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A multiscale/stabilized formulation of the incompressible Navier-Stokes equations for moving boundary flows and fluid-structure interaction. (English) Zbl 1184.76720

This paper presents a multiscale/stabilized finite element method for incompressible Navier-Stokes equations on moving grids written in an ALE (arbitrary Lagrangian Eulerian) frame. In this method the stabilization terms appear as a result of the existence of fine scales in the problem, and the method exhibits superior stability properties like SUPG and GLS methods. An important feature of the proposed method is that the definition of stability tensor appears naturally via the solution of a fine-scale problem, and thus this tensor is a function of mesh velocity. The moving mesh scheme is integrated by a stabilized/multiscale method. Finally, the authors apply the approach to a typical fluid-structure interaction problem involving large-amplitude oscillations of an elastic beam in the fluid domain.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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