Applications of variable-node finite elements for fluid-solid interaction problems

Abstract

In this works, a novel numerical method for coupling non-matching interfaces between dissimilar meshes for the simulation of fluid-solid interaction problems using finite element method is proposed. The non-matching meshes at the interfaces are re-defined by a single entity through connecting interface nodes without penetrations and gaps, and variable-node elements are utilized to join the dissimilar finite element meshes in fluid and solid domains. The variable-node elements satisfy the interface conditions of continuity, compatibility and completeness across the non-matching meshes. As a result, the present method provides a seamless connection between dissimilar finite element meshes and a correct load transfer across non-matching interfaces for an efficient approach to the solution for fluid-solid interaction problems. The flow considered is governed by the incompressible Navier-Stokes equations, and the stabilized equal order velocity-pressure elements are used for fluid motion. The updated Lagrangian method is formulated in the motion of solid to accommodate finite deformations of an elastic solid. To accommodate a deformable solid moving or rotating in a fluid domain, a sliding mesh technique by using two or three-dimensional variable-node elements is developed in this study. In order to avoid an entanglement of a fluid mesh attached to the fluid-solid interface boundaries, the fluid finite elements bordering on a layer in the fluid domain are replaced by variable-node elements for sliding each other. Non-matching meshes at the sliding interface and at the fluid-solid interface can be effectively connected by using the variable-node elements with satisfying the interface conditions. As a result, the exterior fluid meshes of the sliding interface can be controlled independently to the motion of a solid even though a group of fluid meshes surrounding a solid is moving and rotating together with the solid motion. In addition, a free motion of a solid bod...