虚拟区域法在流固耦合问题中的应用

APPLICATION OF THE FICTITIOUS DOMAIN METHOD IN FLUID-STRUCTURE INTERACTION

将多相流领域内的虚拟区域法引入到流固耦合问题的分析中,将固体视为应变率为零的虚拟流体,对流体和虚拟流体均以速度和压强作为基本变量,采用Navier-Stokes方程作为控制方程,同时求解流体域和虚拟流体域,得到整个计算域的流场分布,应用分布式拉格朗日乘子法在虚拟流体域上施加刚体约束,以保持虚拟流体的刚体外形和运动形式,最终建立一种流固耦合模型及其数值求解方法.通过对粒子流问题和流固耦合问题进行数值模拟,验证了此模型的正确性和求解大变形/运动流固耦合问题的有效性.

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.