Arbitrary Lagrangian-Eulerian formulation for fluid-rigid body interaction

Abstract

A new formulation for two-dimensional fluid-rigid body interaction problems is developed. In particular, vortex-induced oscillations of a rigid boy in viscous incompressible flow are studied. The incompressible Naiver-Stokes equations are used to describe the motion of the fluid, while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot. An arbitrary Lagrangian-Eulerian formulation (ALE) is used in order to account for large boundary motion. A general formulation for coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations. This general formulation ca be easily applied to multi-body problems. Two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid-rigid body interaction.