Application of the fictitious domain method in fluid-structure interaction

Fluid-Structure Interaction (FSI) is an engineering problem with many practical aspects such as the swash of seabed, the stagnation of contamination, the settlement of sand around coastal structures, and the resonance of structures under internal/external current excitations. Many numerical schemes had been presented in the past two decades. This paper deals with a finite element method to simulate the interaction of a coupled incompressible fluid-rigid structure system. Based on the Fictitious Domain (FD) method in the multi-phase flows field, a set of fully coupled FSI governing equations is presented. In this monolithic approach, the structure is taken as fictitious fluid with zero strain rate and the whole computational domain is modeled by the Navier-Stokes equations. However, to keep the rigid body shape and behaviors of the fictitious fluid, the Distributed Lagrange Multiplier (DLM) method is applied on this domain. The whole field, including fluid region and structure region, is described by velocity and pressure, and the entire set of model equations is discretised with fixed Eulerian mesh. Three major advantages of the present formulation include: (i) The unitized governing equations both for fluid and structure help capturing the predominant physics of interaction phenomena; (ii) The interfacial force/displacement between fluid and structure are internal actions for the overall system. Therefore, the stress/velocity consistency conditions on the fluid-structure interface are automatically satisfied in this fully coupled model; (iii) For the using of fixed Eulerian mesh, it is not necessary to remesh the computational domain, and thus free from mesh distortions. Results from numerical simulations on particulate flow and FSI problems provide convincing evidences for the model's high accuracy and the suitability for the simulation of large-deformation/movement FSI problems.