Finite element simulations of fluid-structure interactions via overset meshes and sharp embedded interfacial conditions

摘要

Many fluid-structure applications involve a solid phase that is subject to large relative motion but only small deformation. In this regime, the domain of the fluid between the solids may be significantly distorted, and Arbitrary Lagrangian Eulerian (ALE) methods are unable to maintain mesh integrity without frequent remeshing steps. In this work, an overset mesh approach is developed in the context of finite element methods. The motion of a Lagrangian solid is coupled to an Eulerian fluid along the interface of the solid. A Lagrange multiplier is used to implement the no-slip and normal stress balance along the solid surface. When implemented using standard finite elements, however, it is shown that this method cannot capture the discontinuous velocity gradient that occurs at the interface. To address this, an extended finite element (XFEM) approach is developed that uses enriched finite elements to impose sharp interfacial conditions. The Lagrange multiplier method is applied, both with and without XFEM, to flow around a cylinder and the deformation of a flexible blade due to viscous flow. Even without XFEM, acceptable results are obtained away from the interface. However, the sharp interfacial conditions are shown to improve the accuracy of the solution near the interface.