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A multiscale stabilized ALE formulation for incompressible flows with moving boundaries. (English) Zbl 1301.76057

Summary: This paper presents a variational multiscale stabilized finite element method for the incompressible Navier-Stokes equations. The formulation is written in an Arbitrary Lagrangian-Eulerian (ALE) frame to model problems with moving boundaries. The structure of the stabilization parameter is derived via the solution of the fine-scale problem that is furnished by the variational multiscale framework. The projection of the fine-scale solution onto the coarse-scale space leads to the new stabilized method. The formulation is integrated with a mesh moving scheme that adapts the computational grid to the evolving fluid boundaries and fluid-solid interfaces. Several test problems are presented to show the accuracy and stability of the new formulation.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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