A Simulation Method for Fluid-Structure Interaction Problems with Free Surface based on the Finite Cover Method

Abstract

This paper presents a new Eulerian type numerical method for Fluid-Structure Interaction (FSI) problems with free surface based on the finite cover method (FCM). Since the physical domain is defined independently of the mathematical domain in the FCM, which is known as a generalized version of the FEM, the physical boundaries of the structure are represented explicitly in a spatially fixed mesh so that the continuity condition can be imposed directly on the actual interface within the framework of Eulerian approach. The VOF and Level Set method are employed to represent interfaces, and the stabilized method based on the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods are employed for flow analysis. The weak coupling scheme is employed for the interaction between fluid and structure. The proposed method is applied to several numerical examples to show the validity and efficiency of the method.