On continuum immersed strategies for Fluid-Structure Interaction

Continuum immersed strategies are widely used these days for the computational simulation of Fluid-Structure Interaction problems. The principal characteristic of such immersed techniques is the representation of the immersed solid via a momentum forcing source in the Navier-Stokes equations. In this paper, the Immersed Finite Element Method (IFEM), introduced by Zhang et al. (2004) [41] for the analysis of deformable solids immersed in an incompressible Newtonian viscous fluid, is further enhanced by means of three new improvements. A first update deals with the modification of the conservation of mass equation in the background fluid in order to account for non-isochoric deformations within the solid phase. A second update deals with the incompressibility constraint for the solid phase in the case of isochoric deformations, where an enhanced evaluation of the deformation gradient tensor is introduced in a multifield Hu-Washizu variational sense in order to overcome locking effects. The third update is focussed on the improvement of the robustness of the overall scheme, by introducing an implicit one-step time integration scheme with enhanced stability properties, in conjunction with a consistent Newton-Raphson linearisation strategy for optimal quadratic convergence. The resulting monolithic methodology is thoroughly studied for a range of Lagrangian and NURBS based shape finite element functions for a series of numerical examples, with the purpose of studying the effect of the spatial semi-discretisation in the solution. Comparisons are also established with the newly developed Immersed Structural Potential Method (ISPM) by Gil et al. (2010) [7] for benchmarking and assessment of the quality of the new formulation.