Computation of Fluid Inertial Term in XFEM for Fluid-Structure Interaction

Abstract

This paper addresses an advance issue in the computational fluid-structure interaction (FSI) method that applies an extended finite element method (XFEM) to interface of fluid and structure to reproduce requisite flow discontinuities at the interface. We especially focus on how the inertial term of the incompressible Navier-Stokes equations is discretized by the XFEM in the FSI method where the velocity function is enriched. We show the inertial term includes a spatial time derivative of the enrichment function and show the importance of computing the derivative to obtain a stable computation result in time. To verify the result, we also introduce an interface-tracking FSI computation method that is based on an arbitrary Lagrangian-Eulerian (ALE) formulation.