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.