A Multiscale/stabilized Formulation of the Incompressible Navier–Stokes Equations for Moving Boundary Flows and Fluid–structure Interaction

This paper presents a multiscale/stabilized finite element formulation for the incompressible Navier–Stokes equations written in an Arbitrary Lagrangian–Eulerian (ALE) frame to model flow problems that involve moving and deforming meshes. The new formulation is derived based on the variational multiscale method proposed by Hughes (Comput Methods Appl Mech Eng 127:387–401, 1995) and employed in Masud and Khurram in (Comput Methods Appl Mech Eng 193:1997–2018, 2006); Masud and Khurram in (Comput Methods Appl Mech Eng 195:1750–1777, 2006) to study advection dominated transport phenomena. A significant feature of the formulation is that the structure of the stabilization terms and the definition of the stabilization tensor appear naturally via the solution of the sub-grid scale problem. A mesh moving technique is integrated in this formulation to accommodate the motion and deformation of the computational grid, and to map the moving boundaries in a rational way. Some benchmark problems are shown, and simulations of an elastic beam undergoing large amplitude periodic oscillations in a viscous fluid domain are presented.