This paper presents a stabilized finite element formulation for the incompressible Navier-Stokes equations, written in an arbitrary Lagrangian-Eulerian frame to model flow problems that involve moving and deforming meshes. The stabilized formulation is derived based on the variational multiscale method proposed by Hughes [1], and employed in [2,3] to study advection dominated diffusion phenomena. A significant feature of the present method is that the definition of the stabilization terms appear naturally, and therefore the formulation is free of any user-defined parameters. A mesh moving technique is integrated in this formulation to accommodate the motion of the computational domain and to map the moving boundaries in a rational way. The method is tested on a periodic oscillating elastic beam in a fluid domain.
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