness of the moving mesh algorithm and their extensive computational cost. A moving mesh algorithm coupled to local mesh optimizations has proved its efficiency in dealing with large deformation of the mesh without re-meshing. In this paper, the coupling of this algorithm with two mesh deformation techniques is studied: an elasticity PDE-based one and an explicit Inverse Distance Weighted interpolation one, and both techniques are compared. The efficiency of this method is demonstrated on challenging test cases, involving large body deformations, boundary layers and large displacements with shearing. Finally, the moving mesh algorithm is coupled to a CFD flow solver.